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arXiv · 2210.12012

Generic Orthotopes

David Richter
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Abstract

This article studies a large, general class of orthogonal polytopes which we may call "generic orthotopes". These objects emerged from a desire to represent a Coxeter complex by an orthogonal polytope that is particularly nice with respect to traditional topological, structural, or combinatorial considerations. Generic orthotopes have a pleasant "homogeneity" property, somewhat like a smoothly bounded compact subset of Euclidean space. Thus, as soon as we demand that every vertex of an orthogonal polytope be a floral arrangement, as defined here, many derivative structures such as faces and cross-sections are also described by floral arrangements. We also give formulas for the volume and Euler characteristic of a generic orthotope using a couple of statistics that are defined naturally for floral arrangements.

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David Richter. 2022-10-21. Generic Orthotopes. https://arxiv.org/abs/2210.12012

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