Schlegel diagram

Examples colored by the number of sides on each face. Yellow triangles, red squares, and green pentagons.

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.

单词	Schlegel diagram
释义	Schlegel diagram 英语百科 Schlegel diagram 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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