We discuss representations of non-finite polyhedra as quotients of regular polytopes. We provide some structural results about the minimal regular covers of non-finite polyhedra and about the stabilizer subgroups of their flags under the flag action of the automorphism group of the covering polytope. As motivating examples we discuss the minimal regular covers of the Archimedean tilings, and we construct explicit minimal regular covers for three of them.
@article{10_37236_2512,
author = {Daniel Pellicer and Gordon Williams},
title = {Minimal covers of the {Archimedean} tilings. {I}},
journal = {The electronic journal of combinatorics},
year = {2012},
volume = {19},
number = {3},
doi = {10.37236/2512},
zbl = {1258.51013},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2512/}
}
TY - JOUR
AU - Daniel Pellicer
AU - Gordon Williams
TI - Minimal covers of the Archimedean tilings. I
JO - The electronic journal of combinatorics
PY - 2012
VL - 19
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/2512/
DO - 10.37236/2512
ID - 10_37236_2512
ER -
%0 Journal Article
%A Daniel Pellicer
%A Gordon Williams
%T Minimal covers of the Archimedean tilings. I
%J The electronic journal of combinatorics
%D 2012
%V 19
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/2512/
%R 10.37236/2512
%F 10_37236_2512
Daniel Pellicer; Gordon Williams. Minimal covers of the Archimedean tilings. I. The electronic journal of combinatorics, Tome 19 (2012) no. 3. doi: 10.37236/2512
