A $k$-orbit map is a map with its automorphism group partitioning the set of flags into $k$ orbits. Recently $k$-orbit maps were studied by Orbanić, Pellicer and Weiss, for $k \leq 4$. In this paper we use symmetry type graphs to extend such study and classify all the types of $5$-orbit maps, as well as all self-dual, properly and improperly, symmetry type of $k$-orbit maps with $k\leq 7$. Moreover, we determine, for small values of $k$, all types of $k$-orbits maps that are medial maps. Self-dualities constitute an important tool in this quest.
@article{10_37236_3114,
author = {Isabel Hubard and Mar{\'\i}a del R{\'\i}o Francos and Alen Orbani\'c and Toma\v{z} Pisanski},
title = {Medial symmetry type graphs},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {3},
doi = {10.37236/3114},
zbl = {1301.05170},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3114/}
}
TY - JOUR
AU - Isabel Hubard
AU - María del Río Francos
AU - Alen Orbanić
AU - Tomaž Pisanski
TI - Medial symmetry type graphs
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/3114/
DO - 10.37236/3114
ID - 10_37236_3114
ER -
%0 Journal Article
%A Isabel Hubard
%A María del Río Francos
%A Alen Orbanić
%A Tomaž Pisanski
%T Medial symmetry type graphs
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/3114/
%R 10.37236/3114
%F 10_37236_3114
Isabel Hubard; María del Río Francos; Alen Orbanić; Tomaž Pisanski. Medial symmetry type graphs. The electronic journal of combinatorics, Tome 20 (2013) no. 3. doi: 10.37236/3114
