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A notation is a set of well-defined rules for representing quantities and operations with symbols.

Given a planar graph G, a geometric dual graph and combinatorial dual graph can be defined. Whitney showed that these are equivalent (Harary 1994), so that one may speak of ...

A polyhedron that is dual to itself. For example, the tetrahedron is self-dual. Naturally, the skeleton of a self-dual polyhedron is a self-dual graph. Pyramids are ...

A dual bivector is defined by X^~_(ab)=1/2epsilon_(abcd)X^(cd), and a self-dual bivector by X_(ab)^*=X_(ab)+iX^~_(ab).

A number of areas of mathematics have the notion of a "dual" which can be applies to objects of that particular area. Whenever an object A has the property that it is equal ...

Given a vector bundle pi:E->M, its dual bundle is a vector bundle pi^*:E^*->M. The fiber bundle of E^* over a point p in M is the dual vector space to the fiber of E.

The dual of a regular tessellation is formed by taking the center of each polygon as a vertex and joining the centers of adjacent polygons. The triangular and hexagonal ...

By the duality principle, for every polyhedron, there exists another polyhedron in which faces and polyhedron vertices occupy complementary locations. This polyhedron is ...

A self-dual graphs is a graph that is dual to itself. Wheel graphs are self-dual, as are the examples illustrated above. Naturally, the skeleton of a self-dual polyhedron is ...

Given a contravariant basis {e^->_1,...,e^->_n}, its dual covariant basis is given by e^->^alpha·e^->_beta=g(e^->^alpha,e^->_beta)=delta_beta^alpha, where g is the metric and ...