Dissection of Two Stellated Dodecahedra

A small stellated dodecahedron (s.s.d.) and a great stellated dodecahedron (g.s.d.) are dissected and reassembled into a rhombic triacontahedron and a rhombic hexecontahedron.


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The prolate rhombohedron (red frame) is a twentieth of a hexecontahedron; the solid pyramid (cyan frame) is a spike of the great stellated dodecahedron. So the rhombohedron has a surplus of three pyramids over the twentieth of the great stellated dodecahedron. Since there are 20 rhombohedra, the surplus is 60 pyramids. The pyramid (cyan frame) is a spike of the small stellated dodecahedron. The red pyramid is a part of the triacontahedron. The triacontahedron has five pyramids fewer than a spike of the small stellated dodecahedron. Since there are 12 spikes, the total deficit is 60 pyramids. So the surplus and deficit cancel.
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