28 citations · 62 across the 29 of their papers we have counts for
5 papers · 1 filter
Problem on Mutant Pairs of Hyperbolic Polyhedra
Croix Gyurek, Roland Roeder
We present a notion of mutation of hyperbolic polyhedra, analogous to mutation in knot theory, and then present a general question about commensurability of mutant pairs of polyhed…
Computing arithmetic invariants for hyperbolic reflection groups
Omar Antolin-Camarena, Gregory R. Maloney, Roland K. W. Roeder
We describe a collection of computer scripts written in PARI/GP to compute, for reflection groups determined by finite-volume polyhedra in , the commensurability inva…
Constructing hyperbolic polyhedra using Newton's Method
Roland K. W. Roeder
We demonstrate how to construct three-dimensional compact hyperbolic polyhedra using Newton's Method. Under the restriction that the dihedral angles are non-obtuse, Andreev's Theor…
Compact hyperbolic tetrahedra with non-obtuse dihedral angles
Roland K. W. Roeder
Given a combinatorial description of a polyhedron having edges, the space of dihedral angles of all compact hyperbolic polyhedra that realize is generally not a convex…
Andreev's Theorem on hyperbolic polyhedra
Roland K. W. Roeder, John H. Hubbard, William D. Dunbar
In 1970, E. M. Andreev published a classification of all three-dimensional compact hyperbolic polyhedra having non-obtuse dihedral angles. Given a combinatorial description of a po…