fissiary polyhedra

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

fissiary polyhedra

Postby dodecahedron » Wed Oct 24, 2012 12:26 am

Does anyone know where to find a list.
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Re: fissiary polyhedra

Postby Keiji » Sun Feb 03, 2013 3:59 pm

What's a fissiary polyhedron?

A Google search only comes straight back to this page!
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Re: fissiary polyhedra

Postby Klitzing » Mon Feb 04, 2013 12:40 am

first of all: its not called "fissiary" but "fissary".

then: where to find about that topic?
Its a term being used by hedrondude. It even can be looked up in his glossary, where he states:
Fissary - A polytope like object that has peaks or lower dimensional elements that coincide completely. Fissary polychora either have compound vertex figures or edge figures that can split into two or more components.


if "peak" in turn is not known: here his according definition:
Peak - An n-3 dimensional element of an n-dimensional polytope. Example: vertices of polyhedra, edges of polychora, faces of polytera. If they are somewhat sharp, they will feel pointy, for example - if you were in the fourth dimension holding a tesseract, the edges (its peaks) will feel pointy (like a cube's corners).


thus: the application of that term onto polyhedra asks for such objects which have coincident vertices, without having coincident higher elements, which still are polyhedra - i.e. do not fall apart into being a compound.

finally: figures with (arbitrary) coincident elements often are implicitely or explicitely excluded from polytopes. Other authors OTOH do allow these. One of the best knowns here is Branko Grünbaum (esp. Are your polyhedra the same as my polyhedra?. This is why I usually call such figures simply "Grünbaumian".

--- rk
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Re: fissiary polyhedra

Postby ubersketch » Fri Dec 15, 2017 1:21 am

There's only 2 I know of.
Small complex icosidodecahedron and great complex icosidodecahedron.
(sorry for necroposting)
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