## 17 Citations

### Orthogonal trees

- MathematicsSCG '91
- 1991

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

- Physics
- 2022

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.

- Materials Science, ChemistryActa crystallographica. Section A, Foundations and advances
- 2021

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

- MathematicsICST
- 2020

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.

- Materials ScienceActa crystallographica Section B, Structural science, crystal engineering and materials
- 2020

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

- MathematicsJournal 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

- Mathematics
- 2018

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

- MathematicsDiscrete & Computational Geometry
- 2016

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

- MathematicsDiscret. Comput. Geom.
- 2016

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

- Computer Science
- 2016

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.