The 16-Cell and Some Relatives


The 16-cell is the dual to the hypercube. It consists of 16 regular tetrahedra arranged so that each edge is shared by 4 tetrahedra. There is a remarkable trio of "natural" Zome models of the 16-cell. Each is constructed using the same set of pieces, 8 balls, 6 long reds, 6 medium reds, 6 long yellows, and 6 long blues. In fact, this is an instance of triality.



The vertex configuration of the 16-cell is the octahedron. Another way to say this is that one obtains octahedra as a result of truncating the vertices. Here are some models of the truncated 16-cell, each obtained so that the resulting faces are either equilateral triangles or regular hexagons. These are examples of uniform polytopes:



Here one sees the 16-cell projections along with their truncations:





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