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In geometry, an infinite skew polygon or skew apeirogon is an infinite 2-polytope with vertices that are not all colinear. Infinite zig-zag skew polygons are 2-dimensional infinite skew polygons with vertices alternating between two parallel lines. Infinite helical polygons are 3-dimensional infinite skew polygons with 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 constructed a single operator as the composite of all the reflections of the Coxeter group.
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geometry, an infiniteskewpolygon or skew apeirogon is an infinite 2-polytope with vertices that are not all colinear. Infinite zig-zag skewpolygons are 2-dimensional...
such a polygon is not uniquely defined. Skewinfinitepolygons (apeirogons) have vertices which are not all colinear. A zig-zag skewpolygon or antiprismatic...
In geometry, a Petrie polygon for a regular polytope of n dimensions is a skewpolygon in which every n – 1 consecutive sides (but no n) belongs to one...
distribution Skew field or division ring Skew-Hermitian matrix Skew lattice Skewpolygon, whose vertices do not lie on a plane Infiniteskew polyhedron Skew-symmetric...
In geometry, a skew apeirohedron is an infiniteskew polyhedron consisting of nonplanar faces or nonplanar vertex figures, allowing the figure to extend...
length). Regular polygons may be either convex, star or skew. In the limit, a sequence of regular polygons with an increasing number of sides approximates a...
polygons there are infinitely many regular skewpolygons. Skewpolygons can be created via the blending operation. The blend of two polygons P and Q, written...
self-intersecting polygons. Some sources also consider closed polygonal chains in Euclidean space to be a type of polygon (a skewpolygon), even when the...
in a "zigzag line" form by using seismograph. Serpentine shape Infiniteskewpolygon Liberman, Anatoly (2009). Word Origins...And How We Know Them: Etymology...
Ancient Greek ἄπειρος apeiros 'infinite, boundless', and γωνία gonia 'angle') or infinitepolygon is a polygon with an infinite number of sides. Apeirogons...
looked at skew vertex figures which created new 4-dimensional regular polyhedra, and much later Branko Grünbaum looked at regular skew faces. Infinite regular...
direct. An indirect equiangular polygon can include angles turning right or left in any combination. A skew equiangular polygon may be isogonal, but can't...
In geometry, a regular skew apeirohedron is an infinite regular skew polyhedron. They have either skew regular faces or skew regular vertex figures. In...
are regular skewpolygons, vertices zig-zagging between two planes. Finite regular skew polyhedra exist in 4-space. These finite regular skew polyhedra...
In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words quadri...
non-uniform deltahedra. There are infinitely many non-convex examples. Infinite sponge-like examples called infiniteskew polyhedra exist in some of these...
polytopes with infinitely many faces. A simple example of a skew apeirogon would be a zig-zag. It seems to satisfy the definition of a regular polygon — all the...
known as the "Petrie polygon" and has many applications. The Petrie polygon of a regular polyhedron can be defined as the skewpolygon (whose vertices do...
because they have infinitely many cells. Among these, there are regular forms including the regular skew polyhedra and the infinite series of tilings...
5/2-antiprisms. Grand antiprism, a four-dimensional polytope Skewpolygon, a three-dimensional polygon whose convex hull is an antiprism N.W. Johnson: Geometries...
dimensions Regular polytope, a generalization of a regular polygon to higher dimensions Regular skew polyhedron Axiom of Regularity, also called the Axiom...
type of a right symmetric di-n-gonal bipyramid, with a regular zigzag skewpolygon base. A regular right symmetric di-n-gonal scalenohedron has n two-fold...
photo. Correspondingly, one can infinitely zoom in on e.g., a circle arc, and it remains smooth. On the other hand, a polygon representing a curve will reveal...
symmetry group. For example, any abstract polygon is regular, since angles, edge-lengths, edge curvature, skewness etc. do not exist for abstract polytopes...
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