The infinite cyclohedron and its automorphism group

2014/11/13 by Ariadna Fossas Tenas, Jon McCammond, Tenas, Ariadna Fossas +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #math.CO #math.GR #math.GT

paper · pdf · doi:10.48550/arxiv.1411.3647

18 pages, 8 figures

arxiv created 2014/11/13 · openalex publication_date 2014/11/13 · arxiv updated 2014/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Cyclohedra are a well-known infinite familiy of finite-dimensional polytopes that can be constructed from centrally symmetric triangulations of even-sided polygons. In this article we introduce an infinite-dimensional analogue and prove that the group of symmetries of our construction is a semidirect product of a degree 2 central extension of Thompson's infinite finitely presented simple group T with the cyclic group of order 2. These results are inspired by a similar recent analysis by the first author of the automorphism group of an infinite-dimensional associahedron.

Citations

• The infinite associahedron and R.J. Thompson's group T

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