Fig. 3: Alignment of pairs of icosahedral, octahedral, and tetrahedral Platonic solids.
From: A Keplerian Ag90 nest of Platonic and Archimedean polyhedra in different symmetry groups
The solids, arbitrarily scaled, are labeled by their vertex descriptions: the icosahedral dodecahedron (555) and icosahedron (33333), the octahedral cube (444) and octahedron (3333), and the tetrahedral tetrahedron (333), where 5, 4, and 3 represent faces, respectively, 5-gons, 4-gons, and 3-gons. a Arrangement of the icosahedral solids with alignment along five-, three- and twofold rotational axes. b Arrangement of the octahedral solids with alignment along four-, three- and twofold axes. c Arrangement of the tetrahedron with its self-dual, another tetrahedron, with alignment along threefold axes with a face in front, threefold axes with a vertex in front, and twofold axes.
