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).

**References**

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

Jessop, C. §13 in *Quartic Surfaces with Singular Points.* Cambridge, England: Cambridge University Press, 1916.

© 1996-9

1999-05-24