More Roundahedra

19Apr07

After figuring out why the equation in the last post described a tetrahedron, I was able to apply the same technique to generate the four other Platonic solids. By popular demand, here they are!

Four Roundahedra

The rounded cube has equation
(1-x2)(1-y2)+(1-y2)(1-z2)+(1-z2)(1-x2)=0
and the rounded octahedron is
1-2(x2+y2+z2)-2(x2y2+z2x2+y2z2)+x4+y4+z4=0.

I won’t post the icosahedron and dodecahedron’s formulas because they are pretty big and ugly (they involve the square root of 5, and respectively have degrees 12 and 9).

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