Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

It seems, at least in the 2-D case, that all polytopes are going to be convex. Does this hold if the dimensions are increased?

share|cite|improve this question
Do you mean regular polygons? – M.B. Oct 31 '12 at 14:53
I'm specifically referring to polytopes created from a combination of half spaces. – Wesley Tansey Oct 31 '12 at 14:57
up vote 2 down vote accepted

Regular polygons are convex whereas regular polytopes may not be. Furthermore, the Platonic solids are indeed convex. Maybe you want to read about convex polytopes?

edit: seeing your comment I guess you are really interested in interesections of halfspaces?

share|cite|improve this answer
That was it! Thanks! – Wesley Tansey Oct 31 '12 at 15:01

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.