Posts Tagged ‘math’
Octahedron Platonic
August 17th, 2010 Posted 4:42 pm
What is the ratio of edge lengths in the platonic solids?
What is the ratio of edge lengths in the platonic solids such that all 5 solids would be the same height when placed flat on a plane?
I ask because I am building models of the 5 platonic solids for an art project and would like them all to be the same size.
For instance, if the edge length on the tetrahedron = 1, then
cube = 0.8
octahedron = 0.6
etc...
Let them all have an arbitrary height of 1. Below are the respective edge lengths:
tetrahedron: √(6) / 2
cube: 1
octahedron: √(6) / 2 (same as the tetrahedron)
dodecahedron: √[50 - 22√(5)] / 2
icosahedron: [3√(3) - √(15)] / 2
Magformers - Octahedron
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