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

What are the names of the convex polyhedron with five, six, or seven vertices, where all vertices lie at distinct corners of a cube? I'm particularly interested in the five vertex case.

share|cite|improve this question
up vote 4 down vote accepted

With five vertices, depending on which ones you choose, you can get an oblique square pyramid, an oblique rectangular pyramid, or an irregular triangular bipyramid with $S_3$ symmetry.

With six vertices, you can get a right isosceles triangular prism, an equilateral triangular right antiprism, or an irregular octahedron with $S_2$ symmetry.

I don't think the seven-vertex figure has any particular name.

Neither of these names are precise enough to express the fact that the vertices are chosen among the vertices of a cube.

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.