Vertex-Transitive Polyhedra of Higher Genus, I
نویسندگان
چکیده
منابع مشابه
Vertex-Transitive Polyhedra in 3-Space
In addition to regular and chiral polyhedra, which have been extensively studied, the vertextransitive polyhedra of higher genus also present an attractive and worthwhile challenge. While the definition is combinatorial, the problem at hand is the realization in Euclidean 3-space as a highly symmetric, non-self-intersecting polyhedron in the more classical sense (with flat, non-self-intersectin...
متن کاملThe maximum genus of vertex-transitive graphs
Graphs possessing a high degree of symmetry have often been considered in topological graph theory. For instance, a number of constructions of genus embeddings by means of current or voltage graphs is based on the observation that a graph can be represented as a Cayley graph for some group. Another kind of embedding problems where symmetrical graphs are encountered is connected with regular map...
متن کاملVertex-Unfoldings of Simplicial Polyhedra
We present two algorithms for unfolding the surface of any polyhedron, all of whose faces are triangles, to a nonoverlapping, connected planar layout. The surface is cut only along polyhedron edges. The layout is connected, but it may have a disconnected interior: the triangles are connected at vertices, but not necessarily joined along edges.
متن کاملVertex unfoldings of tight polyhedra
An unfolding of a polyhedron along its edges is called a vertex unfolding if adjacent faces are allowed to be connected at not only an edge but also a vertex. Demaine et al [1] showed that every triangulated polyhedron has a vertex unfolding. We extend this result to a tight polyhedron, where a polyhedron is tight if its non-triangular faces are mutually non-incident.
متن کاملVertex-transitive CIS graphs
A CIS graph is a graph in which every maximal stable set and every maximal clique intersect. A graph is well-covered if all its maximal stable sets are of the same size, co-well-covered if its complement is well-covered, and vertex-transitive if, for every pair of vertices, there exists an automorphism of the graph mapping one to the other. We show that a vertex-transitive graph is CIS if and o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2016
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-016-9828-9