2 research outputs found
A Local Characterization of Combinatorial Multihedrality in Tilings
A locally finite face-to-face tiling of euclidean d-space by convex polytopes
is called combinatorially multihedral if its combinatorial automorphism group
has only finitely many orbits on the tiles. The paper describes a local
characterization of combinatorially multihedral tilings in terms of centered
coronas. This generalizes the Local Theorem for Monotypic Tilings, established
in an earlier paper, which characterizes the case of combinatorial
tile-transitivity.Comment: 10 pages (to appear in Contributions to Discrete Mathematics
Combinatorial Space Tiling
The present article studies combinatorial tilings of Euclidean or spherical
spaces by polytopes, serving two main purposes: first, to survey some of the
main developments in combinatorial space tiling; and second, to highlight some
new and some old open problems in this area.Comment: 16 pages; to appear in "Symmetry: Culture and Science