In geometry, a generalized quadrangle is an incidence structure whose main feature is the lack of any triangles (yet containing many quadrangles). A generalized quadrangle is by definition a polar space of rank two. They are the generalized n-gons with n = 4 and near 2n-gons with n = 2. They are also precisely the partial geometries pg(s,t,α) with α = 1.
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a generalizedquadrangle is an incidence structure whose main feature is the lack of any triangles (yet containing many quadrangles). A generalized quadrangle...
special cases projective planes (generalized triangles, n = 3) and generalizedquadrangles (n = 4). Many generalized polygons arise from groups of Lie...
studied as combinatorial objects. A polar space of rank two is a generalizedquadrangle; in this case, in the latter definition, the set of points of a...
n-gon that contains them both. Generalized 3-gons are projective planes. Generalized 4-gons are called generalizedquadrangles. By the Feit-Higman theorem...
continue to be regular and vertex-transitive. H(2,3), which is the generalizedquadrangle G Q (2,1) H(1,q), which is the complete graph Kq H(2,q), which is...
112 and 162 vertices. The former is the colinearity graph of the generalizedquadrangle GQ(3,9). The latter is a strongly regular graph called the local...
line graph of K8, but these four graphs are not isomorphic. Every generalizedquadrangle of order (s, t) gives an srg((s + 1)(st + 1), s(t + 1), s − 1, t...
|{\mathcal {L}}|} . Projective space Affine space Polar space GeneralizedquadrangleGeneralized polygon Near polygon Shult, Ernest E. (2011), Points and Lines...
finite type, via Gabriel's theorem. There is also a link with generalizedquadrangles, as the three non-degenerate GQs with three points on each line...
planes, projective spaces and projective planes, polar spaces, generalizedquadrangles, and partial geometries. A central connecting concept is the "connection...
D. De Caen; G. e. Moorhouse (1999). "The ρ-rank of the Sρ (4,ρ) GeneralizedQuadrangle" (PDF). Archived from the original (PDF) on 2012-06-19. Retrieved...
near polygons. These structures generalise the notion of generalized polygon as every generalized 2n-gon is a near 2n-gon of a particular kind. Near polygons...
linear space which is the unique triple cover with no 8-gons of the generalizedquadrangle GQ(2,2). It is named after R. M. Foster, whose Foster census of...
Beethoven quadrangle is located in the equatorial region of Mercury, in the center of the area imaged by Mariner 10. Most pictures of the quadrangle were obtained...
a plane always intersect. Thus, given four points forming a complete quadrangle, the lines connecting the points cross in an additional three diagonal...
The Tolstoj quadrangle in the equatorial region of Mercury runs from 144 to 216° longitude and -25 to 25° latitude. It was provisionally called "Tir",...
The Borealis quadrangle is a quadrangle on Mercury surrounding the north pole down to 65° latitude. It was mapped in its entirety by the MESSENGER spacecraft...
( t , s , α ) {\displaystyle \mathrm {pg} (t,s,\alpha )} . The generalizedquadrangles are exactly those partial geometries p g ( s , t , α ) {\displaystyle...
formation crops out underlying the Green River Formation. In the Silt Quadrangle of Garfield County, Colorado, the formation overlies the Williams Fork...
(e.g. pentagon). Since "gon" means "angle", it is analogously called a quadrangle, or 4-angle. A quadrilateral with vertices A {\displaystyle A} , B {\displaystyle...
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