Transforming Some Infinite Polyhedra

Paul Gailiunas
Bridges: Mathematical Connections in Art, Music, and Science (2002)
Pages 189–195


A few infinite polyhedra divide space into congruent pieces. Any dual should have the same symmetries as the original polyhedron, so in these cases should also provide a congruent division of space. These conditions do not define a unique dual, and the polyhedra that satisfy them can be related to each other by continuous deformations, that generate finite space-filling polyhedra in the limit.