9 papers
Chiral extensions of regular toroids
Antonio Montero, Micael Toledo
Abstract polytopes are combinatorial objects that generalise geometric objects such as convex polytopes, maps on surfaces and tilings of the space. Chiral polytopes are those abstr…
Vertex-transitive graphs with small motion and transitive permutation groups with small minimal degree
Antonio Montero, Primož Potočnik
The motion of a graph is the minimum number of vertices that are moved by a non-trivial automorphism. Equivalently, it can be defined as the minimal degree of its automorphism grou…
Symmetries of voltage operations on polytopes, maps and maniplexes
Isabel Hubard, Elías Mochán, Antonio Montero
Voltage operations extend traditional geometric and combinatorial operations (such as medial, truncation, prism, and pyramid over a polytope) to operations on maniplexes, maps, pol…
Voltage operations on maniplexes
Isabel Hubard, Elías Mochán, Antonio Montero
Classical geometric and topological operations on polyhedra, maps and polytopes often give rise to structures with the same symmetry group as the original one, but with more flags.…
Proper locally spherical hypertopes of hyperbolic type
Antonio Montero, Asia Ivić Weiss
Given any irreducible Coxeter group of hyperbolic type with non-linear diagram and rank at least , whose maximal parabolic subgroups are finite, we construct an infinite fam…
On the Schläfli symbol of chiral extensions of polytopes
Antonio Montero
Given an abstract -polytope , an abstract -polytope is an extension of if all the facets of are isomorphic to $\mat…
Locally spherical hypertopes from generlised cubes
Antonio Montero, Asia Ivić Weiss
We show that every non-degenerate regular polytope can be used to construct a thin, residually-connected, chamber-transitive incidence geometry, i.e. a regular hypertope, with a ta…
Equivelar toroids with few flag-orbits
José Collins, Antonio Montero
An -toroid is a quotient of a tessellation of the -dimensional Euclidean space with a lattice group. Toroids are generalizations of maps in the torus on higher dimensions…
Regular polyhedra in the 3-torus
Antonio Montero
In this paper we discuss the classification rank lattices preserved by finite orthogonal groups of isometries and derive from it the classification of regular polyhedra in the…