Polyhedron Vertices

Date: 02/25/2003 at 18:14:16
From: John
Subject: Polyhedron

What is the least number of vertices that a polyhedron may have?

Date: 02/25/2003 at 19:46:51
From: Doctor Douglas

Hi, John,

Thanks for submitting your question to the Math Forum.

Three vertices are necessary to define the first (triangular) face of 
any polyhedron (if that face is a polygon with more sides, then more 
vertices are required). But these three points (and the face defined 
by them) are coplanar, and so are insufficient to make the polyhedron 
a three-dimensional object.

What about four?  Four vertices suffice, because we can make a
tetrahedron (a triangular pyramid) with four vertices.

Hence the answer is four.

- Doctor Douglas, The Math Forum
  http://mathforum.org/dr.math/