
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
 

Regular tetrahedron 


Octahedron 
2 

Cube 
6 
1 
Icosahedron 


Dodecahedron 


Cheers,
Harley
 