## Desmic Surface

Let , , and be tetrahedra in projective 3-space . Then the tetrahedra are said to be desmically related if there exist constants , , and such that

A desmic surface is then defined as a Quartic Surface which can be written as

for desmically related tetrahedra , , and . Desmic surfaces have 12 Ordinary Double Points, which are the vertices of three tetrahedra in 3-space (Hunt).

Hunt, B. Desmic Surfaces.'' §B.5.2 in The Geometry of Some Special Arithmetic Quotients. New York: Springer-Verlag, pp. 311-315, 1996.