PreprintCC BY 4.0arXiv
Triangulation, Volume, and Symmetries of the Dihedral Group Analogue of the Permutohedron
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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BibTeX
@misc{olairez2026triangulation,
title = {{Triangulation, Volume, and Symmetries of the Dihedral Group Analogue of the Permutohedron}},
author = {Colin Olairez},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28672},
eprint = {2610.28672},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28672},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Triangulation, Volume, and Symmetries of the Dihedral Group Analogue of the Permutohedron
AU - Colin Olairez
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.28672
UR - https://arxiv.org/abs/2610.28672
AB - 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.
ER -