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...

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...

a regular polygon in orthogonal projection. In the infinite limit regular skew polygons become skew apeirogons. A non-convex regular polygon is a regular...

In geometry, a skew apeirohedron is an infinite skew polyhedron consisting of nonplanar faces or nonplanar vertex figures, allowing the figure to extend...

distribution Skew field or division ring Skew-Hermitian matrix Skew lattice Skew polygon, whose vertices do not lie on a plane Infinite skew polyhedron Skew-symmetric...

In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon in which every n – 1 consecutive sides (but no n) belongs to one...

in a "zigzag line" form by using seismograph. Serpentine shape Infinite skew polygon Liberman, Anatoly (2009). Word Origins...And How We Know Them: Etymology...

self-intersecting polygons. Some sources also consider closed polygonal chains in Euclidean space to be a type of polygon (a skew polygon), even when the...

Ancient Greek ἄπειροv apeiron 'infinite, boundless' and γωνία gonia 'angle') or infinite polygon is a polygon with an infinite number of sides. Apeirogons...

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 skew polygons, vertices zig-zagging between two planes. Finite regular skew polyhedra exist in 4-space. These finite regular skew polyhedra...

polygons there are infinitely many regular skew polygons. Skew polygons can be created via the blending operation. The blend of two polygons P and Q, written...

looked at skew vertex figures which created new 4-dimensional regular polyhedra, and much later Branko Grünbaum looked at regular skew faces. Infinite regular...

because they have infinitely many cells. Among these, there are regular forms including the regular skew polyhedra and the infinite series of tilings...

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...

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...

segments come together, such as at the corners of triangles and other polygons. An angle can be considered as the region of the plane bounded by the sides...

Polyhedron Stereoscopy (3-D imaging) 3-manifold Axis of rotation Knots Skew lines Skew polygon Volume 4 dimensions Spacetime Fourth spatial dimension Convex regular...

known as the "Petrie polygon" and has many applications. The Petrie polygon of a regular polyhedron can be defined as the skew polygon (whose vertices do...

bifrustum Hexagonal truncated trapezohedron Hill tetrahedron Holyhedron Infinite skew polyhedron Jessen's icosahedron Near-miss Johnson solid Parallelepiped...

any dimension bivectors can be identified with skew-symmetric matrices, so the product between a skew-symmetric matrix and vector is equivalent to the...

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...

with infinitely many faces. Examples of apeirohedra include: tilings or tessellations of the plane, and sponge-like structures called infinite skew polyhedra...

Regular skew polyhedron Abstract polytope 11-cell 57-cell Convex polygon Concave polygon Constructible polygon Cyclic polygon Equiangular polygon Equilateral...

segment's end points are vertices of a polygon or polyhedron, the line segment is either an edge (of that polygon or polyhedron) if they are adjacent vertices...

self-intersecting and topologically self-dual. Projective polyhedron Skew apeirohedron (infinite skew polyhedron) Spherical polyhedron Toroidal graph Whiteley (1979);...

equivalent ways. If a polygon in the Euclidean plane satisfies any one of the following criteria, it satisfies all of them: A square is a polygon with four equal...

dimensions Regular polytope, a generalization of a regular polygon to higher dimensions Regular skew polyhedron Axiom of Regularity, also called the Axiom...

polyhedra, and faces are regular polygons. There are 47 non-prismatic convex uniform 4-polytopes. There are two infinite sets of convex prismatic forms...

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...