Rhombicosidodecahedron

Archimedean solid, one of the thirteen solids described by Archimedes, which, without being regular, have all their solid angles alike, all their faces regular, and not less than four faces of any one kind; […] They are […] the rhombicosidodecahedron, the truncated icosidodecahedron, and the snub-dodecahedron.

The purpose of this article is to offer a method of approach for investigating the stellation pattern of the deltoidal hexecontahedron, the dual of the rhombicosidodecahedron.

There are two distinct rhombicosidodecahedra, one bearing the unmodified name and the other called the great rhombicosidodecahedron. Like the rhombus, the icosahedron and the dodecahedron, all of the great rhombicosidodecahedron’s 62 faces are either [square] rhombi (30), equilateral triangles (20) or regular pentagons (12).

Next, the totality of 31 axes is illustrated in a rhombicosidodecahedron, an Archimedean solid composed of 30 squares, 20 triangles, and 12 pentagons[…], with a view to the inside of the model showing the center of the group, the point of invariancy O […] Finally, the other dihedral subgroups are also illustrated on a rhombicosidodecahedron: D#95;3 of order 6 and index 10 […] and D#95;5 of order 10 and index 6[…].

[…] I noticed that the little balls (rhombicosidodecahedrons) had openings shaped in the form of triangles, rectangles, and pentagons.