Snub Ball Tutorial (Snub Dodecahedron, Zen Magnets) @boydedwards5475

Boyd Edwards This is a video tutorial showing how to make the snub ball, a double-thickness hollow sphere, with Zen Magnets. The snub ball surpasses the 1860-magnet ultimate ball in size, weight, sphericity, strength, rigidity, and scalability.

While the ultimate ball is based on the icosahedron, the snub ball is based on the snub dodecahedron, which has the largest number of faces (92) and the largest sphericity (it most closely resembles a sphere) of the eighteen highly-symmetric Platonic and Archimedean solids.

The design requires:
* 60 double-thickness vertex pieces with 12 magnets each, made of double hexagon rings,
* 150 double-thickness edge pieces of edge length L with 4L magnets each, made from double rings of 2L magnets,
* 12 single-thickness pentagonal faces with edge length L+2 and 5(L+1)(L+2)/2 magnets each, and
* 80 single-thickness triangular faces with edge length L-1 and L(L-1)/2 magnets each.
In all, the design requires 70L*L + 650L + 780 magnets. For L = 2, 3, 4, 5, and 6, this total is 2360, 3360, 4500, 5780, and 7200 magnets, respectively.

For L = 2, the 80 triangular "faces" have only one magnet each. Single magnets don't fit well into the gap between the three edge pieces that outline the triangle. The L = 2 frame is strong even without these 80 magnets, and can be built with only 2280 magnets.

Shown in the video is the construction for L = 4 with 4500 magnets. A separate video entitled "Zen Ball Art" shows the L = 2, L = 3, and L = 4 sizes, along with the ultimate ball. For smaller sizes of the snub dodecahedron, you might consider the single-thickness 960-magnet and 1320-magnet designs by Yumirugars.

The snub dodecahedron comes in clockwise and counterclockwise chiral forms, each the mirror image of the other. This video shows how to build the clockwise form of the snub ball. Another tutorial video, called "Snub Dodecahedron Frame Tutorial," shows how to build both forms of the snub dodecahedron frame, which includes the vertex and edge pieces and excludes the pentagonal and triangular faces so the symmetry is easier to see.

All three sizes of the snub ball rest stably on a flat solid surface on a pentagonal face, with little to no flattening of the ball for L = 2 and some flattening of the ball, but no permanent damage, for L = 4.

Jan. 21, 2014 Update: Jonathan Minond found a way to reinforce the triangles in order to build an L = 5 snub ball (http://youtu.be/zZCLZdJi4Jg) with about 6100 magnets. I used similar triangle reinforcement and also reinforced the pentagons in order to build an L = 5 snub ball with 6720 magnets that can be supported atop a double-walled tube (http://youtu.be/cJ6ZebVTMOA). The L = 5 snub ball might be the largest self-supporting double-thickness hollow sphere that you can make with Zen Magnets.

June 4, 2014 Update: Ledwatchman built an 8424-magnet L = 6 snub ball using a beautiful two-color scheme. See http://youtu.be/mNn5ni6bWLU.

updated 13 years ago

Snub Ball Tutorial (Snub Dodecahedron, Zen Magnets)

Boyd Edwards 2013-04-04 | This is a video tutorial showing how to make the snub ball, a double-thickness hollow sphere, with Zen Magnets. The snub ball surpasses the 1860-magnet ultimate ball in size, weight, sphericity, strength, rigidity, and scalability.

While the ultimate ball is based on the icosahedron, the snub ball is based on the snub dodecahedron, which has the largest number of faces (92) and the largest sphericity (it most closely resembles a sphere) of the eighteen highly-symmetric Platonic and Archimedean solids.

The design requires:
* 60 double-thickness vertex pieces with 12 magnets each, made of double hexagon rings,
* 150 double-thickness edge pieces of edge length L with 4L magnets each, made from double rings of 2L magnets,
* 12 single-thickness pentagonal faces with edge length L+2 and 5(L+1)(L+2)/2 magnets each, and
* 80 single-thickness triangular faces with edge length L-1 and L(L-1)/2 magnets each.
In all, the design requires 70L*L + 650L + 780 magnets. For L = 2, 3, 4, 5, and 6, this total is 2360, 3360, 4500, 5780, and 7200 magnets, respectively.

For L = 2, the 80 triangular "faces" have only one magnet each. Single magnets don't fit well into the gap between the three edge pieces that outline the triangle. The L = 2 frame is strong even without these 80 magnets, and can be built with only 2280 magnets.

Shown in the video is the construction for L = 4 with 4500 magnets. A separate video entitled "Zen Ball Art" shows the L = 2, L = 3, and L = 4 sizes, along with the ultimate ball. For smaller sizes of the snub dodecahedron, you might consider the single-thickness 960-magnet and 1320-magnet designs by Yumirugars.

The snub dodecahedron comes in clockwise and counterclockwise chiral forms, each the mirror image of the other. This video shows how to build the clockwise form of the snub ball. Another tutorial video, called "Snub Dodecahedron Frame Tutorial," shows how to build both forms of the snub dodecahedron frame, which includes the vertex and edge pieces and excludes the pentagonal and triangular faces so the symmetry is easier to see.

All three sizes of the snub ball rest stably on a flat solid surface on a pentagonal face, with little to no flattening of the ball for L = 2 and some flattening of the ball, but no permanent damage, for L = 4.

Jan. 21, 2014 Update: Jonathan Minond found a way to reinforce the triangles in order to build an L = 5 snub ball (http://youtu.be/zZCLZdJi4Jg) with about 6100 magnets. I used similar triangle reinforcement and also reinforced the pentagons in order to build an L = 5 snub ball with 6720 magnets that can be supported atop a double-walled tube (http://youtu.be/cJ6ZebVTMOA). The L = 5 snub ball might be the largest self-supporting double-thickness hollow sphere that you can make with Zen Magnets.

June 4, 2014 Update: Ledwatchman built an 8424-magnet L = 6 snub ball using a beautiful two-color scheme. See http://youtu.be/mNn5ni6bWLU.

Reinforced Double Walled Octahedron (Zen Magnets)

Boyd Edwards 2018-08-03 | This video shows how to use Zen Magnets to reinforce the top and bottom faces of the double-walled octahedron (youtu.be/SnlT607K_OY). The resulting structure is robust and easy to build in large sizes.

The following table gives information necessary to build the reinforced double-walled octahedron in various sizes. The video shows how to build this shape for edge count 13 (second line in the table).

edge, layer 1, layer 2, layer 3, column, magnets
10, 2 x 8, 2 x 9, 2 x 2, 4, 586
13, 2 x 11, 2 x 12, 2 x 5, 7, 1114
16, 2 x 14, 2 x 15, 2 x 8, 10, 1804
19, 2 x 17, 2 x 18, 2 x 11, 13, 2656
22, 2 x 20, 2 x 21, 2 x 14, 16, 3670
25, 2 x 23, 2 x 24, 2 x 17, 19, 4846
28, 2 x 26, 2 x 27, 2 x 20, 22, 6184
31, 2 x 29, 2 x 30, 2 x 23, 25, 7684
34, 2 x 32, 2 x 33, 2 x 26, 28, 9346
37, 2 x 35, 2 x 36, 2 x 29, 31, 11170
40, 2 x 38, 2 x 39, 2 x 32, 34, 13156
43, 2 x 41, 2 x 42, 2 x 35, 37, 15304
46, 2 x 44, 2 x 45, 2 x 38, 40, 17614
49, 2 x 47, 2 x 48, 2 x 41, 43, 20086
52, 2 x 50, 2 x 51, 2 x 44, 46, 22720
55, 2 x 53, 2 x 54, 2 x 47, 49, 25516
58, 2 x 56, 2 x 57, 2 x 50, 52, 28474
61, 2 x 59, 2 x 60, 2 x 53, 55, 31594
64, 2 x 62, 2 x 63, 2 x 56, 58, 34876
67, 2 x 65, 2 x 66, 2 x 59, 61, 38320
70, 2 x 68, 2 x 69, 2 x 62, 64, 41926
73, 2 x 71, 2 x 72, 2 x 65, 67, 45694
76, 2 x 74, 2 x 75, 2 x 68, 70, 49624
79, 2 x 77, 2 x 78, 2 x 71, 73, 53716
82, 2 x 80, 2 x 81, 2 x 74, 76, 57970
85, 2 x 83, 2 x 84, 2 x 77, 79, 62386
88, 2 x 86, 2 x 87, 2 x 80, 82, 66964
91, 2 x 89, 2 x 90, 2 x 83, 85, 71704
94, 2 x 92, 2 x 93, 2 x 86, 88, 76606
97, 2 x 95, 2 x 96, 2 x 89, 91, 81670
100, 2 x 98, 2 x 99, 2 x 92, 94, 86896

