Abstract polytopes are combinatorial objects that generalise geometric objects such as convex polytopes, maps on surfaces and tilings of the space. Chiral polytopes are those abstract polytopes that admit full combinatorial rotational symmetry but do not admit reflections. In this paper we build chiral polytopes whose facets (maximal faces) are isomorphic to a prescribed regular cubic tessellation of the n-dimensional torus (\(n \geqslant 2\)). As a consequence, we prove that for every \(d \geqslant 3\) there exist infinitely many chiral d-polytopes.

中文翻译：

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常规环形线圈的手性延伸

摘要多面体是概括几何对象（如凸面多面体、曲面映射和空间平铺）的组合对象。手性多位体是那些抽象多位体，它们承认完全组合旋转对称性，但不允许反射。在本文中，我们构建了手性多面体，其面（最大面）与 n 维圆环 （\（n \geqslant 2\）） 的规定规则三次镶嵌同构。因此，我们证明了对于每个 \（d \geqslant 3\） 存在无限多的手性 d 多位面。