Regular and semi-regular polytopes. III

  title={Regular and semi-regular polytopes. III},
  author={H. S. M. Coxeter},
  journal={Mathematische Zeitschrift},
  • H. Coxeter
  • Published 1988
  • Mathematics
  • Mathematische Zeitschrift

Orthogonal trees

This investigation was inspired by a letter from Edward Pervin of Carnegie-Mellon University. He had noticed an unexpected property of the fundamental regions for the infinite Euclidean reflection

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

Spiral tetrahedral packing in the β-Mn crystal as symmetry realization of the 8D E8 lattice.

Experimental values of atomic positions in the β-Mn crystal permit one to distinguish among them a fragment of the helix containing 15 interpenetrating distorted icosahedra, 90 vertices and 225

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.

Crystal structures of alpha and beta modifications of Mn as packing of tetrahedral helices extracted from a four-dimensional {3, 3, 5} polytope.

The crystal structures of both α- and β-Mn modifications have been presented as packing of tetrahedral helices extracted from four-dimensional {3, 3, 5} polytope construction. Presentation of the

Branes and polytopes

  • L. Romano
  • Mathematics
    Journal of Physics A: Mathematical and Theoretical
  • 2019
We investigate the hierarchies of half-supersymmetric branes in maximal supergravity theories. By studying the action of the Weyl group of the U-duality group of maximal supergravities we discover a

Integral binary Hamiltonian forms and their waterworlds

We give a graphical theory of integral indefinite binary Hamiltonian forms $f$ analogous to the one by Conway for binary quadratic forms and the one of Bestvina-Savin for binary Hermitian forms.

Wythoffian Skeletal Polyhedra in Ordinary Space, I

Skeletal polyhedra are discrete structures made up of finite, flat or skew, or infinite, helical or zigzag, polygons as faces, with two faces on each edge and a circular vertex-figure at each vertex.

Wythoffian Skeletal Polyhedra in Ordinary Space, I

The blueprint for the construction is described and the Wythoffians for distinguished classes of regular polyhedra are treated, which are vertex-transitive and often feature vertex configurations with an attractive mix of different face shapes.

Geometric and Information-Theoretic Properties of the Hoggar Lines

Investigating the shape of this representation of state space leads to an intriguing link between the questions of real and of complex equiangular lines and relations between quantum information theory and mathematical topics like octonionic integers and the 28 bitangents to a quartic curve.