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Desmic Surface

Let $\Delta_1$, $\Delta_2$, and $\Delta_3$ be tetrahedra in projective 3-space $\Bbb{P}^3$. Then the tetrahedra are said to be desmically related if there exist constants $\alpha$, $\beta$, and $\gamma$ such that


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


for desmically related tetrahedra $\Delta_1$, $\Delta_2$, and $\Delta_3$. Desmic surfaces have 12 Ordinary Double Points, which are the vertices of three tetrahedra in 3-space (Hunt).

See also Quartic Surface


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 Eric W. Weisstein