The Regge symmetry is a scissors congruence in hyperbolic space

Abstract

We give a constructive proof that the Regge symmetry is a scissors congruence in hyperbolic space. The main tool is Leibon's construction for computing the volume of a general hyperbolic tetrahedron. The proof consists of identifying the key elements in Leibon's construction and permuting them.

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-1.abs.html

References in corpus (1)

• Classical 6j-symbols and the tetrahedron

Cited by in corpus (8)

• 6j-symbols, hyperbolic structures and the Volume Conjecture
• Hamiltonian dynamics of a quantum of space: hidden symmetries and spectrum of the volume operator, and discrete orthogonal polynomials
• The screen representation of vector coupling coefficients or Wigner 3j symbols: exact computation and illustration of the asymptotic behavior
• 23040 symmetries of hyperbolic tetrahedra
• Quadrilaterals on the square screen of their diagonals: Regge symmetries of quantum-mechanical spin-networks and Grashof classical mechanisms of four-bar linkages
• Space vectors forming rational angles
• Formulas on hyperbolic volume
• Hyperbolic 3-manifolds with geodesic boundary: Enumeration and volume calculation