Bowtie Cubes in a Polyhedral Honeycomb

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This polyhedron has been described here as a “bowtie cube.” It is possible to augment its six dodecagonal faces with additional bowtie cubes. Also, the bowtie cube’s hexagonal faces may be augmented by truncated octahedra.

bizarre

These two polyhedra “tessellate” space, together which square pyramidal bifrustrums, meeting in pairs, which fill the blue-and-green “holes” seen above. This last image shows more of the “honeycomb” produced after yet more of these same polyhedra have been added.

bizarrer

This pattern may be expanded into space without limit. I discovered it while playing with Stella 4d, software you may try for free at this website.  

 

 

Tetrahedrally-Symmetric Creatures with Polyhedral Legs

Each of these has a tetrahedron hidden from view in the center.

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augmented-tetra-2

augmented-tetra-3

augmented-tetra-4

These were made using Stella 4d, which you may try for yourself here.

A Crinkled Octahedron

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“Crinkled” is merely descriptive; I offer no mathematical definition of the term. This was a polyhedron I stumbled along while doing random-walk polyhedral manipulations with Stella 4d, available at this website.

The Compound of the Rhombic Dodecahedron and Its Own Third Stellation

compound-of-rd-plus-stellation-of-rd

I used Stella 4d to make this polyhedral compound, and this program may be tried for free at this website.