# non-convex Polytope definition

I have a simple question. I read that given a vector space $N_{\mathbb{R}}$ over $\mathbb{R}$, we can define a convex polytope in the following way:

$$P:= \Big\{ \sum_{u\in S} \mu_u u \,\Big| \, \mu_u \geq 0 , \sum_{u\in S} \mu_u =1 \Big\} \subset N_{\mathbb{R}}$$

with $S$ finite.

What is the definition of polytope and regular polytope in general?

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Apparently wikipedia has a very broad definition of polytope en.wikipedia.org/wiki/Polytope But I have only seen polytope be used to mean that definition, which immediately implies that it is convex –  David Benson-Putnins May 11 '13 at 20:07
There are various definitions of what regularity should mean in Coxeter's book Regular polytopes. –  Mariano Suárez-Alvarez May 11 '13 at 20:12
The title of your question ("non-convex") does not match the question itself. Perhaps you are seeking a definition of a polytopal complex? This is defined in Ziegler's Lectures on Polytopes. –  Joseph O'Rourke May 12 '13 at 0:54