special cases projective planes (generalized triangles, n = 3) and generalized quadrangles (n = 4). Many generalized polygons arise from groups of Lie type...

geometries which they called near polygons. These structures generalise the notion of generalized polygon as every generalized 2n-gon is a near 2n-gon of a...

geometric progression and let the sides be a, ar, ar2, ar3. Then the generalized polygon inequality requires that 0 < a < a r + a r 2 + a r 3 0 < a r < a...

4-gon is a generalized quadrangle (possibly degenerate). Every finite generalized polygon except the projective planes is a near polygon. Any connected...

In geometry, a generalized polygon can be called a polygram, and named specifically by its number of sides. All polygons are polygrams, but they can also...

Concave polygon Constructible polygon Convex polygon Cyclic polygon Equiangular polygon Equilateral polygon Penrose tile Polyform Regular polygon Simple...

be viewed as a representation of a graph with two vertices, see "Generalized polygon". A regular digon has both angles equal and both sides equal and...

around the polygon makes one full turn, so the sum of the exterior angles must be 360°. This argument can be generalized to concave simple polygons, if external...

current top 20 generalized Fermat primes and the current top 100 generalized Fermat primes. Constructible polygon: which regular polygons are constructible...

vertices of a star polygon. They include the Petersen graph and generalize one of the ways of constructing the Petersen graph. The generalized Petersen graph...

Fermat theorem on polygonal numbers" in the Annals of Mathematics, "Representation by Extended Polygonal Numbers and by Generalized Polygonal Numbers" and...

regular polygon, while there are no faces. 2D orthogonal projections of complex polygons 2{r}q Polygons of the form 2{4}q are called generalized orthoplexes...

2 are precisely the generalized polygons, and a plethora of examples exist. (There are free constructions of infinite generalized n-gons for every n ≥...

projective plane. Discrete space Finite space Generalized polygon Incidence geometry Linear space (geometry) Near polygon Partial geometry Polar space Laywine...

In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called...

geometry, an equilateral polygon is a polygon which has all sides of the same length. Except in the triangle case, an equilateral polygon does not need to also...

tiling Apeirogonal prism Apeirogonal antiprism Teragon, a fractal generalized polygon that also has infinitely many sides McMullen & Schulte (2002) provide...

{C} } ^{n}} . A p-generalized n-orthoplex has pn vertices. Generalized orthoplexes have regular simplexes (real) as facets. Generalized orthoplexes make...

yielding the groups directly. In the rank-2 case spherical building are generalized n-gons, and in joint work with Richard Weiss he classified these when...

establishing a common relation between them. However, the parts cannot be generalized into a whole—until a common relation is established among all parts....

} An equilateral polygon is a polygon which has all sides of the same length (for example, a rhombus is a 4-sided equilateral polygon). To calculate the...

York: Dover, 1973. (sec 2.6 Petrie Polygons pp. 24–25, and Chapter 12, pp. 213–235, The generalized Petrie polygon ) Coxeter, H.S.M. (1974) Regular complex...

polygon is a closed polygonal chain in Euclidean space. It is a figure similar to a polygon except its vertices are not all coplanar. While a polygon...

directions in which a given simple polygon is monotone. It was generalized to report all ways to decompose a simple polygon into two monotone chains (possibly...

Buekenhout, Francis (2000), Prehistory and History of Polar Spaces and of Generalized Polygons (PDF) Buekenhout, Francis; Cohen, Arjeh M. (2013), Diagram Geometry:...

these operations has the same circumcenter of mass as the original polygon. The generalized Euler line makes other appearances in the theory of integrable...

has multiple proofs, and can be generalized to formulas for certain kinds of non-simple polygons. Suppose that a polygon has integer coordinates for all...

Things, ISBN 978-1-56881-220-5 (Chapter 20, Generalized Schaefli symbols, Types of symmetry of a polygon pp. 275–278) The Lighter Side of Mathematics:...

projective plane. Combinatorial design Difference set Incidence structure Generalized polygon Projective geometry Non-Desarguesian plane Smooth projective plane...

of a polygon is the number of times that the polygonal boundary winds around its center. For convex polygons, and more generally simple polygons (not...