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# Calculating verts/faces for regular polyhedra

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I thought this was going to be pretty lightweight compared to some of the questions here, but after searching Google for the answer, I might be getting in over my head. I''m looking for a function to calculate the vertices and face edges to define the surfaces that make up a regular polyhedra with an arbitrary number of edges on each surface. For example, cube has 4 edges on each surface; a diamond (two pyramids placed base-to-base) has 3 edges on each surface. Quasi-regular would be nice, too, but I suspect that''s a lot more complicated. From my attempts to Google for an answer, I think these are sometimes referred to as "shells". Sounds simple enough, but most of the references I''ve read assume you already know where your surfaces are (and are looking to do something interesting with them such as collision detection), or it goes into a detailed discussion of Wythoff Symbols, Euler-Descartes topographical relationships, and other crazy stuff that seems unrelated to my basic goal (and leaves me choking in their mathetmatical dust...) I suppose it doesn''t matter, but I''m using Managed D3D and C#. Cranking out the results as a series of triangle fans would be especially nice, but I could figure that out on my own easily enough. Surely it can''t be as hideously complex as this paper seems to suggest?

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What is your input data? This might help us help you. Most game developers are given the vertices and faces directly by their artists, who create them in a modeling package such as discreet 3ds max. But, there are some applications that generate geometry algorithmically.

Also, since you''ve asked this using terminology that is fairly academic, rather than game development lingo, please tell us what your application is.

Graham Rhodes
Principal Scientist
Applied Research Associates, Inc.

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I was planning to display various instances of these objects in a simple screen saver I was using as a testbed to play with various features of D3D.

However, after giving it further thought I realized that given the very limited number of regular polyhedra (e.g. the five Platonic and maybe the quasi-regular Archimedian solids), it probably makes more sense to just predefine them. Since they are abstract and "regular" my gut instinct was to calculate them, but after digging deeper, I doubt there would be any benefit.

I am still personally curious, but considering how complicated the answer seems to be (quite a bit more Google work has turned up some good leads on the subject), it''ll have to wait until I''m less-distracted by the issues I was originally planning to investigate.

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