Double Walled Octahedron (Zen Magnets)

Boyd Edwards 2018-08-02 | This video shows how to build a double-walled octahedron using Zen Magnets. It's a particularly simple build for a particularly lovely and symmetric shape, and it can be built (for edge counts 4 and 7) using only a single set of Zen Magnets. Here's a table showing the number of magnets needed for each size:

edge, layer 1, layer 2, magnets
4, 2 x 2, 3 x 2, 44
7, 2 x 5, 2 x 6, 212
10, 2 x 8, 2 x 9, 524
13, 2 x 11, 2 x 12, 980
16, 2 x 14, 2 x 15, 1580
19, 2 x 17, 2 x 18, 2324
22, 2 x 20, 2 x 21, 3212
25, 2 x 23, 2 x 24, 4244
28, 2 x 26, 2 x 27, 5420
31, 2 x 29, 2 x 30, 6740
34, 2 x 32, 2 x 33, 8204
37, 2 x 35, 2 x 36, 9812
40, 2 x 38, 2 x 39, 11564
43, 2 x 41, 2 x 42, 13460
46, 2 x 44, 2 x 45, 15500
49, 2 x 47, 2 x 48, 17684
52, 2 x 50, 2 x 51, 20012
55, 2 x 53, 2 x 54, 22484
58, 2 x 56, 2 x 57, 25100
61, 2 x 59, 2 x 60, 27860
64, 2 x 62, 2 x 63, 30764
67, 2 x 65, 2 x 66, 33812
70, 2 x 68, 2 x 69, 37004
73, 2 x 71, 2 x 72, 40340
76, 2 x 74, 2 x 75, 43820
79, 2 x 77, 2 x 78, 47444
82, 2 x 80, 2 x 81, 51212
85, 2 x 83, 2 x 84, 55124
88, 2 x 86, 2 x 87, 59180
91, 2 x 89, 2 x 90, 63380
94, 2 x 92, 2 x 93, 67724
97, 2 x 95, 2 x 96, 72212
100, 2 x 98, 2 x 99, 76844

Mathnetisms Sierpinski Tetrahedron (Zen Magnets)

Boyd Edwards 2016-04-19 | This video is shows how to build Mathnetism's amazing three-level fractal Sierpinski Tetrahedron using vertex stickers (imgur.com/a/Kwpj7) to keep track of polarities. Mathnetism built the shape with subunit edge length 9 and 10,756 magnets. This video shows how to build the same shape, in a larger size, with subunit edge length 13 and 16,900 magnets.

What follows is information needed to build the shape in any size, with:
L = subunit edge length
R = ring length used to build the subunits
C = chain length used to build legs added to the subunits
N0 = magnet count of the subunits, the smallest tetrahedra in the shape
N1 = magnet count of medium-sized tetrahedra
N2 = magnet count of large tetrahedra
N3 = magnet count of extra-large tetrahedra
N4 = magnet count of extra-extra large tetrahedra

At the size shown in the video, L = 13, R = 40, C = 9, N0 = 268, N1 = 1060, N2 = 4228, and N3 = 16,900. This is a three-level fractal, terminating with N3. To build a four-level fractal at this size, the total magnet count would be N4 = 67,588, and the shape would not be strong enough to support itself on a solid surface under earth's gravity.

The shape is Mathnetism's invention - my main contributions are: (a) to introduce vertex stickers (imgur.com/a/Kwpj7) as a construction aid and (b) to supply the table below, showing how many magnets you'll need to build the shape in any size. You can, of course, stop at N0, N1, or N2 if you like - you can build the basic subunit N0 for L = 5, 6, 7, 8, 9, 10, or 11 with just a single set of Zen Magnets, including spares. Or you can go for N4 if you have at least 18,436 magnets (for edge length L = 5). I don't have quite enough magnets to do this, but my trials indicate that the four-level fractal should be stable for L = 5 and L = 6 (requiring 24,580 magnets).

L, R, C, N0, N1, N2, N3, N4
5, 8, 1, 76, 292, 1156, 4612, 18436
6, 12, 2, 100, 388, 1540, 6148, 24580
7, 16, 3, 124, 484, 1924, 7684, 30724
8, 20, 4, 148, 580, 2308, 9220, 36868
9, 24, 5, 172, 676, 2692, 10756, 43012
10, 28, 6, 196, 772, 3076, 12292, 49156
11, 32, 7, 220, 868, 3460, 13828, 55300
12, 36, 8, 244, 964, 3844, 15364, 61444
13, 40, 9, 268, 1060, 4228, 16900, 67588
14, 44, 10, 292, 1156, 4612, 18436, 73732
15, 48, 11, 316, 1252, 4996, 19972, 79876
16, 52, 12, 340, 1348, 5380, 21508, 86020
17, 56, 13, 364, 1444, 5764, 23044, 92164
18, 60, 14, 388, 1540, 6148, 24580, 98308
19, 64, 15, 412, 1636, 6532, 26116, 104452
20, 68, 16, 436, 1732, 6916, 27652, 110596
21, 72, 17, 460, 1828, 7300, 29188, 116740
22, 76, 18, 484, 1924, 7684, 30724, 122884
23, 80, 19, 508, 2020, 8068, 32260, 129028
24, 84, 20, 532, 2116, 8452, 33796, 135172
25, 88, 21, 556, 2212, 8836, 35332, 141316
26, 92, 22, 580, 2308, 9220, 36868, 147460
27, 96, 23, 604, 2404, 9604, 38404, 153604
28, 100, 24, 628, 2500, 9988, 39940, 159748
29, 104, 25, 652, 2596, 10372, 41476, 165892
30, 108, 26, 676, 2692, 10756, 43012, 172036
31, 112, 27, 700, 2788, 11140, 44548, 178180
32, 116, 28, 724, 2884, 11524, 46084, 184324
33, 120, 29, 748, 2980, 11908, 47620, 190468
34, 124, 30, 772, 3076, 12292, 49156, 196612
35, 128, 31, 796, 3172, 12676, 50692, 202756
36, 132, 32, 820, 3268, 13060, 52228, 208900
37, 136, 33, 844, 3364, 13444, 53764, 215044
38, 140, 34, 868, 3460, 13828, 55300, 221188
39, 144, 35, 892, 3556, 14212, 56836, 227332
40, 148, 36, 916, 3652, 14596, 58372, 233476
41, 152, 37, 940, 3748, 14980, 59908, 239620
42, 156, 38, 964, 3844, 15364, 61444, 245764
43, 160, 39, 988, 3940, 15748, 62980, 251908
44, 164, 40, 1012, 4036, 16132, 64516, 258052
45, 168, 41, 1036, 4132, 16516, 66052, 264196
46, 172, 42, 1060, 4228, 16900, 67588, 270340
47, 176, 43, 1084, 4324, 17284, 69124, 276484
48, 180, 44, 1108, 4420, 17668, 70660, 282628
49, 184, 45, 1132, 4516, 18052, 72196, 288772
50, 188, 46, 1156, 4612, 18436, 73732, 294916

Mathnetisms Seamless Tetrahedron Frame (Zen Magnets)

Boyd Edwards 2016-01-17 | This video shows how to build a seamless tetrahedron frame out of Zen Magnets using a technique I learned from Mathnetism in his Sierpinski Tetrahedron Tutorial (youtu.be/QJL5ztV_Z2c). In Mathnetism's tutorial, the technique for building a seamless tetrahedron is buried in the details of building the Sierpinski tetrahedron, which is built from many seamless tetrahedra. The purpose of the present video is to show how to build a single seamless tetrahedron frame.

