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Every flag of the configuration (an incident point-line pair) can be taken to every other flag by a symmetry in this group. [1] The Cremona–Richmond configuration is self-dual: it is possible to exchange points for lines while preserving all the incidences of the configuration. This duality gives the Tutte–Coxeter graph additional ...
It is also self-dual, meaning that if the points are replaced by lines and vice versa using projective duality, the same configuration results. Graphs associated with the Desargues configuration include the Desargues graph (its graph of point-line incidences) and the Petersen graph (its graph of non-incident lines).
A collineation, automorphism, or symmetry of the Fano plane is a permutation of the 7 points that preserves collinearity: that is, it carries collinear points (on the same line) to collinear points. By the Fundamental theorem of projective geometry , the full collineation group (or automorphism group , or symmetry group ) is the projective ...
Configurations (4 3 6 2) (a complete quadrangle, at left) and (6 2 4 3) (a complete quadrilateral, at right).. 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 number of lines and each line is incident to the same number of points.
The number of non-absolute points (lines) incident with a non-absolute line (point) is even. Furthermore, [18] The polarity π has at least n + 1 absolute points and if n is not a square, exactly n + 1 absolute points. If π has exactly n + 1 absolute points then; if n is odd, the absolute points form an oval whose tangents are the absolute ...
The Pappus graph. The Levi graph of the Pappus configuration is known as the Pappus graph.It is a bipartite symmetric cubic graph with 18 vertices and 27 edges. [3]Adding three more parallel lines to the Pappus configuration, through each triple of points that are not already connected by lines of the configuration, produces the Hesse configuration.
The axis of symmetry of a two-dimensional figure is a line such that, if a perpendicular is constructed, any two points lying on the perpendicular at equal distances from the axis of symmetry are identical. Another way to think about it is that if the shape were to be folded in half over the axis, the two halves would be identical as mirror ...
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. [9] Such a drawing is called a plane graph or planar embedding of the graph.