Regular and semi-regular polytopes. I

  title={Regular and semi-regular polytopes. I},
  author={H. S. M. Coxeter},
  journal={Mathematische Zeitschrift},
  • H. Coxeter
  • Published 1940
  • Mathematics
  • Mathematische Zeitschrift

Quantum entanglement and contextuality with complexifications of $E_8$ root system

The Witting configuration with 40 complex rays was suggested as a possible reformulation of Penrose model with two spin-3/2 systems based on geometry of dodecahedron and used for analysis of

Regular Polygonal Complexes in Space, II

A polygonal complex in euclidean 3-space is a discrete polyhedron-like structure with finite or infinite polygons as faces and finite graphs as vertex-figures, such that a fixed number r of faces

Optimal Finite Homogeneous Sphere Approximation

  • Omer Lavi
  • Mathematics
    Discrete & Computational Geometry
  • 2022
The two-dimensional sphere can’t be approximated by finite homogeneous spaces. We describe the optimal approximation and its distance from the sphere. We compare this distance to the distance

Enabling four-dimensional conformal hybrid meshing with cubic pyramids

A novel refinement strategy for four-dimensional hybrid meshes based on cubic pyramids and a new class of fully symmetric quadrature rules with positive weights are generated for the cubic pyramid.

Platonic solids, Archimedean solids and semi-equivelar maps on the sphere

The Polyhedral-Surface Cutting-Plane Method for Linear Combinatorial Optimization

A justification of applicability of PSCM for linear permutation-based and Boolean optimization problems is given, which opens perspectives to solve in a reasonable time a significantly wider class of realworld tasks modelled as combinatorial optimization problems.

Integration bounds for the regular simplex in n-dimensional space

The purpose of this article is to provide an explicit formula for the bounds of integration of the regular simplex centred at the origin. Furthermore, this article rigorously proves that these

Constructing highly regular expanders from hyperbolic Coxeter groups

A graph $X$ is defined inductively to be $(a_0,\dots,a_{n-1})$-regular if $X$ is $a_0$-regular and for every vertex $v$ of $X$, the sphere of radius $1$ around $v$ is an $(a_1,\dots,a_{n-1})$-regular

Symmetry of hyper-adamantanes

Abstract Hyper-adamantane is an adamantine in which vertices are changed by a cell/shape. Some mathematical properties of hyper-adamantanes built with several symmetrical shapes are detailed.

The Assembly Problem for Alternating Semiregular Polytopes

This paper continues the study of alternating abstract semiregular polytopes with two kinds of abstract regular facets, and finds that for some interlacing number k, k copies each of P and Q can be assembled around each face of co-rank 2 in S.