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The red edges of this tetragonal disphenoid represent a regular zig-zag skew quadrilateral.
In geometry, a skew polygon is a polygon whose vertices are not all coplanar.[1] Skew polygons must have at least four vertices. The interior surface (or area) of such a polygon is not uniquely defined.
Skew infinite polygons (apeirogons) have vertices which are not all colinear.
A zig-zag skew polygon or antiprismatic polygon[2] has vertices which alternate on two parallel planes, and thus must be even-sided.
Regular skew polygons in 3 dimensions (and regular skew apeirogons in two dimensions) are always zig-zag.
^Coxeter 1973, §1.1 Regular polygons; "If the vertices are all coplanar, we speak of a plane polygon, otherwise a skew polygon."
In geometry, a skewpolygon is a polygon whose vertices are not all coplanar. Skewpolygons must have at least four vertices. The interior surface (or...
an infinite skewpolygon or skew apeirogon is an infinite 2-polytope with vertices that are not all colinear. Infinite zig-zag skewpolygons are 2-dimensional...
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...
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 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...
quasitruncations: t{12/11}={24/11}, and t{12/7}={24/7}. A skew icositetragon is a skewpolygon with 24 vertices and edges but not existing on the same plane...
up to 16-fold rotations and chiral forms in reflection. A skew hexadecagon is a skewpolygon with 24 vertices and edges but not existing on the same plane...
are infinitely many regular skewpolygons. Skewpolygons can be created via the blending operation. The blend of two polygons P and Q, written P#Q, can...
triangular antiprism) have regular skew hexagons as petrie polygons. The regular skew hexagon is the Petrie polygon for these higher dimensional regular...
symmetry. The polygons on the perimeter of these projections are regular skew decagons. The regular skew decagon is the Petrie polygon for many higher-dimensional...
distribution Skew field or division ring Skew-Hermitian matrix Skew lattice Skewpolygon, whose vertices do not lie on a plane Infinite skew polyhedron Skew-symmetric...
is a skewpolygon with 12 vertices and edges but not existing on the same plane. The interior of such a dodecagon is not generally defined. A skew zig-zag...
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...
squares and rhombs are used in the Ammann–Beenker tilings. A skew octagon is a skewpolygon with eight vertices and edges but not existing on the same plane...
are regular skewpolygons, vertices zig-zagging between two planes. Finite regular skew polyhedra exist in 4-space. These finite regular skew polyhedra...
figures. In 1926 John Flinders Petrie took the concept of a regular skewpolygons, polygons whose vertices are not all in the same plane, and extended it to...
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...
Flinders Petrie generalized the concept of regular skewpolygons (nonplanar polygons) to regular skew polyhedra. Coxeter offered a modified Schläfli symbol...
surface. Skew apeirohedra have also been called polyhedral sponges. Many are directly related to a convex uniform honeycomb, being the polygonal surface...
a "zigzag line" form by using seismograph. Serpentine shape Infinite skewpolygon Liberman, Anatoly (2009). Word Origins...And How We Know Them: Etymology...
rectangle with two equal opposite sides and two diagonals of a square. Skewpolygon Coxeter, H.S.M., M. S. Longuet-Higgins and J.C.P Miller, Uniform Polyhedra...
or less. A skewpolygon is a polygon whose vertices are not coplanar. Such a polygon must have at least four vertices; there are no skew triangles. A...
5/2-antiprisms. Grand antiprism, a four-dimensional polytope Skewpolygon, a three-dimensional polygon whose convex hull is an antiprism N.W. Johnson: Geometries...
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...
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...
generate a compound regular skewpolygon, with 3 skew squares. Each tetrahedron contains one skew square. This regular compound polygon containing the same symmetry...
apeiros 'infinite, boundless', and γωνία gonia 'angle') or infinite polygon is a polygon with an infinite number of sides. Apeirogons are the rank 2 case...
rotates around the prism's centerline and breaks the square faces into skewpolygons. Each square face can be re-triangulated with two triangles to form...
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