# Six Decagons and Six Great Circles of a Sphere

Six Decagons and Six Great Circles of a Sphere

Rotate five of six overlapping horizontal circles or decagons around horizontal axes aligned at 72 degrees to each other. When the rotating angle is , where is the golden ratio, the intersections of the circles and the vertices of the decagons are at the vertices of an icosidodecahedron.

2arctan(1/ϕ)

ϕ