Vertices and Edges of PolyhedraDate: 04/24/2002 at 19:36:23 From: Leo Jiang Subject: Number of Vertices and Edges of Polyhedron Hi, We are doing the Polyhedron Activity. I know the formula V+F-E = 2. Can you help me find the number of vertices and edges for the following polyhedra: heptahedron, nonahedronn and decahedron? Thank you for your help. Date: 04/24/2002 at 23:10:03 From: Doctor Peterson Subject: Re: Number of Vertices and Edges of Polyhedron Hi, Leo. No, there are different kinds of heptahedra, etc., which will have different numbers of edges and vertices. For example, a hexagonal pyramid has a base and six sides, making it a heptahedron with 12 edges and 7 vertices; but a pentagonal prism has two bases and five sides, making it a heptahedron with 15 edges and 10 vertices. In both cases the formula works: V - E + F = 2 7 - 12 + 7 = 2 10 - 15 + 7 = 2 Polyhedra are very slippery things! The name, and the number of faces it implies, is not enough to fully determine what polyhedron you have. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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