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Six Decagons and Six Great Circles of a Sphere

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show decagons
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show icosidodecahedron
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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.
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