Vertex cell configuration?

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

Vertex cell configuration?

Postby quickfur » Wed Dec 01, 2010 9:39 pm

I'm starting to render some projections of cells surrounding a single vertex in uniform polychora. It's sorta like the vertex figure, except that you show the cells around a vertex instead of cutting it off. What should I call them? "Vertex configuration" already refers to something else; maybe "vertex cell configuration"? "Cell-vertex configuration"? Something else?
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Re: Vertex cell configuration?

Postby wendy » Thu Dec 02, 2010 6:27 am

I use 'vertex verge' or 'vertex configuration', or 'vertex-arrounds'.

All of these refer to the complete list attached to a vertex. Corresponding ones exist for edges etc.
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Re: Vertex cell configuration?

Postby Klitzing » Thu Sep 20, 2012 1:29 pm

Coxeter used "complex" for any not closed configuration of polytopes.
Thus it could be the vertex complex of the relevant uniform polytope.
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Re: Vertex cell configuration?

Postby wendy » Sat Sep 22, 2012 11:00 am

Coxeter and Johnson and Conway might well be brilliant mathematicians, but they're not crash hot on a consistant name scheme across the dimensions.

You get the same thing in languages, though, where the general becomes the specific, eg german 'gift' (something given becomes poison), english nim (taken, becomes loony = taken of the senses), english undertaker (one who undertakes becomes .. a burial).

complex already means not simple, or in numbers with sqrt(-1). Likewise, real means variously not involving sqrt(-1), or not discrete (ie the set of real numbers).

In the pg, 'verge' has been selected as the term for a closure around something, in the way a road verge closes around a road. A vertex-verge is the closure of surtopes around a vertrx, an edge=verge is the closure around edges. Verges of the surtopes of polytope are governed by the same laws as the surtopes are themselves, except they work upwards.
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Re: Vertex cell configuration?

Postby quickfur » Mon Sep 24, 2012 4:38 am

I agree with wendy, "complex" has been too overloaded with too many meanings. I'll use "verge".
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Re: Vertex cell configuration?

Postby Klitzing » Mon Sep 24, 2012 11:36 am

quickfur wrote:I agree with wendy, "complex" has been too overloaded with too many meanings. I'll use "verge".


I just use complex (noun) for some (open) configuration in the sense of Coxeter, while complex (adjective) might variously be used informal (i.e. translating to: not-simple), or formal in the sense of complex numbers.

Even Coxeter himself used it that way. His book on "Complex Polytopes" clearly uses this word as adjective. Accordingly it is not meant in the sense of configuration. Non the less it requires reading the book to deduce that the adjective is being used in the formal sense here - hehe.

So, I don't think it is too overloded. - But you are free to use whatever you feel appropriate, for sure. Its more a matter of getting new definitions being generally known. (This most probably would be the reason why lots of not well-chosen definitions still are being in use...)

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