Compact hyperbolic coxeter thin cubes

Kalita, Pranab; Kalita, Bichitra

Eng. Math. Lett. 2014 (2014), Article ID 18

Compact hyperbolic coxeter thin cubes

Pranab Kalita, Bichitra Kalita

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Abstract

Andreev’s Theorem provides a complete characterization of 3-dimensional compact hyperbolic combinatorial polytope having non-obtuse dihedral angles. Cube is one of such polytope. In this article, with the help of Andreev’s Theorem, a special type of compact hyperbolic coxeter cube, called thin cube has been studied. Using graph theory and combinatorics, it has been found that there are exactly 3 such cubes in hyperbolic space upto symmetry.

Published: 29 August 2014
Volume: 2014 (2014)
License: CC BY 3.0

Copyright © 2014 Pranab Kalita, Bichitra Kalita. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Cite this article

P. Kalita, B. Kalita, Compact hyperbolic coxeter thin cubes, Eng. Math. Lett. 2014 (2014), 18.

BibTeX

@article{Kalita2014,
  author  = {Kalita, Pranab and Kalita, Bichitra},
  title   = {Compact hyperbolic coxeter thin cubes},
  journal = {Eng. Math. Lett.},
  volume  = {2014},
  year    = {2014},
  pages   = {18},
  doi     = {}
}