With just four triangular faces, the tetrahedron is the simplest of the five regular Platonic solids. Plato associated the tetrahedron with the classical element of fire.

The design is very strong, and the shape can be built in large sizes. Shown in the video are seamless tetrahedra with edge lengths 10, 20, 30, 40, 50, and 60, and respective magnet counts 196, 436, 676, 916, 1156, and 1396. I expect that the shape can be built in even larger sizes.

In magnet lore, the word “seamless” means that every magnet fits into a hollow created by its neighbors. Seamless connections result when nearby chains have parallel magnetic orientations, which results in stronger connections and closer packings than antiparallel connections, where magnets meet side by side instead of fitting into hollows created by their neighbors. These antiparallel connections are called “seams.”

The standard, weaker tetrahedron design (also shown in the video) has a seam running along each edge (youtu.be/S6kt_oQDDOk, youtu.be/hvVF_ZugkyQ). To my knowledge, the largest tetrahedron frame built using this design is Jasonbbb711’s frame of edge length 42 and magnet count 948 (flickr.com/photos/56124497@N07/5194554900). This is considerably smaller than the seamless frame of edge length 60 shown in the video.

To demonstrate the build technique, I build a small seamless tetrahedron with edge length 10 using 196 magnets. To build this tetrahedron, you start with a ring of 28 magnets and, later in the build, use chains of length 6 to build the two missing sides.

What follows is a list of sizes along with information about how to build the seamless tetrahedron in each size. In the list, “L” is the edge length, “N = 24L - 44” is the total magnet count, “Ring = 4L - 12” is the number of magnets in the ring used to begin building the shape, and “Chain = L - 4” is the length of the chains needed for the two missing sides. The listing below for L = 10 corresponds to the small tetrahedron used in the video to demonstrate the technique.

L, N, Ring, Chain
5, 76, 8, 1
6, 100, 12, 2
7, 124, 16, 3
8, 148, 20, 4
9, 172, 24, 5
10, 196, 28, 6
11, 220, 32, 7
12, 244, 36, 8
13, 268, 40, 9
14, 292, 44, 10
15, 316, 48, 11
16, 340, 52, 12
17, 364, 56, 13
18, 388, 60, 14
19, 412, 64, 15
20, 436, 68, 16
21, 460, 72, 17
22, 484, 76, 18
23, 508, 80, 19
24, 532, 84, 20
25, 556, 88, 21
26, 580, 92, 22
27, 604, 96, 23
28, 628, 100, 24
29, 652, 104, 25
30, 676, 108, 26
31, 700, 112, 27
32, 724, 116, 28
33, 748, 120, 29
34, 772, 124, 30
35, 796, 128, 31
36, 820, 132, 32
37, 844, 136, 33
38, 868, 140, 34
39, 892, 144, 35
40, 916, 148, 36
41, 940, 152, 37
42, 964, 156, 38
43, 988, 160, 39
44, 1012, 164, 40
45, 1036, 168, 41
46, 1060, 172, 42
47, 1084, 176, 43
48, 1108, 180, 44
49, 1132, 184, 45
50, 1156, 188, 46
51, 1180, 192, 47
52, 1204, 196, 48
53, 1228, 200, 49
54, 1252, 204, 50
55, 1276, 208, 51
56, 1300, 212, 52
57, 1324, 216, 53
58, 1348, 220, 54
59, 1372, 224, 55
60, 1396, 228, 56
61, 1420, 232, 57
62, 1444, 236, 58
63, 1468, 240, 59
64, 1492, 244, 60
65, 1516, 248, 61
66, 1540, 252, 62
67, 1564, 256, 63
68, 1588, 260, 64
69, 1612, 264, 65
70, 1636, 268, 66
71, 1660, 272, 67
72, 1684, 276, 68
73, 1708, 280, 69
74, 1732, 284, 70
75, 1756, 288, 71
76, 1780, 292, 72
77, 1804, 296, 73
78, 1828, 300, 74
79, 1852, 304, 75
80, 1876, 308, 76
81, 1900, 312, 77
82, 1924, 316, 78
83, 1948, 320, 79
84, 1972, 324, 80
85, 1996, 328, 81
86, 2020, 332, 82
87, 2044, 336, 83
88, 2068, 340, 84
89, 2092, 344, 85
90, 2116, 348, 86
91, 2140, 352, 87
92, 2164, 356, 88
93, 2188, 360, 89
94, 2212, 364, 90
95, 2236, 368, 91
96, 2260, 372, 92
97, 2284, 376, 93
98, 2308, 380, 94
99, 2332, 384, 95
100, 2356, 388, 96

Mathnetisms Diagonal Cube Frame (Zen Magnets)

Boyd Edwards 2015-11-13 | This video shows how to build diagonal cube frames of any size using a technique by Mathnetism (see youtu.be/b-GQd_km0aA comments and youtu.be/SUC1T6RteEs?t=2m36s).

For an edge count n, the number of magnets required is N = 300n – 848, which gives:

n, N
8, 1552
9, 1852
10, 2152
11, 2452
12, 2752
13, 3052
14, 3352
15, 3652
16, 3952
17, 4252
18, 4552
19, 4852
20, 5152
21, 5452
22, 5752
23, 6052
24, 6352
25, 6652
26, 6952
27, 7252
28, 7552
29, 7852
30, 8152

The tutorial video is for n = 12, requiring 2752 magnets. Also shown briefly near the beginning is a large diagonal cube frame with n = 28, requiring 7552 magnets.

The video shows that the total edge count of n = 12 includes 4 from each of two corner pieces and 4 from the edge piece; the edge count for the edge pieces is 8 less than the total edge count. This applies for other sizes as well. As a second example, the large frame with n = 28 requires edge pieces with edge count of 20.

An edge count of n = 28 is near the practical limit for this shape. The four horizontal edge pieces on the top of the cube tend to sag and break under their own weight for larger edge counts.

Mathnetisms Rhombic Triacontahedron (Zen Magnets)

Boyd Edwards 2015-11-04 | This video shows how to build Mathnetism’s ingenious rhombic triacontahedron (youtu.be/ZnAKcOEZK7w). For edge length L, the number of magnets required is N = 720L + 1604:

L, N
1, 2324
2, 3044
3, 3764
4, 4484
5, 5204
6, 5924
7, 6644
8, 7364
9, 8084
10, 8804
11, 9524
12, 10244
13, 10964
14, 11684
15, 12404
16, 13124
17, 13844
18, 14564
19, 15284
20, 16004

The video shows how to build the shape for L = 6, which requires N = 5924 magnets. The shape is quite strong at this size, and I suspect that it can be built for larger sizes. It can certainly be built in smaller sizes.

Magnet Cleaner (Zen Magnets)

Boyd Edwards 2015-10-31 | In this video, I introduce a magnet cleaning device of my own design, and discuss its merits compared with other methods of cleaning Zen Magnets.

The north and south poles of magnets attract ferric dirt particles. These iron particles become trapped between adjacent magnets, which attract pole to pole. As adjacent magnets move against each other, these particles quickly erode the magnetic coatings, especially at the poles.

These particles find their way onto magnets from contact with dirty hands and dirty surfaces. Ferric particles are also released from the coatings of the magnets themselves as they wear against each other, especially while kneading, grinding, or smashing magnets forcibly against each other. The coatings on Zen Magnets are harder and smoother than coatings on other brands, but even Zen Magnet coatings can wear away. In my early months as a Zen Magnets user, I used my magnets on a hard Formica surface and wore a visible ring around magnet equators by sliding magnet chains along this surface.

To minimize wear on your magnets, it’s important to protect them from dirt, to avoid kneading them, to wash your hands before using them, and to work on a clean surface that is softer than the magnetic coatings.

Some accumulation of ferric particles on the magnets is inevitable. These ferric particles accumulate at the north and south poles of the magnets, where they are attracted most strongly by the magnetic force. The removal of these particles is the subject of this video.

First, a review of techniques that folks have used to clean magnets.

1. The Zen Magnets website (http://www.zenmagnets.com) suggests a simple cleaning method, to roll individual magnets around on tape, silly putty, sticky tack, cleaning putty, or the like.

