Uploaded February 2014 | Updated September 2026, 1 week ago
With the unit infinite slightly different lattices can be produced. In this video just 2 of them are shown. When all units in are placed in the same position the TT surface is produced, a lattice with straight triangular tunnels. The cell for producing the surface is simply the unit itself. A tutorial for the 72 dots subunit (of which 6 are needed to produce a unit) will follow later, a link will be placed in this video as well as in this description then as well.
When all units are placed such that each 2 bordering units mirror each other, a lattice similar to the I-WP surface is produced. The main difference is that there are various locations where 8 triangles meet in a point. These 8 triangles form 2 pyramids meeting each other at the top. When these pyramids are replaced with a square catanoid (a sandglass shape) the lattice turns into a valid continuous surface. The cell for this surface is a cube of 8 units combined, that each have had the same catanoid adaptation.
The cubic cell shown in the video is the 3rd possible option for a cubic cell with diagonal symmetry, where the lattice can be placed in 3D space such that in X, Y and Z direction the lattice is the same. For this reason, the pattern produced on planes between 2 touching layers of units turns out to be the same in all 3 directions. The pattern is shown at 2:51. The idea is to start with a 2x2x2 section of the TT surface, to which 3 1x2x2 sections of the TT surface in mirror position get attached. Then, add 3 1x1x2 sections, each touching 2 1x2x2 sections, again in mirror position. Finally add a single unit in the remaining corner in the 3x3x3 cube, in mirror position compared to the 3 1x1x2 sections. In this lattice also a catanoid adaptation is needed to turn it into a valid surface. In addition, to turn it into a minimal surface in some places 4 triangle (bottomless) pyramids must be flattened.
Finally, a cell of 3x4x4 units is shown. Because it doesn't have the diagonal symmetry described before, it generates 3 different patterns on planes between layers of units. These patterns are shown from 3:09 to 3:21.
The way to make the 36 dots subunit is shown in:
youtube.com/watch?v=XLwYI7nVevg
With the unit infinite slightly different lattices can be produced. In this video just 2 of them are shown. When all units in are placed in the same position the TT surface is produced, a lattice with straight triangular tunnels. The cell for producing the surface is simply the unit itself. A tutorial for the 72 dots subunit (of which 6 are needed to produce a unit) will follow later, a link will be placed in this video as well as in this description then as well.
When all units are placed such that each 2 bordering units mirror each other, a lattice similar to the I-WP surface is produced. The main difference is that there are various locations where 8 triangles meet in a point. These 8 triangles form 2 pyramids meeting each other at the top. When these pyramids are replaced with a square catanoid (a sandglass shape) the lattice turns into a valid continuous surface. The cell for this surface is a cube of 8 units combined, that each have had the same catanoid adaptation.
The cubic cell shown in the video is the 3rd possible option for a cubic cell with diagonal symmetry, where the lattice can be placed in 3D space such that in X, Y and Z direction the lattice is the same. For this reason, the pattern produced on planes between 2 touching layers of units turns out to be the same in all 3 directions. The pattern is shown at 2:51. The idea is to start with a 2x2x2 section of the TT surface, to which 3 1x2x2 sections of the TT surface in mirror position get attached. Then, add 3 1x1x2 sections, each touching 2 1x2x2 sections, again in mirror position. Finally add a single unit in the remaining corner in the 3x3x3 cube, in mirror position compared to the 3 1x1x2 sections. In this lattice also a catanoid adaptation is needed to turn it into a valid surface. In addition, to turn it into a minimal surface in some places 4 triangle (bottomless) pyramids must be flattened.
Finally, a cell of 3x4x4 units is shown. Because it doesn't have the diagonal symmetry described before, it generates 3 different patterns on planes between layers of units. These patterns are shown from 3:09 to 3:21.
The way to make the 36 dots subunit is shown in:
youtube.com/watch?v=XLwYI7nVevg
