Rectangular and
Crossed-Rectangular
Faced Polyhedra
Rectangular faced
Polyhedra
Four isohedral
polyhdedra with rectangular faces were first described by Coxeter and
Grunbaum between 1998 and 2001. In January 2026 Benjamin Klein
discovered two further cases.
Crossed-Rectangular
faced Polyhedra
To my knowledge, isohedral polyhdedra
with
crossed
rectangular
faces have not been
described elsewhere. I first wrote about
these here in September 2025. Subsequently Benjamin Klein in
January
2026 discovered a number of further cases and also provided a
methodology for their categorisation.
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