Desmic system
![Two desmic tetrahedra. The third tetrahedron of this system is not shown, but has one vertex at the center and the other three on the plane at infinity.](/Images/godic/202501/08/Compound_of_two_tetrahedra2534.png")
![The Reye configuration with the same 12 vertices as a desmic system](/Images/godic/202501/08/Reye_configuration.svg2534.png")
In projective geometry, a desmic system is a set of three tetrahedra in 3-dimensional projective space, such that any two are desmic, (i.e. related such that each edge of one cuts a pair of opposite edges of the other). It was introduced by Stephanos (1879). The three tetrahedra of a desmic system are contained in a pencil of quartic surfaces. The name "desmic" comes from the Greek word δεσμός, meaning band or chain, referring to the pencil of quartics.