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Date: Mon, 30 Nov 1998 16:26:43 EST
To: QandQ@MathCentral.uregina.ca
Subject: area
How do you find the surface area of the 5 platonic solids, when they each have a volume of one cubic inch?
Thanks Rachel
Hi Rachel
In the Quandaries and Queries section of Math Central there is a note called What is the volume of a regular tetrahedron? that will give you enough information to answer this question for a tetrahedron.
In the book H.S.M. Coxeter, Regular Polytopes (second edition), The Macmillan Company, New York, 1948 there is a table that relates several properties of regular polytopes. Two of the columns in this table contain the information needed to solve your problem. Using Coxeter's notation that C is the volume, S is the surface area, 2L is the edge length and , the appropriate information is contained in the table.
Name
| ![](bidwell1.1.gif) |
![](bidwell1.2.gif) |
Regular tetrahedron |
![](bidwell1.3.gif) |
![](bidwell1.4.gif) |
Octahedron |
2 ![](bidwell1.3.gif) |
![](bidwell1.5.gif) |
Cube |
6 |
1 |
Icosahedron |
![](bidwell1.6.gif) |
![](bidwell1.7.gif) |
Dodecahedron |
![](bidwell1.8.gif) |
![](bidwell1.9.gif) |
Cheers,
Harley
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