## A Conversation for Calculating the Volume and Surface Area of Various Solid Objects

### Volumes of Platonic, Some Archimedian Solids

Researcher 188058 Started conversation Dec 14, 2001

Some other useful volume formulas VERY RARELY taught are those for the Archimedian and Platonic solids. The formulas all depend on the length of a side (s) cubed.

They are:

Tetrahedron - sqrt(2)/12 * s^3

Octahedron - sqrt(2)/3 * s^3

Cube (Hexahedron) - s^3

Dodecahedron - (15+7sqrt(5))/4 * s^3

Icosahedron - 5(3+sqrt(5))/12 * s^3

Truncated Tetrahedron - 23sqrt(2)/12 * s^3

Truncated Cube - (14sqrt(2)+21)/3 * s^3

Truncated Octahedron - 8sqrt(2) * s^3

Truncated Dodecahedron - (235sqrt(5)+495)/12 * s^3

Truncated Icosahedron - (43sqrt(5)+125)/4 * s^3

Cuboctahedron - 5sqrt(2)/3 * s^3

Truncated Cuboctahedron - (14sqrt(2)+22) * s^3

Rhombicuboctahedron - (10sqrt(2)+12)/3 * s^3

Icosidodecahedron - (17sqrt(5)+45)/6 * s^3

I am still missing the Truncated Icosidodecahedron, Rhombicosidodecahedron, Snub Cube, and Snub Dodecahedron. If someone could fill that in, it would be very nice.

1+8/8+0+5*8

### Volumes of Platonic, Some Archimedian Solids

Peter aka Krans Posted Feb 6, 2002

I'm sorry I haven't replied to this for a while - I should check my articles more.

These are incredibly useful formulae - thank you very much for contributing them! I'm sorry I can't update the article myself - let's just hope that someday , somehow, someone will update the article with this information...

### Volumes of Platonic, Some Archimedian Solids

Wøñkø Posted Jul 28, 2003

Woah! I don't even know what most of those are!

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