Schlegel Diagram

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In geometry, a Schlegel diagram is a projection of a polytope from Rd into Rd ¿ 1 through a point beyond one of its facets. The resulting entity is a polytopal subdivision of the facet in Rd ¿ 1 that is combinatorially equivalent to the original polytope. At the beginning of the 20th century, Schlegel diagrams were an important 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 polychoron to 3-space, respectively. As such, Schlegel diagrams are commonly used as a means of visualizing four-dimensional polytopes.