Category Signatures

Discussion of tapertopes, uniform polytopes, and other shapes with flat hypercells.

Category Signatures

Postby ubersketch » Sun Feb 23, 2020 6:40 pm

In snubless semiuniform polytopes, there are only 2 face types. Regular (o) and truncate (x). Using this, we can notate the face types of a polytope. For example, co gets oo, sirco gets oox, tic gets ox, etc.

The number of letters determines the number of face types so oo would mean 2 face types which are regular. Extending this to 4d we could have [o][oo] for rit, as it has two cell types, regular and quasiregular.

You can also notate for non-snubless semiuniforms. For example, the isosceles triangle gets o|x. The o represents the vertex with two similar edges and the x represents the vertices with two different edges.

We can extend this into a system for notating polytopes. (Polytopes with snubless semiuniform verfs also get the signature for their verf at the end) Of course, cases like the tetrahedral octahemihexahedron and the rhombicosahedron cannot be distiguished, even including the verf, so this notation is not perfect yet.

Code: Select all
tet - 3o(3o)
oct - 3o(4o)
cube - 4o(3o)
ike - 3o(5o)
doe - 5o(3o)
tic - 4x3o
sirco - 4o3o2x
co - 4o3o(2x)
rit - [4o3o][3o(3)](3o2x)
gogishi - [5/2o(3)](3o(3))
squappy - 4o[1o|2x(4)]
sidtid - 5/2o3o(3x)
gid - 5/2o3o(2x)
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