2. MagnetNerd cleans a sheet of magnets using duct tape (youtu.be/o787PTQIypk).

3. The Zen Magnets website also suggests using a cloth to clean magnets, and supplies microfiber cloths for this purpose. This can be done either with a chain with magnets alternating on either side of the cloth (youtu.be/Ykr2xJ10Xg4, youtu.be/WZwB8o_Vk8U), or with a chain of magnets all on one side of the cloth (youtu.be/G8c_f6Q4r4Y).

4. Some have used soap and water to clean magnets (youtu.be/nDpuOL4P1t4). Others express concern over the effectiveness of this technique.

5. ErazorX uses paper to clean a chain of magnets, one magnet at a time, (youtu.be/z0jgB_8XHxQ), by sandwiching the paper between two magnets and wiping off the dirt between them by sliding them along the paper. This removes little more than half of the dirt. To remove most of the rest of the dirt, you have to tip the chain over and do it again, so that the total time required per magnet is about 5 seconds. I have used this technique to clean thousands of magnets. Magazz Monty uses a similar technique, substituting tape for paper (youtu.be/RmZGkePe8Ec).

My magnet cleaner is a slab of reinforced pine with 25 channels, each holding a chain of 100 magnets. A sliding frame is used to move magnets into position for cleaning, with 25 steel rods glued to the left side of the frame to draw the magnets along. To clean magnets, slide the frame to center the contact points of 25 pairs of magnets above a slot cut through the slab, and insert a microfiber cloth through the slot to clean these 25 contact points, moving the cloth both upward and downward through the slot. Then slide the frame to center the next set of contact points above the slot, etc. As more and more magnets are exposed, strips of one-eighth inch thick aluminum confine these exposed magnets to their channels.

A strip of thin aluminum flashing, to which the microfiber cloth is taped, provides the framework that enables the microfiber cloth to be pushed through the contact points.

This device can be used to clean 2500 magnets in 35 minutes, which amounts to 0.85 seconds per magnet. In contrast, cleaning 2500 magnets using ErazorX’s paper technique takes over 3 hours, which amounts to 4.3 seconds per magnet. Thus, compared with EraZorX’s technique, my technique is more effective in removing ferric particles, and is at five times faster.

Worlds Largest Hollow Diagonal Cube (Zen Magnets)

Boyd Edwards 2015-10-11 | In this video, I show how to build a giant hollow diagonal cube out of Zen Magnets. The cube has triple-thickness walls, edge count 23, and 17,451 magnets. It weighs 19 pounds and is very strong. As far as I know, it is the largest and heaviest hollow diagonal cube that has ever been built. The technique is an extension of Mathnetism’s technique for building hollow cubes with double-thickness walls (see youtu.be/stZyv-_H8IU, youtu.be/b-GQd_km0aA, and youtu.be/A3U_gBjltxU).

The number of magnets required for a hollow diagonal cube with triple thickness walls is given by N = 36n^2 - 72n + 63, for edge count n = 3 and larger. This gives:

n, N
3, 171
4, 351
5, 603
6, 927
7, 1323
8, 1791
9, 2331
10, 2943
11, 3627
12, 4383
13, 5211
14, 6111
15, 7083
16, 8127
17, 9243
18, 10431
19, 11691
20, 13023
21, 14427
22, 15903
23, 17451
24, 19071
25, 20763
26, 22527
27, 24363
28, 26271
29, 28251
30, 30303
31, 32427
32, 34623
33, 36891
34, 39231
35, 41643
36, 44127
37, 46683
38, 49311
39, 52011
40, 54783
41, 57627
42, 60543
43, 63531
44, 66591
45, 69723
46, 72927
47, 76203
48, 79551
49, 82971
50, 86463

Hollow Cuboctahedron Tutorial (Zen Magnets)

Boyd Edwards 2015-10-07 | This video shows how to build a double-thickness hollow cuboctahedron out of Zen Magnets. The technique is an adaptation of Mathnetism’s hollow diagonal cube technique (see youtu.be/stZyv-_H8IU, youtu.be/b-GQd_km0aA, and youtu.be/A3U_gBjltxU). For even edge lengths n = 4 and larger, the hollow cuboctahedron uses N = 20n^2-60n+54 magnets.

N is the difference between the number 3(10n^3-15n^2+11n-3) of magnets in a solid cuboctahedron of edge length n and the number 3[10(n-2)^3-15(n-2)^2+11(n-2)-3] of magnets in a smaller solid cuboctahedron of edge length n-2. This smaller cuboctahedron is the size and shape and number of magnets of the hollow space inside of the hollow cuboctahedron.

Building the hollow cuboctahedron actually requires more than N magnets, magnets that you cut off at the last step. The number of extra magnets required is a few magnets shy of the number M = 6n(n-1)+1 of magnets in the triple-thickness slab used to build the top and the bottom of the cuboctahedron. You can cut off these magnets as you build the shape, but it’s trickier to complete this way.

n, N, M
4, 134, 73
6, 414, 181
8, 854, 337
10, 1454, 541
12, 2214, 793
14, 3134, 1093
16, 4214, 1441
18, 5454, 1837
20, 6854, 2281

In the video, I show completed cuboctahedra with edge lengths n = 4, 6, 8, 10, 12, and 14, and I build the shape from start to finish for n = 8 (854 magnets). The shape can be built in sizes larger than n = 14, but their angled walls and vertices are less stable than for smaller sizes.

Mathnetisms Hollow Diagonal Cube (Zen Magnets)

Boyd Edwards 2015-09-23 | This video describes how to use Zen Magnets to build a hollow diagonal cube using Mathnetism's ingenious technique (see youtu.be/stZyv-_H8IU and youtu.be/b-GQd_km0aA). The shape has double-thickness walls and is amazingly strong. For edge lengths n equal to 2 or larger, the shape requires a total magnet count of N = 24n(n-1)+14, giving:

n, N
2, 62
3, 158
4, 302
5, 494
6, 734
7, 1022
8, 1358
9, 1742
10, 2174
11, 2654
12, 3182
13, 3758
14, 4382
15, 5054
16, 5774
17, 6542
18, 7358
19, 8222
20, 9134
21, 10094
22, 11102
23, 12158
24, 13262
25, 14414
26, 15614
27, 16862
28, 18158
29, 19502
30, 20894

Shown in the video are cubes of edge length 5 (494 magnets) and edge length 20 (9134 magnets). The magnet count equation was derived by subtracting the magnet count of a solid diagonal cube of edge length n-2 from that of a solid diagonal cube of edge length n, that is, by hollowing out a solid cube and seeing how many magnets are left. For more information about solid diagonal cubes, see youtu.be/VMGpfXAByW4.

Massive Diagonal Cube (Zen Magnets)

Boyd Edwards 2015-09-22 | This video shows how to build a massive diagonal cube using a direct construction technique described in another YouTube video and its written description (youtu.be/VMGpfXAByW4). To my knowledge, this is the largest solid diagonal cube that has ever been built using Zen Magnets, with edge count 16 and 17,968 magnets. It has three-magnet corners. In second place is a cube with one-magnet corners built by NexusTesla with edge count 16 and 14,911 magnets (youtu.be/1za9EQbSJLo), which is about the same size as a cube with three-magnet corners and edge count 15, which requires 14,895 magnets. In third place is a cube with three-magnet corners built by Magnenaut with edge count 13 and 9841 magnets (youtu.be/-DUDMObUIiM).

Electric Unicycle

Boyd Edwards 2015-01-02 | This is day 1 learning how to ride my new electric unicycle.

Magnet Spool Construction Tutorial (Zen Magnets)

Boyd Edwards 2014-05-08 | This video shows how to build a spool that conveniently stores and dispenses over 3400 Zen Magnets.

Two challenges of Zen Magnets are: (1) how to store magnets conveniently between projects, and (2) how to dispense them while building a project. Most projects are built using a single-strand chain, which can inadvertently stick to itself or to the project during construction unless wound up in some way. Storing magnets in hexagonal form requires extra effort to put the magnets into this form for storage, and extra effort to pull these hexagons into a chain for the next project. A spirally-wound free-standing cylinder of magnets works well for storage and works reasonably well during construction, but becomes unwieldy for large numbers of magnets.

