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).