Icosahedron Joint
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A Regular Icosahedron is a polyhedron that's constructed entirely out of equilateral triangles, 20 of them actually.
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- Creative Commons — Attribution
This shape is famously recognized as the D-20 dice and the basis for soccer balls (though often truncated—these joint ends effectively handle that for you).
To build a full icosahedron, you’ll need 12 of these joints and 30 equal lengths of 38mm x 38mm (2" x 2") wood.
Special thanks to Jaap Scherphuis for the invaluable help in calculating the precise angles: Link.
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