Realizations, symmetry and monodromy groups of abstract polytopes

抽象多胞体的实现、对称性和单峰群

• 批准号: 4818-2011
• 负责人: Monson, Barry
• 金额: $ 0.73万
• 依托单位: University of New Brunswick
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=544224
• 关键词: Realizations; symmetry; monodromy; groups; abstract

An ordinary cube is a familiar example of a regular polytope: it has various square faces (top, bottom, front, back, left, right), separated by several edges (twelve of them), which meet by threes in a particular way at the eight corners. Usually such a cube suggests to the imagination a very symmetrical and rigid object, i.e. a Euclidean realization; but if we consider instead a rubber copy, then we can imagine twisting and distorting the cube in fantastic ways which destroy its symmetry. Nevertheless, the `combinatorial features' of the cube would survive this attempt at destruction; there would still be 6 square faces, 12 edges and 8 corners, interconnected as before.

普通的立方体是常规多层人士的一个熟悉的例子：它具有各种正方形的面（顶部，底部，前，背，左，右），被几个边缘（十二个）隔开，在八个角落以特定方式相遇。通常，这样的立方体暗示了一个非常对称和僵硬的物体，即欧几里得实现的。但是，如果我们考虑使用橡胶副本，那么我们可以想象以奇妙的方式扭曲和扭曲了立方体，从而破坏其对称性。然而，立方体的“组合特征”将幸免于这种破坏的尝试。仍然像以前一样互连，仍然有6个正方形的面，12个边缘和8个角落。