Realizations of regular polytopes, IV
Realizations of regular polytopes, IV
复制标题
规则多面体的实现，IV
DOI：
--
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
P. McMullen
中科院分区：
文献类型：
--
作者：
P. McMullen
在早期的论文中，已经建立了一个丰富的理论的几何实现的一个抽象的规则多面体。最近，描述了一种产品，以添加混合和缩放作为组合实现的方式。本文引入了规范化实现的余弦向量的内积，并证明了它具有一定的正交性，与诱导余弦向量一起，为研究实现提供了强有力的新工具。增强的理论是通过重新访问实现域的几个多面体，包括24细胞和600细胞。
In earlier papers, a rich theory of geometric realizations of an abstract regular polytope has been built up. More recently, a product was described, to add to blending and scaling as a way of combining realizations. This paper introduces an inner product of cosine vectors of normalized realizations, and shows that it has certain orthogonality properties; together with induced cosine vectors, these provide powerful new tools for investigating realizations. The enhanced theory is illustrated by revisiting the realization domains of several polytopes, including the 24-cell and 600-cell.