Projective geometry

Desmic system

In projective geometry, a desmic system (from Greek δεσμός 'band, chain') 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 Stephanos. 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. (Wikipedia).

Desmic system
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Related pages

Edge (geometry) | Projective space | Journal of Combinatorial Theory | Projective geometry | Reye configuration | Quartic surface | Tetrahedron