Cremona–Richmond configuration

This duality gives the Tutte–Coxeter graph additional symmetries beyond those of the Cremona–Richmond configuration, which swap the two sides of its bipartition.

[1] The Cremona–Richmond configuration also has a one-parameter family of realizations in the plane with order-five cyclic symmetry.

The specific incidence pattern of Schläfli's lines and planes was later published by Luigi Cremona (1868).

H. F. Baker used the four-dimensional realization of this configuration as the frontispiece for two volumes of his 1922–1925 textbook, Principles of Geometry.

Zacharias (1951) also rediscovered the same configuration, and found a realization of it with order-five cyclic symmetry.

[3] The name of the configuration comes from the studies of it by Cremona (1868, 1877) and Richmond (1900); perhaps due to some mistakes in his work, the contemporaneous contribution of Martinetti fell into obscurity.