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Figure 1
(a) Platonian icosahedron – a solid with 20 faces of equilateral triangular shape and 12 vertices. It has six fivefold, ten threefold and 15 twofold symmetry axes and 15 symmetry planes. The non-crystallographic Laue class related to icosahedral symmetry is [m{\overline 3}{\overline 5}]. (b) Keplerian triaconta­hedron (KTH) – solid object with 30 golden rhombuses on faces and 32 vertices. It has the same symmetry elements as the icosahedron. (c) Keplerian dodecahedron – a polyhedron dual to a Platonian icosahedron.

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ISSN: 2053-2733
Volume 71| Part 3| March 2015| Pages 279-290
doi:10.1107/S2053273315001473
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