The best solution, in my experience, is a magnet spool. It's quick to wind a chain spirally onto a spool, and effortless to pull the chain from the spool during construction. This video shows how to build a magnet spool that provides a convenient, effectively infinite chain of magnets of known polarity.

The spool is a mailing tube of outer diameter 3", cut to a length of 12", including end caps. It is covered with a single thickness of poster paper that is held in place with clear tape. With this extra thickness, the tube circumference closely matches the circumference of windings of Zen Magnets around the tube. Holes of diameter 3/8" are drilled in the centers of the plastic end caps, through which a copper rod of length 12" and diameter 3/8" passes. Lengths of rubber weather stripping are measured to fit around the tube. The ends are glued using flexible vinyl adhesive to form rings that are attached to the ends of the tube. These rings confine the magnets to the tube and to provide a grippy surface that can be used to turn the tube.

The stand is made from 1" x 4" pine (actual dimensions 3/4" x 3.5"), cut into three pieces, two end pieces of length 3.5", with the top corners cut away to improve accessibility to the magnets, and a base piece of length 12 1/16". Holes are drilled a distance of 5/16" from the tops of the end pieces, through which two screws pass to support the copper rod. The holes in the end pieces are countersunk to accommodate the screw heads. The two end pieces are glued and nailed to the base piece, and the stand is routed, sanded, and finished with 3 coats of clear lacquer. A 2" x 6" piece of poster paper is formed into a card holder which is glued onto one end of the stand using SuperGlue. A 13 1/4" x 3 1/4" inch piece of non-slip rug pad is glued to the base to prevent the spool from slipping during use.

Three magnets of known polarity are glued to one end of each spool using steel-reinforced epoxy to ensure that magnet chains taken from all of the spools have the same polarity. Chains that are wound around the spool always start from the same end of these three fixed magnets, which enables counting of magnets by marking the spool surfaces with a permanent marker every 100 magnets.

To see such 3" spools in action, see my cuboctahedron tutorials (http://youtu.be/wO6f1g-AT14, http://youtu.be/mvplVhmzkfE). To see a 6" spool in action, see my Giant Spherical Frame II video (http://youtu.be/kfYmmvobhuQ). The 6" spool is hard to turn when there are lots of magnets on it, and it's easy to break a chain if you pull too hard. It is easier to pull magnet chains from 3" spools. This is because the inertia of the magnets wound around a 3" spool is less than that of a 6" spool, which allows you to quickly accelerate the 3" spool by pulling on the end of the chain. A 3" spool seems to strike the right balance between fitting a lot of magnets and being easy to turn.

Exploding Top in Slow Motion (Zen Magnets)

Boyd Edwards 2014-05-04 | In this video, I build a spinning top out of 177 Zen Magnets, show how it can spin unaided for over 4 minutes, and show how it explodes when it spins too fast to hold itself together. I use the slow-motion video setting on an iPhone 5s to record the explosion at 120 frames per second, and play it at 10% of normal speed to show the explosion in slow motion. I use the shallow valley formed on the bottom of a glass plate to keep the top centered in a small area, and use a straw to spin it. I wear goggles to protect my eyes and use a cardboard fence to protect the magnets when the top explodes. The top explodes when the sound of its spinning reaches a "G" on the musical scale.

The top design is by dindongpie (http://youtu.be/-UXTyj-IXaM) and the original idea of an exploding top is by MagnetNerd (http://youtu.be/q7bFLchsPyM). For more on exploding tops made of neodymium magnet spheres, both regular tops and suspended spinners, see:
http://youtu.be/CMB7tKilw2A
http://youtu.be/K5l7YA0fEK8
http://youtu.be/EpjJ4kF7p4k
http://youtu.be/GPd5oBD1_V8
http://youtu.be/C5fGUVq8xQ8
http://youtu.be/kNbH8Y1HgQQ

Playing with Plato (Zen Magnets)

Boyd Edwards 2014-04-28 | This video illustrates the wonder and versatility of Zen Magnets by using them to build the five Platonic solids. The video won Zen Magnets Flagship Video Contest 39 (http://contest.zenmagnets.com).

Plato (427-347 BC) associated the five regular solids with the five classical elements [1 - 3]:

0:56 Tetrahedron (pyramid with four triangular faces) = Fire
1:38 Octahedron (with eight triangular faces) = Air
2:26 Icosahedron (with twenty triangular faces) = Water
4:33 Hexahedron (cube with six square faces) = Earth
3:36 Dodecahedron (with twelve pentagonal faces) = Universe

These "Platonic solids" are the only convex polyhedra with regular identical polygonal faces meeting at identical vertices. They present an exciting challenge to build using Zen Magnets because of their geometrical beauty and variety. This video shows how to build them using single-strand rings of a single set of 216 Zen Magnets.

Zen Magnets (http://www.zenmagnets.com) are shiny magnet spheres that offer limitless opportunities for creative play, artistic design, and education. They invite individuals to stretch their imaginations for shapes to build, to use critical thinking to figure out how to build them, and to appreciate the beauty of the shapes thus created.

Plato believed in the importance of play in education [4]. He would have loved Zen Magnets.

Audio Tracks:

We gratefully acknowledge the YouTube Audio Library for the two audio tracks in this video: "First to Last," by Gunnar Olsen, and "Fortaleza," by Topher Mohr and Alex Elena.

References:

[1] "Thus, in accordance with the right account and the probable, that solid which has taken the form of a pyramid shall be the element and seed of fire; the second in order of generation we shall affirm to be air, and the third water." -Plato, Timaeus, Section 56b, English translation by Paul Shorey, http://www.perseus.tufts.edu/hopper/.

[2] "To earth let us give the cubic form; for of the four kinds earth is the most immobile and the most plastic body, and of necessity the body which has the most stable bases must be pre-eminently of this character." -Plato, Timaeus, Sections 55d-e, English translation by Paul Shorey, http://www.perseus.tufts.edu/hopper/.

[3] "And seeing that there still remained one other compound figure, the fifth, God used it up for the Universe in his decoration thereof." -Plato, Timaeus, Section 55c, English translation by Paul Shorey, http://www.perseus.tufts.edu/hopper/.

[4] "Do not, then, my friend, keep children to their studies by compulsion but by play." -Plato, Republic, Book 7, Sections 536e - 537a, English translation by Paul Shorey, http://www.perseus.tufts.edu/hopper/.

Double-Walled Tube Tutorial (Zen Magnets)

Boyd Edwards 2014-01-21 | In this video, I show a fast, easy way to use Zen Magnets to build a strong double-walled tube. It is geometrically identical to, but magnetically different from, Damian O'Connor's "perfect cylinder" (http://youtu.be/DnjrmUKe7go, http://dotpedia.com/creations/view/2390). My tube looks exactly the same as his. The difference is in the manner of construction, and how connections are made between magnets.

In the video, I show how to build a 5-ring tube with 400 magnets and a 25-ring tube with 2000 magnets, using a sheet of parallel magnet chains to build the inner wall and pairs of antiparallel chains for the outer wall. It takes just 6 minutes to build the 25-ring tube from scratch. In general, an N-ring tube requires 80N magnets, 80 magnets for each ring.

A lighthouse shape (http://youtu.be/cJ6ZebVTMOA, http://www.flickr.com/photos/91128546@N04/12045753814) shown briefly in the video illustrates the strength of the double-walled tube. The lighthouse is a 4.4-pound (2.0 kg) double-walled tube with 4060 magnets supporting a 7.1-pound (3.2 kg) snub ball with 6590 magnets. Also shown briefly is a long tube with 10,640 magnets.

Forty-column cylinders best match the natural curvature of the double wall. Here's the proof: The column spacing for the square-packed columns in the outer wall is just the magnet diameter, D. If there are n columns in this wall, its circumference will be given approximately by nD = 2πR, where R is its radius. The column spacing for hexagonally-packed columns in the inner wall is d = (√3/2)D. If there are n columns also in this wall, its circumference will be given approximately by nd = 2πr, where r = R - d is its radius. Solving these equations yields the ideal number of columns that best matches the natural curvature, n = 2(3+2√3)π = 40.615. But n must be an integer; you can't have 40.615 columns. In fact, n must be an even number because of the alternating column offsets. Since 40 is the closest even number to 40.615, 40-column cylinders best match the natural curvature of the double wall.

