Collapsing three-dimensional convex polyhedra: correction
Collapsing three-dimensional convex polyhedra: correction
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折叠三维凸多面体：校正
DOI：
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发表时间：
1980
影响因子：
0.8
通讯作者：
D. Chillingworth
中科院分区：
文献类型：
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作者：
D. Chillingworth
Connelly 和 Henderson (2) 的巧妙构造表明，存在一个直线三角剖分的凸多面体 P，其三角剖分的至少一个顶点位于 P 的一个面的内部，但不存在所有顶点都是 P' 的顶点的凸多面体 P' 的同构三角剖分。因此断言从 p 的顶行开始。 (1) 的 354 是假的，这在本质上证明 (1) 的主要结果中留下了空白，即任何直线三角凸多面体都可以简单地折叠到其边界减去 2-单纯形 σ 上。本注释的目的是表明该定理仍然是正确的。在任何情况下，(1) 中的推论 2 和 3 都不会受到错误的影响。
An ingenious construction due to Connelly and Henderson (2) has shown that there exists a rectilinearly triangulated convex polyhedron P in having the property that at least one vertex of the triangulation lies in the interior of a face of P, and yet there is no isomorphic triangulation of a convex polyhedron P′ all of whose vertices are vertices of P′. Thus the assertion beginning on the top line of p. 354 of (1) is false, which leaves a gap in the proof of essentially the main result of (1), namely that any rectilinearly triangulated convex polyhedron incan be simplicially collapsed onto its boundary minus a 2-simplex σ. The purpose of this note is to show that the theorem is nevertheless still true. In any case the Corollaries 2 and 3 in (1) are unaffected by the error.