Model originally uploaded to Thingiverse at https://www.thingiverse.com/thing:184692.

These show a selection of the spherical symmetry groups - the ways in which an object can be symmetrical by rotating about and reflecting through a central point. See the wikipedia page for more details, or better, the book The Symmetries of Things, by John H. Conway, Heidi Burgiel and Chaim Goodman-Strauss.

The labelling of the different symmetry types on the rendered image is in orbifold notation. All of the polyhedral types are shown (3∗2, 332, ∗332, 432, ∗432, 532, ∗532), as well as representatives of the infinite families of cyclic and dihedral types (88, ∗44, 8x, 8∗, 222, 223, 228, 2∗4, ∗224).