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arXiv math/0501050math.MGmath.CO
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普通空间中的手征多面体,II

Chiral polyhedra in ordinary space, II

Egon Schulte

摘要:

手征多面体具有几何对称群,其在旗上具有两个轨道,使得相邻的旗处于不同的轨道中。本文的第一部分描述了具有有限斜面和有限斜顶点图形的欧氏三维空间中的离散手征多面体,它们出现在无限族中,类型为{4,6},{6,4}和{6,6}。第二部分完成了三维空间中所有离散手征多面体的计数。存在几个具有无限螺旋面的手征多面体家族。特别地,除了第一部分中描述的那些之外,没有具有有限面的离散手征多面体。

英文摘要:

A chiral polyhedron has a geometric symmetry group with two orbits on the flags, such that adjacent flags are in distinct orbits. Part I of the paper described the discrete chiral polyhedra in ordinary Euclidean 3-space with finite skew faces and finite skew vertex-figures; they occur in infinite families and are of types {4,6}, {6,4} and {6,6}. Part II completes the enumeration of all discrete chiral polyhedra in 3-space. There exist several families of chiral polyhedra with infinite, helical faces. In particular, there are no discrete chiral polyhedra with finite faces in addition to those described in Part I.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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