Naming of 4D Catalans

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

Naming of 4D Catalans

Postby quickfur » Mon Jan 23, 2023 4:29 pm

So I've started updating my website again, starting with the 3D Catalan solids, and with the plan of eventually covering all the 4D Catalans. But I ran into a little conundrum: what to name each 4D Catalan? In 3D, they have names that directly describe their geometry (rhombic dodecahedron, triakis octahedron, disdyakis hexecontahedron, etc.), but in 4D I don't know of any such names, only that they are duals to the 4D uniforms.

Is there an "official" list of 4D Catalan names? Or some kind of naming scheme I could use for them? I'd like to follow in the spirit of the 3D Catalan names, if possible.
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Re: Naming of 4D Catalans

Postby mr_e_man » Tue Jan 24, 2023 2:36 am

The first few results from a quick search for "4D Catalan polytopes" were these three papers, and Higher Space, and your own site. :roll:

The first one says (in Section 4)
To our surprise duals of the 4D uniform polytopes have not been studied so far.
(though that was 12 years ago).


And don't forget Polyhedron Dude's 4D dice, and the Polytope Wiki.
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Re: Naming of 4D Catalans

Postby quickfur » Tue Jan 24, 2023 3:22 am

Oooh, the polytope wiki seems to have names for the 4D Catalans, nice! Just what I need. I'll probably adopt those names.
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Re: Naming of 4D Catalans

Postby wendy » Wed Jan 25, 2023 3:04 am

Have a look at http://www.os2fan2.com/gloss/polytope.pdf . I give names for the duals of the truncates, rectates, the runcinate (first and last node) and the omnitruncates.

Using kepler style names don't work in 4d and higher, because there really isn't a construction, but a mapping onto the CD.
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