|
|
Polyhedra
What is the ratio of surface area
to volume for the "Five
Platonic Solids" relative to a sphere ?
The Sphere & the 5 Platonic
Solids
| Solid |
Surface Area (A) in units of R2 |
Volume (V) in units of R3 |
Ratio (A/V) in units of 1/R |
| Tetrahedron |
4.618802154.... |
0.513200239.... |
9.000000005.... |
| Cube (Hexahedron) |
8.000000000.... |
1.539600718.... |
5.196152423.... |
| Octahedron |
6.928203230.... |
1.333333333.... |
5.196152423.... |
| Dodecahedron |
10.51462224.... |
2.785163863.... |
3.775225717.... |
| Icosahedron |
9.574541383.... |
2.826232834.... |
3.387739774.... |
| Sphere |
12.56637061.... |
4.188790205.... |
3.000000000.... |
The length R is the distance from the center of the solid to
of its vertices.
|
[ Home|
ModuleMap|
Tips
|Glossary
]
|
Building a truncated icosahedron
|
