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An Archimedean solid is a convex, uniform, irregular, non prismatic polyhedron/polytope. This page shows the 3D set of these shapes, but does not explain them. If you want an explanation, look to Kuvina's video. The images were rendered by me, and if you click on one it takes you to the polytope wiki page for them. If you hover over them, it gives you a short summary of my subjective thoughts on the shape.

These were really easy to make compared to the 4D ones. Same licensing (or lack there of) applies.

I put these shapes in a different order than the 4D page. In the 4D page I did least to greatest n op for the platonic solid with the fewest facets of the symmetry group, then all the shapes that were n op of the shape and its dual, lowest to highest, and then I did greatest to least n op for the dual platonic solid. That was perhaps an ugly order, I'm not sure. Anyway, the order this time is the truncation series, and then the expansion, and then the omnitruncation. This ordering is less general than the first and so only works in 3D, really.

A3 - Symmetry of the Tetrahedron (1)

B3 - Symmetry of the Cube & Octahedron (5)

H3 - Symmetry of the Dodecahedron & Icosahedron (5)

Non Wythoffian (2)

Before making this page, I knew not of how well the 3D Archimedeans lined up with each other. I still prefer the much richer structure of how the 4D Archimedeans relate, but the simplicity and evenness of the 3D chart is cool. A3 being B3/2 kind of annoys me, but if it weren't for that F4 wouldn't exist so I guess it's necessary. Not like A3 is that pretty anyway. I like the snubs, chiral uniforms are interesting and I'm sad that 4D doesn't have any convex ones.

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