Hexadecahedron

A hexadecahedron (or hexakaidecahedron) is a polyhedron with 16 faces. No hexadecahedron is regular; hence, the name is ambiguous. There are numerous topologically distinct forms of a hexadecahedron, for example the pentadecagonal pyramid, tetradecagonal prism and heptagonal antiprism.

Convex hexadecahedra

There are 387,591,510,244 topologically distinct convex hexadecahedra, excluding mirror images, having at least 10 vertices.[1] (Two polyhedra are "topologically distinct" if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges or the angles between edges or faces.)

Self-dual hexadecahedra

There are 302,404 self-dual hexadecahedron, 1476 with at least order 2 symmetry.[2] The high symmetry self-dual has chiral tetrahedral symmetry, and can be seen topologically by removing 4 of 20 vertices of a regular dodecahedron and is called a tetrahedrally diminished dodecahedron.

Examples

The following list gives examples of hexadecahedra.

gollark: <@332271551481118732> <@!160279332454006795> <@331320482047721472> participate.
gollark: When have I explained nothing? I want an annotated 500-word essay with examples.
gollark: Yes, I am in fact Olivia too.
gollark: Perhaps they're semirandom. Perhaps I devise bespoke bluffs by myself and then share them. Perhaps my bluffs are optimized automatically via testing against high-fidelity computer simulations of all other participants. Perhaps I don't make bluffs but merely disseminate cognitohazards causing perception of bluffs. Perhaps my every word and bluff is meticulously generated to produce minimum guessing of me. Perhaps I never bluff and every word I say is accurate.
gollark: I generate my bluffs via RNG now to avoid the terribleness of human random number generation (heavpoot has data on this), unless I don't and am trying to trick you into not making inferences from them.

References
  1. Counting polyhedra
  2. Symmetries of Canonical Self-Dual Polyhedra


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