منابع مشابه
Asymmetric Combinatorially - Regular Maps *
It is shown that for every g > 3, there exists a combinatorially regular map M of type {3, 7} on a closed orientable surface of genus g, such that M.has trivial symmetry group. Such maps are constructed from Schreier coset graphs corresponding to permutation representations of the (2, 3, 7) triangle group.
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Let T be a regular tiling of R which has the origin 0 as a vertex, and suppose that φ : R → R is a homeomorphism such that i) φ(0) = 0, ii) the image under φ of each tile of T is a union of tiles of T , and iii) the images under φ of any two tiles of T are equivalent by an orientation-preserving isometry which takes vertices to vertices. It is proved here that there is a subset Λ of the vertice...
متن کاملConvex-Faced Combinatorially Regular Polyhedra of Small Genus
Combinatorially regular polyhedra are polyhedral realizations (embeddings) in Euclidean 3-space E of regular maps on (orientable) closed compact surfaces. They are close analogues of the Platonic solids. A surface of genus g > 2 admits only finitely many regular maps, and generally only a small number of them can be realized as polyhedra with convex faces. When the genus g is small, meaning tha...
متن کاملRegular Surfaces and Regular Maps
A regular surface is a closed genus g surface defined as the tubular neighbourhood of the edge graph of a regular map. A regular map is a family of disc type polygons glued together to form a 2-manifold which is flag transitive. The visualization of this highly symmetric surface is an intriguing and challenging problem. Unlike regular maps, regular surfaces can always be visualized as 3D embedd...
متن کاملRegular Homomorphisms and Regular Maps
Regular homomorphisms of oriented maps essentially arise from a factorization by a subgroup of automorphisms. This kind of map homomorphism is studied in detail, and generalized to the case when the induced homomorphism of the underlying graphs is not valency preserving. Reconstruction is treated by means of voltage assignments on angles, a natural extension of the common assignments on darts. ...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 1996
ISSN: 0925-9899,1572-9192
DOI: 10.1007/bf00193182