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.

一个普通的立方体是一个熟悉的正多面体的例子：它有各种各样的正方形面（上、下、前、后、左、右），由几个边（其中12个）分开，在8个角上以一种特殊的方式以3条边相交。通常这样的立方体在想象中使人联想到一个非常对称的刚性物体，即欧几里得的实现；但如果我们考虑一个橡胶复制品，那么我们可以想象以奇妙的方式扭曲和扭曲立方体，从而破坏它的对称性。然而，立方体的“组合特征”将在这种破坏尝试中幸存下来；仍然有6个方面，12条边和8个角，像以前一样相互连接。