Polyhedron VerticesDate: 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/ |
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