$f$-vectors of $3$-polytopes symmetric under rotations and rotary reflections
| Autor: | Ring, Maren H., Schüler, Robert |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | The $f$-vector of a polytope consists of the numbers of its $i$-dimensional faces. An open field of study is the characterization of all possible $f$-vectors. It has been solved in three dimensions by Steinitz in the early 19th century. We state a related question, i.e. to characterize $f$-vectors of three dimensional polytopes respecting a symmetry, given by a finite group of matrices. We give a full answer for all three dimensional polytopes that are symmetric with respect to a finite rotation or rotary reflection group. We solve these cases constructively by developing tools that generalize Steinitz's approach. Comment: 38 pages, 15 figures, 12 tables |
| Databáze: | arXiv |
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