Algebraic and Geometric Topology 3 (2003), paper no. 1, pages 1-31.

The Regge symmetry is a scissors congruence in hyperbolic space

Yana Mohanty

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

AMS subject classification. Primary: 51M10. Secondary: 51M20.

DOI: 10.2140/agt.2003.3.1

E-print: arXiv:math.GT/0301318

Submitted: 8 October 2002. (Revised: 22 December 2002.) Accepted: 10 January 2003. Published: 24 January 2002.

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Yana Mohanty
Department of Mathematics, University of California at San Diego
La Jolla, CA 92093-0112, USA

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