Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

A polyhedron is a convex, three dimensional region bounded by a finite number of polygonal faces.

So is it possible that some of those polygonal faces be concave ? Can concave polygons be used in the process to form a 3D convex region ?

share|cite|improve this question
Excellent question! Mind posting some of your ideas first? – Ahaan S. Rungta Aug 20 '13 at 21:43

No. Every intersection of two convex shapes (such as a convex polyhedron and the plane through one of its faces) is convex.

share|cite|improve this answer

If you allow two faces to be coplanar (which would be an unusual admission!), then you could build a cube of six copies each of the triangle and nonconvex pentagon shown left below.
But if no two faces are coplanar, then in the neighborhood of a nonconvex point on the boundary of a nonconvex face, there must be two points determining a segment (dashed right above) with the segment exterior to the polyhedron. And this means the polyhedron fails the definition of convexity, and so is itself nonconvex.

share|cite|improve this answer

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.