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Mathematical Background and Notation
Subdivisions and Triangulations
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adjoined vertex affine hull affinely disjoint ap ap Ascent Replacement barycentric coordinates Bibliographical Notes cells chart of Figure collection common face computation convex combination convex hull convex set correspondence between vertices define e i#F Eaves element empty set facet rule following lemma Freudenthal triangulation Given homotopies integral k+1 k+2 n+2 Laan and Talman Leama Lemma lexico linear map locally finite manifold Mathematical Programming matrix n-cell n-simplex v;n;n n-simplexes of F n+1 vertices n+1)-simplex natural restriction nk+1 Note for Figure permutation Proof rate refining triangulations relative interior replacement rules representation and replacement representation rule representation set Rerepresent v;n;n rS-p Section side exit simplex simplicial cones squeeze and shear STOP See Note supporting hyperplane Theorem Todd top exit triangulation F unimodular unique solution variable rate refining vertices of v;n;k;Ti vertices of v;n;n