Schlegel diagram

In geometry, a Schlegel diagram is a projection of a polytope from ${\displaystyle R^{d}}$ into ${\displaystyle R^{d-1}}$ through a point beyond one of its facets or faces. The resulting entity is a polytopal subdivision of the facet in ${\displaystyle R^{d-1}}$ 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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