A curious coincidence

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

A curious coincidence

Postby quickfur » Tue Sep 13, 2011 7:40 pm

Since you people are so quiet, I thought I should stir the pot a little. :P

Here's a challenge:

1) Name a uniform polyhedron with 8 faces, 18 edges, and 12 vertices.

2) Can you name a different polyhedron with 8 faces, 18 edges, and 12 vertices? :) Interesting coincidence, isn't it?

If you found the above too trivial, how about:

3) How many 4D uniform polychora can you name that contains the above two polyhedra as cells?

:)
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Re: A curious coincidence

Postby Hugh » Wed Sep 14, 2011 2:04 am

quickfur wrote:1) Name a uniform polyhedron with 8 faces, 18 edges, and 12 vertices.


a hexagonal prism?
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Re: A curious coincidence

Postby Hugh » Wed Sep 14, 2011 2:08 am

quickfur wrote:2) Can you name a different polyhedron with 8 faces, 18 edges, and 12 vertices? :) Interesting coincidence, isn't it?


a truncated tetrahedron?
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Re: A curious coincidence

Postby quickfur » Wed Sep 14, 2011 2:39 am

Excellent! Now can you answer question (3)? :)
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Re: A curious coincidence

Postby Secret » Wed Sep 14, 2011 1:34 pm

Hexagonal duoprism
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Re: A curious coincidence

Postby quickfur » Wed Sep 14, 2011 3:19 pm

Well, a 6,6-duoprism has hexagonal prisms for cells, but it doesn't have truncated tetrahedra. Which polychora have both?
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Re: A curious coincidence

Postby Mrrl » Wed Sep 14, 2011 7:19 pm

I see four of them - there are runcitruncated simplex, runcitruncated 16-cell, runcitruncated 600-cell and a prism over truncated tetrahedron.
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Re: A curious coincidence

Postby quickfur » Wed Sep 14, 2011 11:10 pm

Cool!! You caught a 4th one that I didn't catch: the truncated tetrahedron prism. The others are right, too. Congrats! Молодец!
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