Six Decagons and Six Great Circles of a Sphere

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Rotate five of six overlapping horizontal circles or decagons around horizontal axes aligned at 72 degrees to each other. When the rotating angle is

2arctan(1/ϕ)

, where

ϕ

is the golden ratio, the intersections of the circles and the vertices of the decagons are at the vertices of an icosidodecahedron.

Sándor Kabai