Given a self-dual map on the sphere, the collection of its self-dual permutations generates a transformation group in which the map automorphism group appears as a subgroup of index two. A careful examination of this pairing yields direct constructions of self-dual maps and provides a classification
Self-dual maps on the sphere
β Scribed by Brigitte Servatius; Herman Servatius
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 615 KB
- Volume
- 134
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
We show how to construct recursively all self-dual maps on the sphere together with their self-dualities, and classify them according to their edge-permutations.
π SIMILAR VOLUMES
The purpose of this paper is to study self-dual embeddings of balanced Cayley maps. Given a Cayley map, necessary and sufficient conditions are given in terms of its underlying group for the map to be isomorphic to its dual embedding. Applications include self-dual embeddings of 2n-dimensional cubes
## Abstract Regular maps are cellular decompositions of surfaces with the βhighest level of symmetryβ, not necessarily orientationβpreserving. Such maps can be identified with threeβgenerator presentations of groups __G__ of the form __G__ = γ__a, b, c__|__a__^2^ = __b__^2^ = __c__^2^ = (__ab__)^__