Incidence geometry (structure)

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An incidence geometry is a mathematical structure composed of objects of various types and an incidence relation between them. The number of types of object used in the structure is called the rank of the incidence geometry.

Incidence geometries can be modelled by vertex-colored graphs. In such a model, the colors correspond to the object types, and adjacent vertices of G correspond to incident objects.

Incidence geometries of rank two are also known as incidence structures.

[edit] Examples

• An abstract polytope can be regarded as an incidence geometry.
• A map on a surface is a rank-3 incidence geometry.

[edit] See also

• Projective configuration
• Levi graph

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