Vertices and Edges of Polyhedra

Date: 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/