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In mathematics, a regular map is a symmetric tessellation of a closed surface. More precisely, a regular map is a decomposition of a two-dimensional manifold (such as a sphere , torus , or real projective plane ) into topological disks such that every flag (an incident vertex-edge-face triple) can be transformed into any other flag by a ...
The term map may be used to distinguish some special types of functions, such as homomorphisms. For example, a linear map is a homomorphism of vector spaces, while the term linear function may have this meaning or it may mean a linear polynomial. [3] [4] In category theory, a map may refer to a morphism. [2]
In elementary geometry, a face is a polygon [note 1] on the boundary of a polyhedron. [3] [4] Other names for a polygonal face include polyhedron side and Euclidean plane tile. For example, any of the six squares that bound a cube is a face of the cube. Sometimes "face" is also used to refer to the 2-dimensional features of a 4-polytope.
Depending on authors, the term "maps" or the term "functions" may be reserved for specific kinds of functions or morphisms (e.g., function as an analytic term and map as a general term). mathematics See mathematics. multivalued A "multivalued function” from a set A to a set B is a function from A to the subsets of B.
A face of a convex set is a subset of such that is also a convex set, and for any points , in and any real number < < with () + in , and must both be in . [11] For example, C {\displaystyle C} itself and the empty set are faces of C {\displaystyle C} ; these are sometimes called the trivial faces of C {\displaystyle C} .
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The process of face mapping has been around for centuries. Skip to main content. News. Need help? Call us! 800-290-4726. Login / Join. Mail. Downloads; Premium Subscriptions; PC Security ...
Every 4-map graph is a 1-planar graph, a graph that can be drawn with at most one crossing per edge, and every optimal 1-planar graph (a graph formed from a planar quadrangulation by adding two crossing diagonals to every quadrilateral face) is a 4-map graph. However, some other 1-planar graphs are not map graphs, because (unlike map graphs ...