# Category: Configurations (geometry)

Pappus configuration
In geometry, the Pappus configuration is a configuration of nine points and nine lines in the Euclidean plane, with three points per line and three lines through each point.
Reye configuration
In geometry, the Reye configuration, introduced by Theodor Reye, is a configuration of 12 points and 16 lines.Each point of the configuration belongs to four lines, and each line contains three points
In mathematics, specifically in incidence geometry and especially in projective geometry, a complete quadrangle is a system of geometric objects consisting of any four points in a plane, no three of w
Miquel configuration
In geometry, the Miquel configuration is a configuration of eight points and six circles in the Euclidean plane, with four points per circle and three circles through each point.Its Levi graph is the
Tutte–Coxeter graph
In the mathematical field of graph theory, the Tutte–Coxeter graph or Tutte eight-cage or Cremona–Richmond graph is a 3-regular graph with 30 vertices and 45 edges. As the unique smallest cubic graph
Danzer's configuration
In mathematics, Danzer's configuration is a self-dual configuration of 35 lines and 35 points, having 4 points on each line and 4 lines through each point. It is named after the German geometer Ludwig
Fano plane
In finite geometry, the Fano plane (after Gino Fano) is a finite projective plane with the smallest possible number of points and lines: 7 points and 7 lines, with 3 points on every line and 3 lines t
Perles configuration
In geometry, the Perles configuration is a system of nine points and nine lines in the Euclidean plane for which every combinatorially equivalent realization has at least one irrational number as one
Möbius–Kantor configuration
In geometry, the Möbius–Kantor configuration is a configuration consisting of eight points and eight lines, with three points on each line and three lines through each point. It is not possible to dra
Kummer configuration
In geometry, the Kummer configuration, named for Ernst Kummer, is a geometric configuration of 16 points and 16 planes such that each point lies on 6 of the planes and each plane contains 6 of the poi
Schläfli double six
In geometry, the Schläfli double six is a configuration of 30 points and 12 lines, introduced by Schläfli . The lines of the configuration can be partitioned into two subsets of six lines: each line i
Gray graph
In the mathematical field of graph theory, the Gray graph is an undirected bipartite graph with 54 vertices and 81 edges. It is a cubic graph: every vertex touches exactly three edges. It was discover
Möbius configuration
In geometry, the Möbius configuration or Möbius tetrads is a certain configuration in Euclidean space or projective space, consisting of two mutually inscribed tetrahedra: each vertex of one tetrahedr
Klein configuration
In geometry, the Klein configuration, studied by Klein, is a geometric configuration related to Kummer surfaces that consists of 60 points and 60 planes, with each point lying on 15 planes and each pl
Desargues configuration
In geometry, the Desargues configuration is a configuration of ten points and ten lines, with three points per line and three lines per point. It is named after Girard Desargues. The Desargues configu
Cremona–Richmond configuration
In mathematics, the Cremona–Richmond configuration is a configuration of 15 lines and 15 points, having 3 points on each line and 3 lines through each point, and containing no triangles. It was studie
Hesse configuration
In geometry, the Hesse configuration, introduced by Colin Maclaurin and studied by Hesse, is a configuration of 9 points and 12 lines with three points per line and four lines through each point. It c
Levi graph
In combinatorial mathematics, a Levi graph or incidence graph is a bipartite graph associated with an incidence structure. From a collection of points and lines in an incidence geometry or a projectiv
Grünbaum–Rigby configuration
In geometry, the Grünbaum–Rigby configuration is a symmetric configuration consisting of 21 points and 21 lines, with four points on each line and four lines through each point. Originally studied by
Sylvester–Gallai configuration
In geometry, a Sylvester–Gallai configuration consists of a finite subset of the points of a projective space with the property that the line through any two of the points in the subset also passes th
Configuration (geometry)
In mathematics, specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point is incident to the same numbe
Similarity system of triangles
A similarity system of triangles is a specific configuration involving a set of triangles. A set of triangles is considered a configuration when all of the triangles share a minimum of one incidence r