scholarly journals Minimal Covers of the Archimedean Tilings, Part 1

10.37236/2512 ◽  
2012 ◽  
Vol 19 (3) ◽  
Author(s):  
Daniel Pellicer ◽  
Gordon Williams
Keyword(s):  
Automorphism Group ◽  
Regular Polytopes

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.

Existence of regular 3-polytopes of order 2𝑛

2019 ◽  
Vol 22 (4) ◽  
pp. 579-616 ◽  
Author(s):  
Dong-Dong Hou ◽  
Yan-Quan Feng ◽  
Dimitri Leemans
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Partial Answer ◽  
Regular Polytopes ◽  
Regular Polytope ◽  
Positive Integers

AbstractIn this paper, we prove that for any positive integers {n,s,t} such that {n\geq 10}, {s,t\geq 2} and {n-1\geq s+t}, there exists a regular polytope with Schläfli type {\{2^{s},2^{t}\}} and its automorphism group is of order {2^{n}}. Furthermore, we classify regular polytopes with automorphism groups of order {2^{n}} and Schläfli types {\{4,2^{n-3}\},\{4,2^{n-4}\}} and {\{4,2^{n-5}\}}, therefore giving a partial answer to a problem proposed by Schulte and Weiss in [Problems on polytopes, their groups, and realizations, Period. Math. Hungar. 53 2006, 1–2, 231–255].

ABSTRACT REGULAR POLYTOPES FOR THE O'NAN GROUP

2014 ◽  
Vol 24 (01) ◽  
pp. 59-68 ◽  
Author(s):  
THOMAS CONNOR ◽  
DIMITRI LEEMANS ◽  
MARK MIXER
Keyword(s):  
Automorphism Group ◽  
Simple Group ◽  
Regular Polytopes ◽  
Sporadic Simple Group ◽  
Regular Polytope ◽  
Abstract Regular Polytope

In this paper, we consider how the O'Nan sporadic simple group acts as the automorphism group of an abstract regular polytope. In particular, we prove that there is no regular polytope of rank at least five with automorphism group isomorphic to O′N. Moreover, we classify all rank four regular polytopes having O′N as their automorphism group.

scholarly journals On the number of abstract regular polytopes whose automorphism group is a Suzuki simple group Sz(q)

2010 ◽  
Vol 117 (8) ◽  
pp. 1248-1257 ◽  
Author(s):  
Ann Kiefer ◽  
Dimitri Leemans
Keyword(s):  
Automorphism Group ◽  
Simple Group ◽  
Regular Polytopes

ON THE AUTOMORPHISM GROUP OF A FINITE P-GROUP WITH CYCLIC FRATTINI SUBGROUP

2008 ◽  
Vol 108 (2) ◽  
pp. 165-175 ◽  
Author(s):  
S. Fouladi ◽  
A. R. Jamali ◽  
R. Orfi
Keyword(s):  
Automorphism Group ◽  
Frattini Subgroup

scholarly journals On the automorphism group of a symplectic half-flat 6-manifold

2019 ◽  
Vol 31 (1) ◽  
pp. 265-273
Author(s):  
Fabio Podestà ◽  
Alberto Raffero
Keyword(s):  
Automorphism Group ◽  
Lie Algebra ◽  
Group Action ◽  
Cohomogeneity One ◽  
Cohomogeneity One Action

Abstract We prove that the automorphism group of a compact 6-manifold M endowed with a symplectic half-flat {\mathrm{SU}(3)} -structure has Abelian Lie algebra with dimension bounded by {\min\{5,b_{1}(M)\}} . Moreover, we study the properties of the automorphism group action and we discuss relevant examples. In particular, we provide new complete examples on {T\mathbb{S}^{3}} which are invariant under a cohomogeneity one action of {\mathrm{SO}(4)} .

scholarly journals ON EDGE-PRIMITIVE GRAPHS WITH SOLUBLE EDGE-STABILIZERS

2021 ◽  
pp. 1-28
Author(s):  
HUA HAN ◽  
HONG CI LIAO ◽  
ZAI PING LU
Keyword(s):  
Automorphism Group

Abstract A graph is edge-primitive if its automorphism group acts primitively on the edge set, and $2$ -arc-transitive if its automorphism group acts transitively on the set of $2$ -arcs. In this paper, we present a classification for those edge-primitive graphs that are $2$ -arc-transitive and have soluble edge-stabilizers.

scholarly journals Affine cones over cubic surfaces are flexible in codimension one

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Alexander Perepechko
Keyword(s):  
Automorphism Group ◽  
Open Subset ◽  
Pezzo Surface ◽  
Ample Divisor ◽  
Transitive Action ◽  
Del Pezzo Surface ◽  
Codimension One ◽  
Cubic Surfaces ◽  
Special Automorphism ◽  
Del Pezzo

AbstractLet Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codimension one. Equivalently, such a cone has an open subset with an infinitely transitive action of the special automorphism group on it.

Automorphism group and representation of a twisted multi-loop algebra

2010 ◽  
Vol 26 (1) ◽  
pp. 143-154 ◽  
Author(s):  
Cui Chen ◽  
Hai Feng Lian ◽  
Shao Bin Tan
Keyword(s):  
Automorphism Group ◽  
Loop Algebra

scholarly journals The automorphism group of the tetrablock

2008 ◽  
Vol 77 (3) ◽  
pp. 757-770 ◽  
Author(s):  
N. J. Young
Keyword(s):  
Automorphism Group
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