Starting from any simplicial triangulation of a compact 3-manifold M, we achieve decompositions of M, either by means of cubes, or by means of octahedra, or by means of dodecahedra, so that any pair of such polyhedra meets in an unique, possibly empty, face.
Platonic decompositions of 3-manifolds / Bandieri, Paola. - In: BOLLETTINO DELL'UNIONE MATEMATICA ITALIANA. B. - ISSN 0392-4041. - STAMPA. - 5:(1991), pp. 745-756.
Platonic decompositions of 3-manifolds
BANDIERI, Paola
1991
Abstract
Starting from any simplicial triangulation of a compact 3-manifold M, we achieve decompositions of M, either by means of cubes, or by means of octahedra, or by means of dodecahedra, so that any pair of such polyhedra meets in an unique, possibly empty, face.
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