geometry, an affine-regular polygon or affinely regular polygon is a polygon that is related to a regular polygon by an affine transformation. Affine transformations...

having vanishing geodesic curvature. More generally, in the presence of an affine connection, a geodesic is defined to be a curve whose tangent vectors remain...

unlike in the affine case, the midpoint between two points may not be uniquely determined. Center (geometry) § Projective conics Midpoint polygon Bisection...

fully, say that a collection P of affine subspaces (or flats) of a complex unitary space V of dimension n is a regular complex polytope if it meets the...

an n-dimensional polytope or n-polytope. For example, a two-dimensional polygon is a 2-polytope and a three-dimensional polyhedron is a 3-polytope. In...

area as a given polygon, and regular polygons of 3, 4, or 5 sides: p. xi  (or one with twice the number of sides of a given polygon: pp. 49–50 ). But...

(1980). "Napoleon's theorem and the parallelogram inequality for affine-regular polygons". The American Mathematical Monthly. 87 (8): 644–648. doi:10.1080/00029890...

vertices on the surface of a cylinder. Regular infinite skew polygons exist in the Petrie polygons of the affine and hyperbolic Coxeter groups. They are...

the k + 1 points u 0 , … , u k {\displaystyle u_{0},\dots ,u_{k}} are affinely independent, which means that the k vectors u 1 − u 0 , … , u k − u 0 {\displaystyle...

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

figures. In 1926 John Flinders Petrie took the concept of a regular skew polygons, polygons whose vertices are not all in the same plane, and extended...

condition for similarity of polygons is that corresponding sides and diagonals are proportional. For given n, all regular n-gons are similar. Several...

circle as the limit of a sequence of regular polygons with an increasing number of sides. The area of a regular polygon is half its perimeter multiplied by...

of regular polygons, form the series I2(p), for p ≥ 3. In three dimensions, the symmetry group of the regular dodecahedron and its dual, the regular icosahedron...

(or regular) does not depend on the choice of a coordinate system in An. When a coordinate system is chosen, the regular functions on the affine n-space...

For instance: The affine hull is the smallest affine subspace of a Euclidean space containing a given set, or the union of all affine combinations of points...

a net of a polyhedron is an arrangement of non-overlapping edge-joined polygons in the plane which can be folded (along edges) to become the faces of the...

Geometry is one of the oldest mathematical sciences. Absolute geometry Affine geometry Algebraic geometry Analytic geometry Birational geometry Complex...

include: Circle, Square, Triangle, Rectangle, Oval, Star (polygon), Rhombus, Semicircle. Regular polygons starting at pentagon follow the naming convention of...

as one of the five Platonic solids, a polyhedron in which all the regular polygons are congruent and the same number of faces meet at each vertex. Every...

be easily generalized. All results stated for a regular polygon also hold for affine-regular polygons; in particular, results concerning the unit square...

full circle (360°), then the result is the helical equivalent of a regular polygon. This case is called n-fold helical symmetry, where n = 360° (such...

hyperbolic if it is neither of finite nor affine type, but every proper connected subdiagram is of finite or affine type. A hyperbolic Coxeter group is compact...

ἕδρον (-hedron)  'base, seat') is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. The term "polyhedron"...

n-dimensional affine subspace. It is homogeneous. An affine space need not be included into a linear space, but is isomorphic to an affine subspace of a...

space as a three-dimensional affine space E ( 3 ) {\displaystyle E(3)} over the real numbers. This is unique up to affine isomorphism. It is sometimes...

Buekenhout geometry Coxeter group (B, N) pair Affine Hecke algebra Bruhat decomposition Generalized polygon Mostow rigidity Coxeter complex Weyl distance...

numbers are required to determine the position of each point. It is an affine space, which includes in particular the concept of parallel lines. It has...

and their common intersection is called the vertex of the pencil. In any affine space (including a Euclidean space) the set of lines parallel to a given...

polytopes) a stronger definition is used: only the regular polygons are considered as uniform, disallowing polygons that alternate between two different lengths...