Lattices composed of Clifford point–circle configurations provide a geometric representation of the discrete Schwarzian KP (dSKP) equation. Based on an An perspective on such lattices, it is shown that their integrability, and hence that of the dSKP equation, is a consequence of a conformal generalization of the classical Desargues theorem of projective geometry.
King, A. D., & Schief, W. K. (2012). Clifford lattices and a conformal generalization of Desargues' theorem. Journal of Geometry and Physics, 62(5), 1088-1096. https://doi.org/10.1016/j.geomphys.2011.12.009