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

Volumes of Platonic, Some Archimedian Solids

Post 1

Researcher 188058

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

Post 2

Peter aka Krans

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

Post 3

Wøñkø

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


Volumes of Platonic, Some Archimedian Solids

Post 4

gsurfer04

Check out Wikipedia. It has an article about almost everything, fromsmiley - caketosmiley - chocsmiley - ok


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