Catalogue of Polyrhons

A poly-rhombic-dodecahedron, or polyrhon, is a figure made of rhombic dodecahedrons joined face to face. Here I show all the free polyrhons of orders 1–4.

Two-sided polyrhons may be reflected as well as rotated. One-sided polyrhons may be rotated but not reflected. The pictures show only two-sided polyrhons.

The Puzzling World of Polyhedral Dissections by Stewart T. Coffin describes polyrhons in Chapter 18. You can find the book on line here. See also Torsten Sillke's notes on polyspheres, which are joined like polyrhons but have an additional symmetry. For example, the red trirhon below lacks mirror symmetry; the corresponding trisphere has it. Abaroth's page Polyspheres presents a description and several constructions for polyspheres.

Enumeration

These are sequences A038173 and A038172 in the On-Line Encyclopedia of Integer Sequences.

OrderFreeOne-Sided
111
211
345
42028
5131225
61 2112 274
712 73424 955
8144 158286 143
91 687 7373 367 443
1020 196 78840 358 811

Monorhon

Dirhon

Trirhons

Tetrarhons

Last revised 2014-11-11.


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George Sicherman [ HOME | MAIL ]