Thursday, October 15, 2015

[yjbljbsv] Quarter octahedron

What is the shape of the space left over after fitting a half-size (1/8 volume) regular octahedra just inside each of the vertices of a full-sized octahedron?  Can that space be filled with other regular polyhedra?  (Update: the leftover space is (conveniently) 8 regular tetrahedra. https://commons.wikimedia.org/wiki/File:TetraOctaHoneycomb-VertexConfig.svg)

Analogously for tetrahedron, the leftover space is an octahedron.  Cube: no space leftover.  Other polyhedra?

Motivation was whether one could do this on a octahedron-tetrahedron honeycomb.

No comments :