Journal ArticleDOI
A Polyhedral Realization of Felix Klein's Map {3, 7}8 on a Riemann Surface of Genus 3
Egon Schulte,J. M. Wills +1 more
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This article is published in Journal of The London Mathematical Society-second Series.The article was published on 1985-12-01. It has received 47 citations till now. The article focuses on the topics: Uniformization theorem & Riemann surface.read more
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Triangulated Manifolds with Few Vertices: Combinatorial Manifolds
TL;DR: A survey on combinatorial properties of triangulated manifolds can be found in this paper, where the authors discuss various lower bounds on the number of vertices of simplicial manifold.
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Realizations of regular polytopes
TL;DR: In this paper, it was shown that the family of all possible realizations (up to congruence) of ℐ forms a closed convex cone, which is also referred to as a realization cone.
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Isomorphism-free lexicographic enumeration of triangulated surfaces and 3-manifolds
Thom Sulanke,Frank H. Lutz +1 more
TL;DR: In this paper, a fast enumeration algorithm for combinatorial 2-and 3-manifolds is presented, which enumerates all triangulated surfaces with 11 and 12 vertices.
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Infinite series of combinatorially regular polyhedra in three-space
TL;DR: In this article, the authors discuss polyhedral realizations in ordinary Euclidean 3-space of Coxeter's regular skew polyhedra {4, p|4p/2]−1} and their duals on an orientable surface of genus 2p−3(p−4)+1.
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Maximally symmetric polyhedral realizations of Dyck's regular map
TL;DR: In this paper, the authors constructed realizations of Dyck's regular map of genus three as polyhedra in ℝ3 and showed that the symmetry groups of these realizations are maximal.