Flail diagram

Flail diagram of the tetrahedron

Schlegel diagram of the hexahedron (cube)

Schlegel diagram of the octahedron

The Schlegel diagram , after Victor Schlegel (1843–1905), is a two-dimensional representation of the structure of the corners , edges and side surfaces of a three-dimensional polyhedron . Each corner of the body appears as a point in the Schlegel diagram, each edge as a line . The side surfaces of the body appear as a polygon surrounded by edges - with the exception of one side surface of the body, which corresponds to the area in the Schlegel diagram, which is bounded by the edges of the projection surface and which frames the figure.

The Schlegel diagram depicts topological properties of the body, such as the touching of edges and surfaces, but it is not true to length and angle .

The concept can be generalized to a -dimensional representation of the corners, edges and sides of a -dimensional polytope . ${\displaystyle (n-1)}$ ${\displaystyle n}$

literature

• Victor Schlegel: Theory of homogeneously composed spatial structures . In: Nova Acta Leop. Carol. (Negotiations of the Imperial Leopoldine-Carolinian German Academy of Natural Scientists), Volume XLIV, No. 4, W. Engelmann, Leipzig 1883.
• Victor Schlegel: About projection models of regular four-dimensional bodies . Waren, 1886.

Web links

Commons : Schlegel diagrams  - collection of images, videos and audio files

• Eric W. Weisstein : Schlegel diagram . In: MathWorld (English).