I now justify the approximations made in this derivation. The approximate circumference nD of the outer wall is the sum of the straight-line distances between the centers of its n columns. The exact but more complicated circumference, 2nR*arcsin(D/2R), is the distance around the arc of the circle of radius R. Replacing the approximate circumferences of the inner and outer walls with the exact circumferences gives a slightly smaller value for the ideal number of columns, n = π/arcsin(1/√3-1/2) = 40.575. Whether using the approximate circumferences or the exact ones, the conclusion is the same: 40-column cylinders best match the natural curvature of the double wall.

Lighthouse Tutorial (Zen Magnets)

Boyd Edwards 2014-01-20 | This video shows how to use 10,650 Zen Magnets to build a lighthouse, a double-walled tube invented by Damian O'Connor (http://youtu.be/DnjrmUKe7go) supporting a snub ball of my own invention (http://youtu.be/biEMiD2mCIw). For photos of the lighthouse lit from within, see my Flickr photo stream, http://www.flickr.com/photos/91128546@N04/12044416153/.

Each of the 51 rings in the tube requires 80 magnets, for a total of 4080 magnets. Removing 20 magnets from the top end of the tube reduces the tube magnet count to 4060. Tubes can be built using my fast technique (http://youtu.be/TuDL1TvAEY4).

The sphere is a snub ball of edge length 5, first built by Jonathan Minond (http://youtu.be/zZCLZdJi4Jg). A complete snub ball requires:
60 vertex pieces made of double hexagon rings
150 edge pieces made from double rings of 10
80 triangular faces made from double rings of 9
12 pentagonal faces with 130 magnets each.
This requires 60*2*6 + 150*2*10 + 80*2*9 + 12*130 = 6720 magnets. Omitting one pentagon (where the ball attaches to the tube) reduces the snub ball magnet count to 6590.

The total magnet count for the lighthouse is 4060 + 6590 = 10,650.

Seamless Cuboctahedron Frame Tutorial (Zen Magnets)

Boyd Edwards 2014-01-05 | In this tutorial video, I show how to modify YoyoBandalore's technique for building seamless cuboctahedron frames (http://youtu.be/8TxME5DPsyk) in order to build very large frames, and demonstrate the method by building a medium-sized frame with edge length L = 10. The comments below describe how to build the frame for edge lengths as small as L = 4 and as large as L = 48. A separate construction video (http://youtu.be/wO6f1g-AT14) shows how to build the L = 48 frame, which might be the largest Archimedean or Platonic solid frame ever built using 5 mm magnet spheres.

In general, to build a seamless cuboctahedron frame with edge length L, you will need eight triangles of edge length L-2, eight triangles of edge length L-1, and a total of 96(L-2) magnets. The triangles can be built from rings, as shown in this video, or can be built directly from a chain of magnets, as shown in the construction video. If using rings, you'll need eight rings of 3(L-3) magnets for the small L-2 triangles and eight rings of 3(L-2) magnets for the large L-1 triangles.

For example, for edge length L = 10 shown in this video, you'll need eight small triangles of edge length 8, eight large triangles of edge length 9, and a total of 768 magnets. To build these triangles, use eight rings of 21 magnets for the small triangles and eight rings of 24 magnets for the large triangles, and pinch these rings into triangles.

Add an extra ring around each small triangle and an extra ring around each large triangle. Place four small triangles atop four large triangles to make four triangular subunits of type A. Turn over the remaining triangles to reverse their polarities. Place the four small triangles atop the four large triangles and remove four magnets from each corner to make four triangular subunits of type B.

Construct the cuboctahedron by placing an A subunit at the bottom, three B subunits at the second level, three A subunits at the third level, and a B subunit at the top, with subunits of different types joined at corners.

Huge Cuboctahedron Frame Construction (Zen Magnets)

Boyd Edwards 2013-12-30 | This video shows the narration-free construction of a huge seamless cuboctahedron frame with edge length 48 and 4,416 magnets. This frame demonstrates the amazing strength of Zen Magnets. Without seeing it, I might not have believed that a frame this open and this large, built using 2 x 2 edge pieces, could support itself under earth's gravity. It just does not seem possible. But here it is.

Like the cube, the cuboctahedron has six square faces. It also has eight triangular faces, like an octahedron. The cuboctahedron is one of 13 Archimedean solids, which have two or more types of regular polygonal faces meeting in identical vertices. The 5 Platonic solids have just one type of regular polygonal face meeting in identical vertices.

This cuboctahedron frame might be the largest Archimedean or Platonic solid frame ever built using 5 mm magnet spheres. The frame is 39 cm (15 3/8") high and encloses 32 liters (8.5 US gallons) of air, compared with just 0.29 liters occupied by its 4,416 magnets. These magnets therefore occupy less than 1% of the volume enclosed by the frame.

To build the four subunits of type A and the four subunits of type B needed for the frame, you need eight rings of 135 magnets pinched into "small" triangles of edge length 46, and eight rings of 138 magnets pinched into "large" triangles of edge length 47. To each of these triangles is added one more ring of magnets. In this video, I conveniently skip the ring step and make the triangles directly from a chain of magnets, with all triangles wound in the same direction.

For A subunits, to mate a small triangle with a large triangle, the small triangle is turned over and one edge joined with the large triangle, then the small triangle is turned over onto the large triangle.

The B subunits have polarity opposite to A subunits. Accordingly, a large triangle is turned over (instead of a small triangle) and one edge joined with a small triangle, then the small triangle is turned over onto the large triangle, as shown. Also, four magnets are removed from each corner of B subunits so they will mate properly with the A subunits.

The frame is assembled by placing an A subunit on the working surface, attaching three B subunits to it supported by cardboard scaffolding, attaching three A subunits to them supported by cardboard scaffolding, attaching a B subunit to the top, and removing the scaffolding.

Video footage is shown of the:

00:00 Completed frame with a full-sized violin within it.
00:26 Assembly of an A subunit.
01:23 Assembly of a B subunit.
02:22 Assembly of the frame.
05:29 Completed frame with a small frame within it.

The small frame shown in at 05:29 is a seamless cuboctahedron frame with edge length 7 and 480 magnets designed by YoyoBandalore (http://youtu.be/8TxME5DPsyk). My magnetic design is the same as his; only the construction techniques differ. My construction techniques are discussed in more detail in a separate tutorial video and written comments (http://youtu.be/mvplVhmzkfE), which discuss how to build the frame in any size between edge length 4 (the smallest) and edge length 48 (the subject of the present video), including YoyoBandalore's frame with edge length 7.

For a photo of the frame and the violin, see http://www.flickr.com/photos/91128546@N04/11639306864/.

The background music is Allegro from Eine Kleine Nachtmusik, by Wolfgang Amadeus Mozart, courtesy the YouTube Audio Library.

Sphere of Spheres Tutorial (Rhombicosidodecahedron, Zen Magnets)

Boyd Edwards 2013-08-21 | This tutorial video shows how to build a 3600-magnet hollow sphere out of 60 hollow mini-spheres. Each mini-sphere is a miniature copy of the large sphere and has 60 Zen Magnets. Each sphere, both mini and large, is a rhombicosidodecahedron with 20 triangular faces, 30 square faces, and 12 pentagonal faces. I learned about the shape from a video by cbrian4, http://youtu.be/et7anYdqHbo.

The Definitive Diagonal Cube Tutorial (Zen Magnets)

Boyd Edwards 2013-07-20 | 1. Overview

This video tutorial shows how to build solid diagonal cubes of any size out of Zen Magnets, with three magnet vertices. Step-by-step instructions show how to build cubes directly, layer by layer, without the need for intermediate octahedron and cuboctahedron steps, using stable three-magnet corners.

Construction is shown explicitly for cubes with edge counts
1 (2:09),
2 (4:55),
3 (8:13), and
4 (17:34).
Schematic diagrams (see 27:51 and http://imgur.com/jJpatbd) show how to build cubes with edge counts up to 12.

Below, we discuss how to build the diagonal cube in even larger sizes. In general, a cube of edge count n requires N = n(4n*n + 6n + 3) magnets.

