论文标题
准式烷烷基氧化物的欧亚裔分类
Quasi--Euclidean classification of Alcoved Convex Polyhedra
论文作者
论文摘要
我们对最大的欧亚裔分类（相对于$ f $ - 矢量）进行了艾尔切后的polyhedra。 $ f $ - 这些最大凸形体的向量为$（20,30,12）$，因此它们是简单的DodeCahedra。我们找到八个准欧国人课。保留角度的分类比已知的组合分类（Jiménez和de la puente在2012年发现）要细，后者只有六个类别。每个Alced polyhedron $ \ Mathcal {p} $由唯一可视化的IDEMPOTENT矩阵$ a $表示。 $ a $的大约2小时是$ \ MATHCAL {p} $的不变性：它们是$ \ Mathcal {p} $的热带边缘长度。
We give the quasi--Euclidean classification of the maximal (with respect to the $f$--vector) alcoved polyhedra. The $f$--vector of these maximal convex bodies is $(20,30,12)$, so they are simple dodecahedra. We find eight quasi--Euclidean classes. This classification, which preserves angles, is finer than the known combinatorial classification (found in 2012 by Jiménez and de la Puente), which has only six classes. Each alcoved polyhedron $\mathcal{P}$ is represented by a unique visualized idempotent matrix $A$. Some 2--minors of $A$ are invariants of $\mathcal{P}$: they are the tropical edge--lengths of $\mathcal{P}$.
