CFP last date
20 January 2025
Call for Paper
February Edition
IJCA solicits high quality original research papers for the upcoming February edition of the journal. The last date of research paper submission is 20 January 2025

Submit your paper
Know more
The week's pick
Responsive image
SFLA-Based Line Balancing and Task Optimization in Master-Slave Controlled Hanger Transportation Systems for Garment Production

Duc Hoang Nguyen
Random Articles
Reseach Article

Complete Set of CHC Tetrahedrons

by Pranab Kalita, Bichitra Kalita
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 87 - Number 11
Year of Publication: 2014
Authors: Pranab Kalita, Bichitra Kalita
10.5120/15252-3891

Pranab Kalita, Bichitra Kalita . Complete Set of CHC Tetrahedrons. International Journal of Computer Applications. 87, 11 ( February 2014), 18-23. DOI=10.5120/15252-3891

@article{ 10.5120/15252-3891,
author = { Pranab Kalita, Bichitra Kalita },
title = { Complete Set of CHC Tetrahedrons },
journal = { International Journal of Computer Applications },
issue_date = { February 2014 },
volume = { 87 },
number = { 11 },
month = { February },
year = { 2014 },
issn = { 0975-8887 },
pages = { 18-23 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume87/number11/15252-3891/ },
doi = { 10.5120/15252-3891 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:05:39.448009+05:30
%A Pranab Kalita
%A Bichitra Kalita
%T Complete Set of CHC Tetrahedrons
%J International Journal of Computer Applications
%@ 0975-8887
%V 87
%N 11
%P 18-23
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this article, using K. W. Roeder's Theorem, some properties of CHC (compact hyperbolic coxeter) tetrahedrons have been developed which are facilitated by the link of graph theory and combinatorics, and it has been found that there are exactly 3 CHC tetrahedrons upto symmetry.

References
  1. P. Kalita and B. Kalita, Properties of Coxeter Andreev's Tetrahedrons, IOSR Journal of Mathematics, Volume 9, Issue 6, pp 81-105, 2014.
  2. John G. Ratcliffe, Foundations of Hyperbolic Manifolds, ©1994 by Springer-Verlag, New York, Inc.
  3. Chris Godsil, Gordon Royle, Algebraic Graph Theory, Springer International Edition.
  4. Gil Kalai, Polytope Skeletons and Paths, ©1997 by CRC Press LLC.
  5. Dipankar Mondal, Introduction to Reflection Groups, April 26, 2013, Triangle Group (Course Project).
  6. Projective Linear Group, http://en. wikipedia. org/wiki/Projective_linear_group, access in October, 2013.
  7. Hyperbolic Tetrahedron, http://mathworld. wolfram. com/Hyperbolic Tetrahedron. html, access in October, 2013.
  8. J. Mcleod, Hyperbolic Coxeter Pyramids, Advances in Pure Mathematics, Scientific Research, 2013, 3, 78-82.
  9. Tetrahedron, Wikipedia, the free encyclopedia, access in October, 2013.
  11. Roland K. W. Roeder, Compact hyperbolic tetrahedra with non-obtuse dihedral angles, August 10, 2013, arxiv. org/pdf/math/0601148.
  12. Aleksandr Kolpakov, On extremal properties of hyperbolic coxeter polytopes and their reflection groups, Thesis No: 1766, e-publi. de, 2012.
  13. Anna Felikson, Pavel Tumaarkin, Coxeter polytopes with a unique pair of non intersecting facets, Journal of Combinatorial Theory, Series A 116 (2009) 875-902.
  14. Pavel Tumarkin, Compact Hyperbolic Coxeter polytopes with facets, The Electronic Journal of Combinatorics 14 (2007).
  15. R. K. W. Roeder, Constructing hyperbolic polyhedral using Newton's method, Experiment. Math. 16, 463-492 (2007).
  16. Roland K. W. Roeder, John H. Hubbard and William D. Dunbar, Andreev's Theorem on Hyperbolic Polyhedra, Ann. Inst. Fourier, Grenoble 57, 3 (2007), 825-882.
  17. D. Cooper, D. Long and M. Thistlethwaite, Computing varieties of representations of hyperbolic 3-manifolds into , Experiment. Math. 15, 291305 (2006).
  18. Yunhi Cho and Hyuk Kim. On the volume formula for hyperbolic tetrahedral. Discrete Comput. Geom. , 22 (3): 347-366, 1999.
  19. Tomaz Pisanski, Milan Randic, Bridges between Geometry and Graph Theory, ISSN 1318-4865, Preprint Series, Vol. 36 (1998), 595.
  20. Raquel diaz, Non-convexity of the space of dihedral angles of hyperbolic polyhedra. C. R. Acad. Sci. Paris Ser. I Math. , 325 (9):993-998, 1997.
  21. E. B. Vinberg, Geometry II, Encyclopedia of Maths, Sc. 29. Springer 1993.
  22. E. B. Vinberg, Hyperbolic Reflection Groups, Uspekhi Mat. Nauk 40, 29-66 (1985).
  23. E. B. Vinberg, The absence of crystallographic groups of reflections in Lobachevskij spaces of large dimensions, Trans. Moscow Math. Soc. 47 (1985), 75-112.
  24. E. M. Andreev, On Convex Polyhedral of Finite Volume in Lobacevskii Space, Math. USSR Sbornik 10, 413-440 (1970).
Index Terms

Computer Science
Information Sciences

Keywords

Dihedral angles Face angles Planar graph Coxeter.

Powered by PhDFocusTM