论文标题
$ f $ - $ 3 $ - polytopes对称的旋转和旋转反射的对称性
$f$-vectors of $3$-polytopes symmetric under rotations and rotary reflections
论文作者
论文摘要
$ f $ - 多层的向量由其$ i $二维面的数量组成。开放的研究领域是所有可能的$ f $ - 向量的表征。在19世纪初期，斯坦尼茨已经在三个维度上解决了它。我们指出了一个相关的问题，即表征有限矩阵群体给出的三维多型的$ f $ - 向量。我们为相对于有限旋转或旋转反射组对称的所有三个维度多型提供了完整的答案。我们通过开发概括Steinitz方法的工具来建设性地解决这些案例。
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.
