The Tetrahemihexahedron and its dual, the Tetrahemihexacron

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

The Tetrahemihexahedron and its dual, the Tetrahemihexacron

Postby ubersketch » Wed Dec 20, 2017 12:48 am

Both of the polyhedra mentioned in the title are very interesting for a few reasons.

The Tetrahemihexahedron for one, is in the same regiment as the Octahedron, yet is not regular itself. No other uniform polyhedron exhibits this strange trait. Another thing is, it's dual is quite strange as well.

The Tetrahemihexacron is a compound, yet its dual is not. Another thing is that it has no caps at the end of its prisms, instead, there is a vertex at infinity. And most of all, it's regular, but it's dual isn't.
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Re: The Tetrahemihexahedron and its dual, the Tetrahemihexac

Postby Mercurial, the Spectre » Wed Dec 20, 2017 1:09 pm

This is what happens if a face is located at the exact center of the polytope, its dual has the vertices extending to infinity.
It is not exactly a compound per se.
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Re: The Tetrahemihexahedron and its dual, the Tetrahemihexac

Postby ubersketch » Wed Dec 20, 2017 3:04 pm

The tetrahemihexacron is a compound, although it's of tetragonal hosohedra. Even if it wasn't, it would still have compound elements, being compounds of 2 diga. The thac (the tetrahemihexacron) is most definitely a compound of 3 tetragonal hosohedra.
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Re: The Tetrahemihexahedron and its dual, the Tetrahemihexac

Postby Mercurial, the Spectre » Wed Dec 20, 2017 8:37 pm

You mean we can use spherical polyhedra as compounds?
Good thinking.
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Re: The Tetrahemihexahedron and its dual, the Tetrahemihexac

Postby ubersketch » Sat Dec 23, 2017 7:41 pm

Mercurial, the Spectre wrote:You mean we can use spherical polyhedra as compounds?
Good thinking.

Yeah, theres no reason to exclude microtopes when talking about compounds.
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