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I wanted an icosahedron module for OpenSCAD, and didn't find anything
on-line that I liked, so I wrote this:
intersection_for
(a_z = [-180 : 72 : 179],
a_y = [atan2 (4, 3 + sqrt (5)),
atan2 (sqrt (10 + sqrt (20)), sqrt (5 - sqrt (20)))])
rotate ([0, a_y, a_z])
cube ([2, 2, sqrt (3/4) + sqrt (5/12)], true);
I thought that I could double-check my math by verifying that my
angles matched POV-Ray's angles. They didn't quite match. A close
view of a POV-Ray icosahedron vertex reveals that it is malformed
(see PNG in message with same subject, in povray.binaries.images).
calculated: 52.6226318593503043571428615050624824299049526181
pov-ray: 52.6625
calculated: 10.8123169635717062912849447744842228988908330822
pov-ray: 10.8125
One of POV-Ray's angles is wrong only in the last digit, but the
other angle has _three_ wrong digits.
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