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File:Spherical icosidodecahedron with colored cicles.png

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Summary

Description
Increasing the small angle of the circle pairs gives the tetrakis hexahedron.
Image series Spherical icosidodecahedron with colored cicles
Perpendiculars of the great circles highlighted with spheres in the same color
Right-handed coordinate system using the same basic colors

Spherical icosidodecahedron showing the six great circles in different colors

The colors red, green and blue correspond to coordinate axes, and there is a pair of two circles (light and dark) intersecting on each one.

Light and dark are assigned to the circles in a pair in such a way, that in a right-hand coordinate system the smaller intersection angle goes from light to dark in positive direction.

perspective 2-fold 3-fold 5-fold

The corresponding icosahedron has a pair of opposite vertices for each great circle. It has a hexagon of dark vertices and two opposite triangles of light vertices. The latter correspond to the two triangles in the icosidodecahedron that have only dark edges. (There are no such triangles that have only light edges.)

 
This image was created with POV-Ray.

POV-Ray sources: spherical icosidodecahedron, icosahedron

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Watchduck
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4 August 2018

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