We introduce a graph structure on the set of Euclidean polytopes. The vertices of this graph are the d-dimensional polytopes contained in ${\mathbb{R}}^d$ and its edges connect any two polytopes that can be obtained from one another by either inserting or deleting a vertex, while keeping their vertex sets otherwise unaffected. We prove several results on the connectivity of this graph, and on a number of its subgraphs. We are especially interested in several families of subgraphs induced by lattice polytopes, such as the subgraphs induced by the lattice polytopes with n or $n+1$ vertices, that turn out to exhibit intriguing properties.

中文翻译：

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格子多面体上的基本移动

我们在欧几里德多拓扑集上引入图结构。该曲线图的顶点是d包含在维多面体${\mathbb{[R}}^d$它的边缘连接可以通过插入或删除一个顶点而彼此获得的任何两个多边形，同时保持它们的顶点集不受影响。我们在该图及其许多子图中的连通性上证明了几个结果。我们对格点多面体引起的几个子图族特别感兴趣，例如由n或n的格点多面体引起的子图。$ñ+\mathrm{1个}$ 顶点，展现出令人着迷的特性。