Convex hulls of face-vertex incident vectors of 3-colorable polytopes
Abstract
The convex hulls of face-vertex incident vectors of 3-face-colorable convex polytopes are computed. It is found that every such convex hull is a d-polytope with d+2 or d+3 vertices. Utilizing Gale transform and Gale diagram, we calculate its combinatorial structure. Finally, a necessary and sufficient criterion for combinatorial equivalence of two such convex hulls is given.
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