HOW TO: Projecting an accurate (i.e. no chance for floating point errors to stack up and ruin your day) dodecahedron onto a sphere in CAD. This is possible because a cube shares some vertices with a dodecahedron as explained in https://www.archive.bridgesmathart.org/2009/bridges2009-123.pdf, img 1).
[NOTE: this took me 10x as long to figure out this process as I initially expected. The face to face angle way using arctan & fractional degree angles is -profoundly- cursed. There be dragons.]
Extrude a cube around the origin. (2)
On one square face, draw two pentagons so that the opposite edges of the square face match up with the longest vertices across a pentagon with the bulk of the pentagon sticking out into space. (3)
Separately, revolve (as "NEW" bodies) two of the larger trapezoidal sides of the pentagons on opposite sides of the square (4)
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