Add to ORKGPreviously we have investigated the medial layer graph G for a finite, self-dual, regular or chiral abstract 4-polytope P. Here we study the Cayley graph C on a natural group generated by polarities of P, show that C covers G in a readily computable way and construct C as a voltage graph over G. We then examine such symmetric graphs for several interesting families of polytopes of type {p, q, p}, p = 3, 4, 5. Key words: abstract regular or chiral polytopes, symmetric graph
Symmetric edge polytopes are a class of lattice polytopes constructed from finite simple graphs. In ...
Pisanski An abstract polytope of rank n is said to be chiral if its automorphism group has two orbit...
In this paper we construct an in nite family of hypertopes of rank four having the complete graph K4...
Previously we have investigated the medial layer graph G for a finite, self-dual, regular or chiral ...
AbstractIn any abstract 4-polytope P, the faces of ranks 1 and 2 constitute, in a natural way, the v...
AbstractEvery finite, self-dual, regular (or chiral) 4-polytope of type {3,q,3} has a trivalent 3-tr...
Every finite, self-dual, regular (or chiral) 4-polytope of type {3, q, 3} has a trivalent 3-transiti...
We give conditions for oriented labeled graphs that must be satisfied in order that such are permut...
Given a polytope P of rank 2n, the faces of middle ranks n - 1 and n constitute the vertices of a bi...
AbstractThe paper describes a construction of abstract polytopes from Cayley graphs of symmetric gro...
The paper describes a construction of abstract polytopes from Cayley graphs of symmetric groups. Giv...
AbstractIn recent years the term ‘chiral’ has been used for geometric and combinatorial figures whic...
AbstractIn a previous paper we constructed a finite regular (abstract) 4-polytope of type {3,3,p} fo...
A Cayley graph is a pictorial representation of the structure of a group G with respect to a generat...
ABSTRACT. Extending the srudy of triangles and tetrahedra in Cayley graphs of cyclic groups, we defi...
Symmetric edge polytopes are a class of lattice polytopes constructed from finite simple graphs. In ...
Pisanski An abstract polytope of rank n is said to be chiral if its automorphism group has two orbit...
In this paper we construct an in nite family of hypertopes of rank four having the complete graph K4...
Previously we have investigated the medial layer graph G for a finite, self-dual, regular or chiral ...
AbstractIn any abstract 4-polytope P, the faces of ranks 1 and 2 constitute, in a natural way, the v...
AbstractEvery finite, self-dual, regular (or chiral) 4-polytope of type {3,q,3} has a trivalent 3-tr...
Every finite, self-dual, regular (or chiral) 4-polytope of type {3, q, 3} has a trivalent 3-transiti...
We give conditions for oriented labeled graphs that must be satisfied in order that such are permut...
Given a polytope P of rank 2n, the faces of middle ranks n - 1 and n constitute the vertices of a bi...
AbstractThe paper describes a construction of abstract polytopes from Cayley graphs of symmetric gro...
The paper describes a construction of abstract polytopes from Cayley graphs of symmetric groups. Giv...
AbstractIn recent years the term ‘chiral’ has been used for geometric and combinatorial figures whic...
AbstractIn a previous paper we constructed a finite regular (abstract) 4-polytope of type {3,3,p} fo...
A Cayley graph is a pictorial representation of the structure of a group G with respect to a generat...
ABSTRACT. Extending the srudy of triangles and tetrahedra in Cayley graphs of cyclic groups, we defi...
Symmetric edge polytopes are a class of lattice polytopes constructed from finite simple graphs. In ...
Pisanski An abstract polytope of rank n is said to be chiral if its automorphism group has two orbit...
In this paper we construct an in nite family of hypertopes of rank four having the complete graph K4...