Discrete Models: Combinatorics, Computation, and Geometry, DMCCG 2001
Robert Cori and Jacques Mazoyer and Michel Morvan and Rémy Mosseri (eds.)
DMTCS Conference Volume AA (2001), pp. 111122
author:  Sergei Bespamyatnikh 

title:  Enumerating Triangulations of Convex Polytopes 
keywords:  polytope, bistellar flip, triangulation, enumeration 
abstract: 
A triangulation of a finite point set
A
in
R
is a geometric simplicial complex which covers the
convex hull of
d
A
and whose vertices are points of
A
. We study the graph of triangulations whose vertices
represent the triangulations and whose edges represent
geometric bistellar flips. The main result of this paper is
that the graph of triangulations in three dimensions is
connected when the points of
A
are in convex position. We introduce a tree of
triangulations and present an algorithm for enumerating
triangulations in
O(log log n)
time per triangulation.

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reference:  Sergei Bespamyatnikh (2001), Enumerating Triangulations of Convex Polytopes, in Discrete Models: Combinatorics, Computation, and Geometry, DMCCG 2001, Robert Cori and Jacques Mazoyer and Michel Morvan and Rémy Mosseri (eds.), Discrete Mathematics and Theoretical Computer Science Proceedings AA, pp. 111122 
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