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arXiv · 2109.08951

The Eisenlohr-Farris Algorithm for fully transitive polyhedra

Eric Pauli Pérez-Contreras
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Abstract

The purpose of this note is to present a method for classifying three-dimensional polyhedra in terms of their symmetry groups. This method is constructive and it is described in terms of the conjugation classes of crystallographic groups in $\mathbb{E}^3$. For each class of groups $\Gamma$ the method can generate without duplication all polyhedra in three-dimensional space on which $\Gamma$ acts fully-transitively. It was proposed by J. M. Eisenlohr and S. L. Farris for generating every fully transitive polyhedra in $\mathbb{E}^d$. We also illustrate how the method can be applied in the euclidean space $\mathbb{E}^3$ by generating a new fully transitive polyhedron.

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Eric Pauli Pérez-Contreras. 2021-09-18. The Eisenlohr-Farris Algorithm for fully transitive polyhedra. https://arxiv.org/abs/2109.08951

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