2002/11/18 by Mathias Rousset, Rousset, Mathias · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.DG #math.GT
paper · pdf · doi:10.48550/arxiv.math/0211280
30 pages
arxiv created 2002/11/18 · arxiv updated 2009/11/30
A hyperbolic semi-ideal polyedron is a polyedron whose vertices lie inside the hyperbolic space H3 or at infinity. A hyperideal polyedron is, in the projective model, the intersection of H3 with a projective polyhedron whose vertices all lie outside of H3, and whose edges all meet H3. We classify semi-ideal polyhedra in terms of their dual metric, using the results of Rivin and Hodgson in \citecomp et \citeidea. This result is used to obtain the classification of hyperideal polyhedra in terms of their combinatorial type and their dihedral angles. These two results are generalized to the case of fuchsian polyhedra.