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词汇 Schlegel diagram
分类 英语词汇 英语翻译词典
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Schlegel diagram

英语百科

Schlegel diagram

Examples colored by the number of sides on each face. Yellow triangles, red squares, and green pentagons.
A tesseract projected into 3-space as a Schlegel diagram. There are 8 cubic cells visible, one in the center, one below each of the six exterior faces, and the last one is inside-out representing the space outside the cubic boundary.

In geometry, a Schlegel diagram is a projection of a polytope from R^d into R^{d-1} through a point beyond one of its facets or faces. The resulting entity is a polytopal subdivision of the facet in R^{d-1} that is combinatorially equivalent to the original polytope. Named for Victor Schlegel, who in 1886 introduced this tool for studying combinatorial and topological properties of polytopes. In dimensions 3 and 4, a Schlegel diagram is a projection of a polyhedron into a plane figure and a projection of a 4-polytope to 3-space, respectively. As such, Schlegel diagrams are commonly used as a means of visualizing four-dimensional polytopes.

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