English

A Schlegel diagram of a 120-cell

Noun

Schlegel diagram ‎(plural Schlegel diagrams)

1. (geometry) A projection of a polytope from n-dimensional space to n-1 dimensions through a point beyond one of its faces; especially such a projection (itself represented in 2 dimensions) of a 3- or 4-dimensional polytope.
   • 1999, R. B. King, 1: Topology in Chemistry, D Bonchev, D.H Rouvray (editors), Chemical Topology: Introduction and Fundamentals, page 21,

     The location of the point x₀ can always be chosen so that the edges in the Schlegel diagram can be drawn as non-intersecting straight lines.

   • 2002, Ian David Brown, The Chemical Bond in Inorganic Chemistry: The Bond Valence , page 150,

     Schlegel diagrams are a useful way to explore how these polyhedra can be linked (Hoppe and Köhler 1988).

   • 2013, Arthur L. Loeb, 5: Polyhedra: Surfaces or Solids?, Marjorie Senechal (editor), Shaping Space: Exploring Polyhedra in Nature, Art, and the Geometrical Imagination, page 69,

     These structures may all be represented on a planar surface by their Schlegel diagrams. A polyhedron Schlegel diagram is its networks of edges and vertices drawn in a special way: if you hold the polyhedron so close to your face that one of faces frames the entire polyhedron and you see all the other edges meeting inside that frame, then you have a Schlegel diagram.

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