Currently on my workbench – epiphany

Late one night, after a long time in the gap, I had an epiphany.

It helped that my Luna lamp, a dodecahedron, was sitting on my desk a few feet in front of the model, and the frame of the icosahedron, which I had just finished earlier that evening, was sitting on another table a few feet away, also in my line of sight.

I realized that if I exploded the dodecahedron, moving each face outward until each vertex was as far from the two vertices it had originally touched as the length of one of the sides of one of the pentagons, I would have the rhombicosidodecahedron! That means the dihedral angle between the pentagon and the square must be ½ the dihedral of the dodecahedron (116º 34'/2 = 58º17') + the 90º of the square = 148º17'.

Additional resources:

• ScienceU.com - icosahedron
• ScienceU.com - dodecahedron

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