In mathematics, a fundamental polygon can be defined for every compact Riemann surface of genus greater than 0. It encodes not only information about...

simple closed curve c on S. Consider the torus represented by a fundamental polygon with edges a and b T 2 ≅ R 2 / Z 2 . {\displaystyle \mathbb {T} ^{2}\cong...

solid polygons, a polygon may refer only to a simple polygon or to a solid polygon. A polygonal chain may cross over itself, creating star polygons and...

1882 by the mathematician Felix Klein. The following square is a fundamental polygon of the Klein bottle. The idea is to 'glue' together the corresponding...

over the fundamental domain, when integrating functions with poles and zeros on the boundary of the domain. Free regular set Fundamental polygon Brillouin...

from a fundamental polygon of a surface turns out to be the sole relation in a presentation of the fundamental group of the surface with the polygon edge...

Riemann surface by associating sides of a hyperbolic icosagon (see fundamental polygon). The identification pattern is given in the adjoining diagram. The...

sporadic groups. An icosagon is a polygon with 20 edges. Bring's curve is a Riemann surface, whose fundamental polygon is a regular hyperbolic icosagon...

two projective planes creates the Klein bottle. The article on the fundamental polygon describes the higher non-orientable surfaces. Real projective space...

Used in raytracing Low poly Polygon, for general polygon information Polygon mesh, for polygon object representation Polygon modeling Bailey, Kat (Apr 18...

20-sided icosagon. By the Gauss-Bonnet theorem, the area of this fundamental polygon is equal to 12 π {\displaystyle 12\pi } . Twelve is the smallest...

together, described as a fundamental polygon ABA−1B−1. The fundamental group of the torus is just the direct product of the fundamental group of the circle...

polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may...

construction of surfaces of the genus g is given in the article on the fundamental polygon. Genus of orientable surfaces Planar graph: genus 0 Toroidal graph:...

Kampen theorem for the fundamental group, and a precise relation exists for homology of dimension one. Similarly to the fundamental group or the higher homotopy...

relation. the Kleinian model, an analogous construction for 3-manifolds Fundamental polygon Matsuzaki, K.; Taniguchi, M.: Hyperbolic manifolds and Kleinian groups...

together, the control points form a polygonal chain called a control polygon. Polygonal chains are also a fundamental data type in computational geometry...

expresses the structure of the fundamental group of a topological space X {\displaystyle X} in terms of the fundamental groups of two open, path-connected...

of the fundamental polygon found using the Gauss–Bonnet theorem. We can say the area of the whole triangle is equal to the number of fundamental triangles...

Topologically a rectangle is the fundamental polygon of a torus, with opposite edges sewn together....

petals, namely the boundary of a fundamental polygon. A rose can have infinitely many petals, leading to a fundamental group which is free on infinitely...

Euclidean spaces, is described by the theory of Caccioppoli sets. Polygons are fundamental to determining perimeters, not only because they are the simplest...

singular generator point inside of the fundamental domain. A planar symmetry group has a polygonal fundamental domain and can be represented by its group...

torsion-free homology class. This corresponds to the fact that in the fundamental polygon of the Klein bottle, only one pair of sides is glued with a twist...

computer graphics, a texel, texture element, or texture pixel is the fundamental unit of a texture map. Textures are represented by arrays of texels representing...

as polygons, and one approach to preparation for electron-beam lithography is to decompose these polygon regions into fundamental figures. Polygon decomposition...

be triangulated and then using the triangulation to construct a fundamental polygon for the surface. Giving spaces simplicial structures can help to...

A megagon or 1,000,000-gon (million-gon) is a circle-like polygon with one million sides (mega-, from the Greek μέγας, meaning "great", being a unit prefix...

Greek πέντε (pente) 'five' and γωνία (gonia) 'angle') is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°....

the facets. The Petrie polygon of a regular polygon is the regular polygon itself; that of a regular polyhedron is a skew polygon such that every two consecutive...