2. Layer Numbers and Dimensions

The cube is built from single-thickness diagonal layers. These layers are horizontal when the cube is oriented with one corner directly above its opposite corner. In this orientation, n triangular layers form the top third of the cube (orange labels on the schematics), n hexagonal layers form the middle third (violet labels), and n triangular layers form the bottom third (orange labels), for a total of 3n layers.

Layer dimensions are denoted by L x M, where L and M are the edge lengths along alternating sides of a hexagon, and with L less than or equal to M by convention. If L = 1, the hexagon becomes a triangle. If L = M, you get a regular hexagon with all six sides of the same length. For L between 1 and M, you get an irregular hexagon with sides alternating between edge length L and edge length M.

The n triangular layers in the top third of the cube and the n triangular layers in the bottom third are duplicates of each other, and have dimensions:

1 x 2
1 x 4
1 x 6...
1 x 2n.

The dimensions of the hexagonal layers in the middle third depend on whether n is even (n = 2, 4, 6, ...) or odd (n = 1, 3, 5, ...). For even n, you'll need two of each of the following:

2 x 2n
4 x (2n - 2)
6 x (2n - 4)...
n x (n+2)

The two n x (n+2) layers meet at the center of the cube.

For odd n, you'll need two of each of the following for the middle third:

2 x 2n
4 x (2n - 2)
6 x (2n - 4)...
(n-1) x (n+3)

and you'll also need one (n+1) x (n+1) regular hexagon at the center of the cube.

3. Layer Construction

We now discuss how to make these layers. At the heart of each layer is one of three cores, a single magnet (1 x 1), a triangle of three magnets (1 x 2), or a triangle of six magnets (1 x 3). The difference M - L between the two sides is 0, 1, and 2 for these three cores, respectively.

For odd n, as discussed above, a single regular hexagon forms the central layer of the cube. This hexagon has a 1 x 1 core. The next layer up (or down) has a 1 x 2 core, then the next layer has a 1 x 3 core, and the core sequence repeats, 1 x 1, 1 x 2, 1 x 3, etc. until you reach the top (or bottom) triangle of the entire cube, which is a 1 x 2 core.

For even n, as discussed above, two hexagons meet at the center of the cube. Each of these has a 1 x 3 core. Starting from the upper (or lower) of these two and moving up (or down), the cores needed for successive layers are 1 x 1, 1 x 2, 1 x 3, 1 x 1, 1 x 2, 1 x 3, etc. until you reach the top (or bottom) triangle of the cube, which again is a 1 x 2 core.

Adding a complete ring (shades of green in the schematics) to an L x M layer converts it into an (L+1) x (M+1) layer. Thus, the difference M - L between the two sides doesn't change when you add a complete ring.

Adding three chains each of length L - 1 along sides of length L of an L x M layer (shown in shades of blue or white in the schematics) converts it into an (L-1) x (M+2) layer, subtracting 1 magnet from the sides of length L and adding 2 magnets to the sides of length M, and increasing the difference M - L by 3.

4. General Layer Construction Procedure

In general, an L x M layer requires (L+M-1)(L+M)/2 + (L-1)(M-1) magnets. To build an L x M layer (with L less than or equal to M), first divide the edge length difference M - L by 3. The quotient Q is the number of chains you need to add (shades of blue and white) to each of the three short sides. The remainder R determines the core that you need to use to build the layer; remainders R of 0, 1, and 2 imply 1 x 1, 1 x 2, and 1 x 3 cores, respectively. The number of complete rings that you need to add around the core (shades of green) is C = L + Q - 1.

For example, a 1 x 14 triangle has L = 1, M = 14, and M - L = 14 - 1 = 13. Dividing 13 by 3 gives a quotient Q = 4, remainder R = 1, and number of complete rings C = 1 + 4 - 1 = 4. Thus, to build the 1 x 14 triangle, start with a 1 x 2 core, wind 4 complete rings around it (shades of green), and add 4 chains (three blue, one white) to each of the three short sides, as shown in the schematic for edge length 7.

Large Snub Ball (Zen Magnets)

Boyd Edwards 2013-04-05 | This is a narration-free video of the large snub ball, a double-thickness hollow sphere made of 4500 Zen Magnets. The video shows close-ups, construction steps, footage of the shape being tossed from hand to hand, and its destruction. This shape surpasses the ultimate ball in size, weight, sphericity, strength, rigidity, and scalability, and may be the largest self-supporting double-thickness hollow sphere that can be made with Zen Magnets. For construction details, see my video entitled "Snub Ball Tutorial."

The footage in this video is also shown at the end of my "Zen Ball Art" video, which compares snub balls of various sizes with the ultimate ball.

Snub Dodecahedron Frame Tutorial (Zen Magnets)

Boyd Edwards 2013-04-04 | This is a video tutorial showing how to make a snub dodecahedron frame using Zen Magnets. The snub dodecahedron is the most spherical of the eighteen highly-symmetric Platonic and Archimedean solids. Sixteen of these are identical to their mirror images. The snub dodecahedron is not, coming in distinct clockwise and counterclockwise chiral forms that are mirror images of each other. This tutorial shows how to build both forms.

The frame requires 60 vertex pieces made of double hexagon rings, 150 edge pieces of length L made of double rings of 2L magnets each, and a total of 120(6+5L) magnets. These pieces fit together to form 80 open triangles and 12 open pentagons. The video shows the construction for L = 6, which requires 4320 magnets. The frame does not support its own weight when resting on a hard flat surface in earth's gravity, and strips of poster paper are used as scaffolding to prevent collapse.

Filling the open triangles and pentagons prevents this collapse and yields a self-supporting hollow sphere, called the snub ball, that surpasses the ultimate ball in size, weight, sphericity, strength, rigidity, and scalability. See my videos entitled "Zen Ball Art" and "Snub Ball Tutorial" for details.

Ultimate Ball Tutorial (Icosahedron, Zen Magnets)

Boyd Edwards 2013-04-04 | This is a tutorial video showing a simple way to make the ultimate ball, also called the ultimate shape, a classic double-thickness hollow sphere with icosahedral symmetry, using 1860 Zen Magnets. To explore larger double-thickness hollow spheres, see my "Zen Ball Art" and "Snub Ball Tutorial" videos.

Zen Ball Art (Ultimate Ball, Snub Ball, Zen Magnets)

Boyd Edwards 2013-04-04 | The video shows four double-thickness hollow spheres that can be made with Zen Magnets, including the ultimate ball with 1860 magnets and snub balls with 2280, 3360, and 4500 magnets. Shown narration-free are the main steps in the constructions, one destruction (at the end), close-up video, and tossing of the larger snub balls from one hand to the other.

The snub ball surpasses the ultimate ball in size, weight, sphericity, strength, rigidity, and scalability. The 4500-magnet snub ball may be the largest self-supporting double-thickness hollow sphere that you can make with Zen Magnets. For more information on how to build these shapes, see my videos entitled "Ultimate Ball Tutorial" and "Snub Ball Tutorial."

The footage of the 4500-magnet snub ball also appears in my "Large Snub Ball" video.

Giant Spherical Frame II (Rhombicosidodecahedron, Zen Magnets)

Boyd Edwards 2013-03-08 | This video shows the narration-free construction and destruction of a giant rhombicosidodecahedron frame with 3660 Zen Magnets, with a subunit edge length of 10 magnets, and with a diameter of 18.5 cm, based on my YouTube video "Giant Spherical Frame Tutorial." To my knowledge, this is the largest self-supporting hollow spherical frame that can be built using 2x2 edge pieces. At this size, the frame barely supports its own weight on a hard flat surface in Earth's gravity. I wonder how large this frame could be made on the Space Shuttle, or the moon. Any takers?

The background music is Hyperventilate, from the album Milliontown by Frost*.

Giant Spherical Frame Tutorial (Rhombicosidodecahedron, Zen Magnets)

Boyd Edwards 2013-02-26 | This is a video tutorial for a giant rhombicosidodecahedron frame, built using Zen Magnets and inspired by a similar design by dinofx35 (http://youtu.be/0gbdlFpbpVU), which is replicated by Magnenaut (http://youtu.be/9xBm6Lj-vCI) and electronicsludge (http://youtu.be/9RQeFX5PlG4).

