Geodesic
The polytope of all triangulations of a point configuration
Documenta mathematica, Tome 1 (1996), pp. 103-119
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We study the convex hull PA​ of the 0-1 incidence vectors of all triangulations of a point configuration A. This was called the universal polytope in citeBIFIST. The affine span of PA​ is described in terms of the co-circuits of the oriented matroid of A. Its intersection with the positive orthant is a quasi-integral polytope QA​ whose integral hull equals PA​. We present the smallest example where QA​ and PA​ differ. The duality theory for regular triangulations in citeBIGEST is extended to cover all triangulations. We discuss potential applications to enumeration and optimization problems regarding all triangulations.
DOI : 10.4171/dm/4
Classification : 52B55, 90C27 
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     title = {The polytope of all triangulations of a point configuration},
     journal = {Documenta mathematica},
     pages = {103--119},
     year = {1996},
     volume = {1},
     doi = {10.4171/dm/4},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/4/}
}
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Jesús de Loera; Serkan Hosten; Francisco Santos; Bernd Sturmfels. The polytope of all triangulations of a point configuration. Documenta mathematica, Tome 1 (1996), pp. 103-119. doi: 10.4171/dm/4

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