The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Vertices and Edges of Polyhedra

Date: 04/24/2002 at 19:36:23
From: Leo Jiang
Subject: Number of Vertices and Edges of Polyhedron


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 
Associated Topics:
Middle School Polyhedra

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.