Configuration (geometry) - Notation

Notation

A configuration in the plane is denoted by (pγ π), where p is the number of points, the number of lines, γ the number of lines per point, and π the number of points per line. These numbers necessarily satisfy the equation

as this product is the number of point-line incidences.

The notation (pγ π) does not determine a projective configuration up to incidence isomorphism. For instance, there exist three different (93 93) configurations: the Pappus configuration and two less notable configurations.

In some configurations, p = and γ = π. These are called symmetric configurations and the notation is often condensed to avoid repetition. For example (93 93) abbreviates to (93).

Read more about this topic:  Configuration (geometry)

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