Let Δ_1, Δ_2, and Δ_3 be tetrahedra in projective three-space P^3. Then the tetrahedra are said to be desmically related if there exist constants α, β, and γ such that αΔ_1 + βΔ_2 + γΔ_3 = 0. A desmic surface is then defined as a quartic surface which can be written as a Δ_1 + b Δ_2 + c Δ_3 = 0 for desmically related tetrahedra Δ_1, Δ_2, and Δ_3. Desmic surfaces have 12 ordinary double points, which are the vertices of three tetrahedra in three-space.
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