Isohedral simple tilings: binodal and by tiles with <or=16 faces.
All isohedral simple tilings of 3D Euclidian space by tiles with </=16 faces have been determined. There are no such tilings by polyhedra with less than 14 faces. For simple polyhedra with 14, 15 and 16 faces, there are respectively 10, 65 and 434 that fill space and a total of 23, 136 and 710 distinct tilings. The tilings by 14-face polyhedra are described in detail as are binodal (vertex 2-transitive) isohedral simple tilings.
Delgado-Friedrichs
Olaf
O
Department of Chemistry, Arizona State University, Tempe, AZ 85287, USA.
O'Keeffe
Michael
M