Coble群与Gosset-Elte多面体和镶嵌的可积性
Coble's group and the integrability of the Gosset-Elte polytopes and tessellations
摘要：
本文考虑了由Coxeter符号$k_{i,j}$标识的组合多面体或镶嵌的平面图形，内接于圆锥曲线，满足每个八面体单元具有中心的几何约束。这种实现是存在的，并且是可移动的，因为某些约束是作为其他约束的结果而得到满足的。一个密切的联系，以双有理数组发现原来由科布尔在不同的背景下不变量的点集在射影空间，允许精确地指定一个确定的子集的顶点，可以自由选择。这给出了一个统一的几何视图的某些可积离散系统在一个，两个和三个维度。在三维的情况下，与以前的几何帐户联系，它显示了该图如何也表现为一个配置的圆圈概括的克利福德格，以及它如何可以应用于构建空间点线配置称为Desargues地图。
英文摘要：
This paper considers the planar figure of a combinatorial polytope or tessellation identified by the Coxeter symbol $k_{i,j}$ , inscribed in a conic, satisfying the geometric constraint that each octahedral cell has a centre. This realisation exists, and is movable, on account of some constraints being satisfied as a consequence of the others. A close connection to the birational group found originally by Coble in the different context of invariants for sets of points in projective space, allows to specify precisely a determining subset of vertices that may be freely chosen. This gives a unified geometric view of certain integrable discrete systems in one, two and three dimensions. Making contact with previous geometric accounts in the case of three dimensions, it is shown how the figure also manifests as a configuration of circles generalising the Clifford lattices, and how it can be applied to construct the spatial point-line configurations called the Desargues maps.
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