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2013•IOSR Journal of MathematicsOpen access

The Complete Set of Orderable and Deformable Compact Coxeter Hyperbolic Tetrahedrons

Dhrubajit Choudhury

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Abstract

We classified the combinatorial structures of 3-dimensional bounded ODCH (orderable and deformable compact hyperbolic) Coxeter polyhedra up to symmetry.Using Plantri graphs and graph theory, we proved that the number of such combinatorial polyhedra is five.One of such combinatorial polyhedra is tetrahedron.Using graph theory and combinatorics, we find that there are six orderable and deformable compact hyperbolic tetrahedra up to symmetry.

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We classified the combinatorial structures of 3-dimensional bounded ODCH (orderable and deformable compact hyperbolic) Coxeter polyhedra up to symmetry.Using Plantri graphs and graph theory, we proved that the number of such combinatorial polyhedra is five.One of such combinatorial polyhedra is tetrahedron.Using graph theory and combinatorics, we find that there are six orderable and deformable compact hyperbolic tetrahedra up to symmetry.

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Available abstract

We classified the combinatorial structures of 3-dimensional bounded ODCH (orderable and deformable compact hyperbolic) Coxeter polyhedra up to symmetry.Using Plantri graphs and graph theory, we proved that the number of such combinatorial polyhedra is five.One of such combinatorial polyhedra is tetrahedron.Using graph theory and combinatorics, we find that there are six orderable and deformable compact hyperbolic tetrahedra up to symmetry.

Key concepts: Coxeter group, Mathematics, Tetrahedron, Set (abstract data type), Pure mathematics, Combinatorics, Geometry, Computer science

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