Let ,, and be tetrahedra in projective three-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 three-space (Hunt 1996).