Uniform Compounds
In 1976 John Skilling published Uniform Compounds of Uniform Polyhedra which enumerated 75 compounds (including 6 as infinite prismatic sets of compounds, #20-#25) made from uniform polyhedra with rotational symmetry. (Every vertex is vertex-transitive and every vertex is transitive with every other vertex.) This list includes the five regular compounds above.
Here is a pictorial table of the 75 uniform compounds as listed by Skilling. Most are singularly colored by each polyhedron element. Some as chiral pairs are colored by symmetry of the faces within each polyhedron.
- 1-19: Miscellaneous (4,5,6,9,17 are the 5 regular compounds)
- 20-25: Prism symmetry embedded in prism symmetry,
- 26-45: Prism symmetry embedded in octahedral or icosahedral symmetry,
- 46-67: Tetrahedral symmetry embedded in octahedral or icosahedral symmetry,
- 68-75: enantiomorph pairs
Read more about this topic: Polyhedral Compound
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