On toroidal groups

Toroidal Embeddings of Right Groups

In this note we study embeddings of Cayley graphs of right groups on surfaces. We characterize those right groups which have a toroidal but no planar Cayley graph, such that the generating system of the right group has a minimal generating system of the group as a factor.

Twisted Groups and Locally Toroidal Regular Polytopes

In recent years, much work has been done on the classification of abstract regular polytopes by their local and global topological type. Abstract regular polytopes are combinatorial structures which generalize the wellknown classical geometric regular polytopes and tessellations. In this context, the classical theory is concerned with those which are of globally or locally spherical type. In a ...

Locally toroidal polytopes and modular linear groups

When the standard representation of a crystallographic Coxeter group G (with string diagram) is reduced modulo the integer d ≥ 2, one obtains a finite group G which is often the automorphism group of an abstract regular polytope. Building on earlier work in the case that d is an odd prime, we here develop methods to handle composite moduli and completely describe the corresponding modular polyt...

On Toroidal Rotating Drops

Functionals on Toroidal Surfaces

We show that the torus in R is a critical point of a sequence of functionalsFn (n = 1, 2, 3, . . .) defined over compact surfaces (closed membranes) in R. When the Lagrange function E is a polynomial of degree n of the mean curvatureH of the torus, the radii (a, r) of the torus are constrained to satisfy a 2 r2 = n−n n2−n−1 , n ≥ 2. A simple generalization of torus in R 3 is a tube of radius r ...