Octahedralizing 3-colorable 3-polytopes
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math.CO
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colorablepolytopeadditionalanswerboundarycomplexcross-polytopaldimension
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We investigate the question of whether any $d$-colorable simplicial $d$-polytope can be octahedralized, i.e., it can be subdivided to a $d$-dimensional geometric cross-polytopal complex. We give a positive answer in dimension $3$, with the additional property that the octahedralization introduces no new vertices on the boundary of the polytope.
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