Uploaded August 2013 | Updated September 2026, 2 weeks ago
The unit looks like a trapezohedron, the 8 faces are congruent (equal) kites. When you make a large solid version, you can expect some strange polarity problems at the points. It can be necessary to reverse the polarity of the octagon and square at the end, which doesn't seem to make sense at all. Making 1-layer large versions becomes more difficult for each next size, I wonder if anyone can break my record. (I didn't try the next size, I found the last one to be difficult enough) The kites on a solid trapezohedron are more flat, yet not completely flat, each kite is slightly bent. In the build of 35 units, the principle is that in an infinite version all units connect to 4 neighbors, just like in the D surface tetrahedral sections connect to 4 neighbor sections. Here, it results in a shifted version of the D surface. Using the same method, it is possible to make a trapezohedron with 10 kite faces, I didn't show that in this video though.
The unit looks like a trapezohedron, the 8 faces are congruent (equal) kites. When you make a large solid version, you can expect some strange polarity problems at the points. It can be necessary to reverse the polarity of the octagon and square at the end, which doesn't seem to make sense at all. Making 1-layer large versions becomes more difficult for each next size, I wonder if anyone can break my record. (I didn't try the next size, I found the last one to be difficult enough) The kites on a solid trapezohedron are more flat, yet not completely flat, each kite is slightly bent. In the build of 35 units, the principle is that in an infinite version all units connect to 4 neighbors, just like in the D surface tetrahedral sections connect to 4 neighbor sections. Here, it results in a shifted version of the D surface. Using the same method, it is possible to make a trapezohedron with 10 kite faces, I didn't show that in this video though.
