Dodecahedral Rhombic Monohedra

solid

1

2

3

4

5

6

This Demonstration shows Grünbaum's classification of dodecahedral rhombic monohedra.

To summarize the situation concerning dodecahedral rhombic monohedra, we have the following polyhedra of spherical type:

Two convex dodecahedra (Kepler's and Bilinski's: 1 and 2)

Three simply indented dodecahedra (one from Kepler's polyhedron and two from Bilinski's: 3, 4, 5)

One doubly indented dodecahedron (Bilinski's polyhedron: 6)[1, p. 14]

[1] B. Grünbaum. "The Bilinski Dodecahedron, and Assorted Parallelohedra, Zonohedra, Monohedra, Isozonohedra and Otherhedra." (Jul 16, 2019) digital.lib.washington.edu/researchworks/bitstream/handle/1773/15593/Bilinski_dodecahedron.pdf.

Izidor Hafner