To familiarize herself with a CNC milling machine, a friend wants to make some 12-sided gaming dice (regular dodecahedrons) out of solid aluminum. Her question: what is the dihedral angle between any two adjacent faces?

Well, according to the answer given, may past solution gives the external angle 243.434948823 degrees (63.434948823 + 180), but a CNC machine doesn't make a 12 side dice from the inside (at least I haven't seen one), you have to give an external reference. But to prove my point, 360 - 243.434948823 = 116.565051177 degrees.

The angle that I used at my last solution (63.434948823 degrees) is the basis an icosahedron in Geodesic geometry, I have studied it for 8 years.

Posted by Antonio on 2003-08-21 20:02:48