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The Regge symmetry is a scissors congruence in hyperbolic space

Yana Mohanty

Algebraic & Geometric Topology 3 (2003) 1–31

arXiv: math.GT/0301318

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.

Keywords
Regge symmetry, hyperbolic tetrahedron, scissors congruence
Mathematical Subject Classification 2000
Primary: 51M10
Secondary: 51M20
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Publication
Received: 8 October 2002
Revised: 22 December 2002
Accepted: 10 January 2003
Published: 24 January 2003
Authors
Yana Mohanty
Department of Mathematics
University of California at San Diego
La Jolla, CA 92093-0112
USA