self-dual
Adjective
Meaning
(linear algebra) Of a vector space, isomorphic to its dual space.
(mathematics, in projective geometry) Of a proposition that is equivalent to its dual.
(mathematics) Of a graph or polyhedron, being the dual of itself.
Source: en.wiktionary.orgExamples
Each of the tetrahedral compounds is self-dual, and the compound of 5 cubes is dual to the compound of 5 octahedra.
Every polygon is topologically self-dual (it has the same number of vertices as edges, and these are switched by duality), but will not in general be geometrically self-dual (up to rigid motion, for instance).
Dualizing this theorem and the first two axioms in the definition of a projective plane shows that the plane dual structure C* is also a projective plane, called the dual plane of C. If C and C* are isomorphic, then C is called self-dual.
If a correlation exists then the projective plane C is self-dual.
If a polyhedron is self-dual, then the compound of the polyhedron with its dual will comprise congruent polyhedra.
If a polytope has the same number of vertices as facets, of edges as ridges, and so forth, and the same connectivities, then the dual figure will be similar to the original and the polytope is self-dual.