Category:Transition from icosahedral to octahedral compound of five cubes

Transition from compound of five cubes to compound of four cubes
The symmetry changes from icosahedral through pyritohedral to octahedral.

The black cube remains fixed. Each of the four other cubes is rotated around the axis through the two vertices it shares with the black cube.
The angle of the rotation is ${\displaystyle 2\cdot \arctan \left({\frac {{\sqrt {5}}-2}{\sqrt {3}}}\right)\approx 15.522^{\circ }}$.

icosahedral pyritohedral	icosahedral pyritohedral
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These images are raytraced with POV-Ray. The source is here.