The Eisenlohr-Farris Algorithm for fully transitive polyhedra
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 metho...
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Zusammenfassung: | 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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DOI: | 10.48550/arxiv.2109.08951 |