More Roundahedra
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!
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).
Comments (0)
Trackbacks (0)
Leave a comment
Trackback
