Algebraic Enumeration of Polypolyhedra

Polypolyhedra are edge-transitive compounds of polyhedra. In this paper we use group theory to determine the number of distinct polypolyhedra whose symmetry group is any given finite irreducible Coxeter group. We apply this result in order to enumerate the 3-dimensional polypolyhedra.

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Journal
The PUMP Journal of Undergraduate Research
Published
2024-10-20
DOI
https://doi.org/10.46787/pump.v7i0.3936
Primary Topic
Advanced Theoretical and Applied Studies in Material Sciences and Geometry
Type
article
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article

Algebraic Enumeration of Polypolyhedra

Jeanette C. McLeod, Michael Langton, Phillip L. Wilson, George Henderson-Walshe
The PUMP Journal of Undergraduate Research
Advanced Theoretical and Applied Studies in Material Sciences and Geometry
article

Algebraic Enumeration of Polypolyhedra

Jeanette C. McLeod, Michael Langton, Phillip L. Wilson, George Henderson-Walshe
article en

Abstract

Polypolyhedra are edge-transitive compounds of polyhedra. In this paper we use group theory to determine the number of distinct polypolyhedra whose symmetry group is any given finite irreducible Coxeter group. We apply this result in order to enumerate the 3-dimensional polypolyhedra.

The PUMP Journal of Undergraduate ResearchVol. 7
University of Canterbury (NZ)
Openalex Percentile: Top 83%
Advanced Theoretical and Applied Studies in Material Sciences and Geometry
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Algebraic Enumeration of Polypolyhedra — Jeanette C. McLeod, Michael Langton, et al. · The PUMP Journal of Undergraduate Research (2024) | TGRS Research Map | TGRS