This frame is constructed from 12 pentagonal subunits and 20 triangular subunits. It can be built for subunit edge lengths of L = 5, 6, 7, 8, 9, and 10 magnets, which respectively require N = 1260, 1740, 2220, 2700, 3180, and 3660 magnets, with N = 480L - 1140 generally. Subunits are built from, respectively,
• 12 rings of 5(L-3) = 10, 15, 20, 25, 30, and 35 magnets for the pentagonal subunits
• 20 rings of 3(L-3) = 6, 9, 12, 15, 18, and 21 magnets for the inside layer of the triangular subunits
• 20 rings of 3(L-4) = 3, 6, 9, 12, 15, and 18 magnets for the outside layer of the triangular subunits

Frames with edge lengths 5 and 9 magnets are shown briefly in the video, and the 7-magnet version is used to demonstrate construction. The 9-magnet version is the largest that I had succeeded in building when I shot the video. A separate video, "Giant Spherical Frame II (Rhombicosidodecahedron, Zen Magnets)," shows the construction of the 10-magnet version, which might be the largest self-supporting hollow spherical frame that can be built using four-strand (2x2) edge pieces.

Hollow Octahedron Tutorial: Six Pyramid Design (Zen Magnets)

Boyd Edwards 2013-02-26 | This tutorial video and the comments below describe how to build a hollow octahedron of arbitrary size using six four-sided pyramids of Zen Magnets, following the technique of PvgAshes.

In the video, I build a 246-magnet octahedron of radius 5, the radius being the number of magnets between one corner of a triangular face and its center, using pyramids of edge length 5. The video also shows completed 1086-magnet and 2526-magnet octahedra of radii 10 and 15, respectively, built using the same technique. The 2526-magnet version is quite delicate.

To build an octahedron of arbitrary radius R (which can be any positive integer), wind six pyramids of edge length R and snap them together. The total number of magnets needed is 12R(R-1)+6.

April 7, 2013 update: I just learned that Coco Aub first came up with this design. He produced a video on August 18, 2011 called "COCOAUB - Blob 2880 Dots" that builds the octahedron with radius R = 16. By my formula above, this would require 2886 magnets. His octahedron requires 2880 magnets because he omits the 6 corner magnets.

Hollow Octahedron Tutorial: Seamless Design (Zen Magnets)

Boyd Edwards 2013-01-19 | This tutorial video and the comments below describe how to build a hollow single-thickness octahedron of arbitrary size using Zen Magnets, using a seamless technique similar to that used by Anson Berns. This technique produces a stronger structure than the six-pyramid technique shown in another tutorial video of mine.

In the video, I build a 194-magnet octahedron of radius 5, the radius being the number of magnets between one corner of a triangular face and its center. This size requires a concave pyramid with 5 complete layers and 3 incomplete layers and a convex pyramid with 6 complete layers. The video also shows completed 974-magnet and 2354-magnet octahedra of radii 10 and 15, respectively, built using the same technique. When building larger octahedra, an extra pair of hands can be helpful.

To build an octahedron of arbitrary radius R (which can be any positive integer), wind a concave pyramid with R complete layers and R-2 incomplete layers of decreasing lengths, the first with chains of length R and the last with chains of length 3, and pinch the last layer to form four vertices. Then, wind a convex pyramid with 2(R-2) complete layers (winding in the same direction as the concave pyramid) and join it with the concave pyramid. Add a magnet to the top and one to the bottom to complete the shape. The total number of magnets needed is 12(R-1)^2+2.

Icosahedron With Diagonal Polygons Tutorial (Zen Magnets)

Boyd Edwards 2013-01-17 | This tutorial video describes how to make small and large versions of this shape, which was invented by saxplayingcompnerd. For the 3,240-magnet small version, each of the 12 subunits requires 190 magnets for the hollow corner piece and 80 magnets for the stubs. The 4,740-magnet large version requires 315 magnets for each corner piece (used by saxplayingcompnerd) and 80 magnets for the stubs. You can use longer or shorter stubs as desired.

13-Atom Icosahedral Cluster Tutorial (Zen Magnets)

Boyd Edwards 2013-01-15 | This is a tutorial video for a model of a 13-atom icosahedral cluster using 3860 Zen Magnets. Ledwatchman has posted two similar shapes, an Atomium Icosahedron (8340 magnets), and a Giant Gold Molecule (7620 magnets). Stable 13-atom clusters can be formed by neon, argon, krypton, xenon, and gold.

Each of the 12 pentagonal subunits (patterned after saxplayingcompnerd in his Icosahedron with Diagonal Polygons) requires 275 magnets: 130 for the hollow pentagon structure, 23 for each of its 5 legs, and 30 for the six stacked pentagon rings. The central sphere unit requires 560 magnets: 5 for each of its 12 pentagons, 7 for each of its 20 filled hexagons, and 30 for each of its 12 stacked pentagon rings.

Deltoidal Hexecontahedron Tutorial (Zen Magnets)

Boyd Edwards 2013-01-11 | This is a tutorial video for a deltoidal hexecontahedron design using 2220 Zen Magnets. The design is tricky to build and is very strong. It can be rested on a triangular face or balanced on one of its icosahedron vertices. Magnenaut posted a tutorial of a design with 2460 magnets that is simpler to build but has no flat faces.

Bubble Icosahedron Tutorial (Zen Magnets)

Boyd Edwards 2012-12-30 | This is a tutorial video for a lovely bubble icosahedron design using 3600 Zen Magnets. Ottiemans created a YouTube video that shows the finished product and that includes written comments about its construction.

Icosahedron Frame Tutorial (Zen Magnets)

Boyd Edwards 2012-12-29 | This 3852-magnet icosahedron frame is built from 20 triangular sub-units, each constructed from two rings, one of 42 magnets and the other of 45 magnets. The design is very strong and can likely be built much larger, though I don't have enough magnets to test this. Adding 3 magnets to each ring increases the edge length by one and increases the total number of magnets needed by 240. Those who attempt larger sizes are invited to share their results in the comments.

Octahedron Frame Tutorial (Zen Magnets)

Boyd Edwards 2012-12-29 | This is a tutorial video for a simple scaffold-free method for building an octahedron frame using Zen Magnets. The tutorial is based on a frame with an edge length of 20 magnets, with 1626 magnets in all. Also shown briefly is a larger frame with an edge length of 40 magnets, with 3786 magnets in all, built using the same method. In general, edge length n requires 108n - 534 magnets.

Solid Diagonal Cube Tutorial (Zen Magnets)

Boyd Edwards 2012-12-15 | This is a tutorial for a direct build of a solid diagonal cube with 3429 Zen Magnets, without the intermediate octahedron and cuboctahedron steps. The cube is built layer by layer using face-centered cubic (fcc) packing for each half cube.

Soccer Ball / Football Tutorial (Zen Magnets)

Boyd Edwards 2012-12-15 | The goal of this project is to model a soccer ball / football with Zen Magnets (spherical 5 mm-diameter neodymium dipole magnets). The traditional soccer ball design is a truncated icosahedron with 12 pentagonal faces, colored black, and 20 hexagonal faces, colored white. Each pentagonal face has five adjoining hexagonal faces. Placing a carbon atom at each of the 60 vertices of a truncated icosahedron produces the famous Buckminsterfullerine, or "buckyball," C60 molecule, discovered in 1985.

Tutorials are presented for two similar designs, a small design with 1092 magnets and a large design with 3912 magnets. To make the symmetry of the faces readily apparent, I filled the pentagonal faces and left the hexagonal faces open. For those interested in trying the small design in different sizes, the number of magnets needed is 30(n-1)(n+8) + 12, where n is the number of magnets along each hexagon / pentagon edge. The tutorial for the small design uses n = 4 magnets along each edge and 1092 magnets in all. For the large design, the number of magnets needed is 30(n-1)(n+16)-228. The tutorial for the large design uses n = 7 magnets along each edge and 3912 magnets in all. The large design is robust, and might hold its own weight when resting on a hexagonal face with n = 8 (4812 magnets) or perhaps n = 9 (5772 magnets), but I don't have enough magnets to verify this.