Category:Archimedian solids
The Archimedian solids are a slightly arbitrary group of thirteen shapes listed by Archimedes in xxxx. They can be considered as the next level of complexity above the Platonic solids.
Characteristics
Where the Platonic solids are regular convex shapes that use a single identical regular polygon for every face, the Archimedian solids use more than one type of regular polygon.
Truncated Platonic solids
These are obtained by taking a Platonic solid and "lopping the corners off":
- Truncated Tetrahedron
- Truncated Cube
- Truncated Octahedron
- Truncated Icosahedron
- Truncated Dodecahedron
- Cuboctahedron
- Icosidodecahedron
Truncated truncated Platonic solids
These are Archimedian solids obtained by truncating other Archimedian solids (specifically, the last two on the previous list):
- Rhombitruncated Cuboctahedron
- Rhombicuboctahedron
- Rhombitruncated Icosidodecahedron
- Rhombicosidodecahedron
Snubbed Platonic solids
- Snub Cube
- Snub Dodecahedron
While "truncation" is a fairly simple process that involves cutting off a regular corner to produce a regular polygon, "snubification" is a non-obvious cutting method that usually cuts away an edge to produce two angled facets whose common edge has a "twist" compared to the alignment of the original edge. These "snubbed" solids are chiral – they can be produced in "left-handed" or "right handed" versions.
Exclusions
Archimedes' list doesn't include prisms or antiprisms. These meet the same general criteria, but ... perhaps Archimedes just didn't like the fact that they had strong twofold symmetry bias and didn't look as pretty.
The list also excludes the pseudorhombicuboctahedron, which goes by other names, and is essentially a rhombcuboctahedron that's been put together wrongly, with one half misaligned with the other. This shape can be excluded by inventing an additional symmetry rule ... but at this point it should be obvious that some of these classificational definitions have just been made up as we go along or created retrospectively to match an existing list, and adjusted when we find something new that we missed.
External links
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