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arXiv · 2610.28672

Triangulation, Volume, and Symmetries of the Dihedral Group Analogue of the Permutohedron

Colin Olairez
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Abstract

We study the analogue of the permutohedron for the dihedral group, which we call the dihedral permutohedron. We determine the facet structure of the dihedral permutohedron, use the facet structure to construct a triangulation, and determine a nice combinatorial formula for the volume of the dihedral permutohedron. Lastly, we find a family of interesting unimodular affine symmetries of the odd dihedral permutohedron.

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Colin Olairez. 2026-10-18. Triangulation, Volume, and Symmetries of the Dihedral Group Analogue of the Permutohedron. https://arxiv.org/abs/2610.28672

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