In projective geometry, a desmic system () is a set of three tetrahedra in 3-dimensional projective space, such that any two are desmic (related such that each edge of one cuts a pair of opposite edges of the other). It was introduced by . The three tetrahedra of a desmic system are contained in a pencil of quartic surfaces.
Every line that passes through two vertices of two tetrahedra in the system also passes through a vertex of the third tetrahedron. The 12 vertices of the desmic system and the 16 lines formed in this way are the points and lines of a Reye configuration.
The three tetrahedra given by the equations
form a desmic system, contained in the pencil of quartics
for a + b + c = 0.