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

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...

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...

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

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...

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...

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...

5 cells. Bring's curve is a Riemann surface of genus four, whose fundamental polygon is a regular hyperbolic twenty-sided icosagon, with an area equal...

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...

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...

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:...

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...

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

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...

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

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...

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

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...

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

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

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

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...

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...

n\geq 0} .[citation needed] To prove this theorem one constructs a fundamental polygon of the surface: This can be done by using the simplicial structure...

the fundamental theorem of linear programming states, in a weak formulation, that the maxima and minima of a linear function over a convex polygonal region...

polygon can be constructed from triangles. All other graphic elements are built up from these primitives. In three dimensions, triangles or polygons positioned...

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

Peter Gustav Lejeune Dirichlet). Voronoi cells are also known as Thiessen polygons, after Alfred H. Thiessen. Voronoi diagrams have practical and theoretical...

divided by 2π. In polygons, the turning number is referred to as the polygon density. For convex polygons, and more generally simple polygons (not self-intersecting)...