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...
9 KB (739 words) - 17:08, 31 March 2025
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...
8 KB (685 words) - 08:01, 6 July 2022
a regular polygon in orthogonal projection. In the infinite limit regular skew polygons become skew apeirogons. A non-convex regular polygon is a regular...
31 KB (3,060 words) - 00:29, 13 July 2025
In geometry, a skew apeirohedron is an infinite skew polyhedron consisting of nonplanar faces or nonplanar vertex figures, allowing the figure to extend...
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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...
37 KB (4,236 words) - 14:28, 13 January 2025
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...
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in a "zigzag line" form by using seismograph. Serpentine shape Infinite skew polygon Liberman, Anatoly (2009). Word Origins...And How We Know Them: Etymology...
3 KB (336 words) - 17:44, 21 May 2025
Apeirogon (redirect from Infinite polygon)
Ancient Greek ἄπειροv apeiron 'infinite, boundless' and γωνία gonia 'angle') or infinite polygon is a polygon with an infinite number of sides. Apeirogons...
10 KB (1,037 words) - 04:50, 7 June 2025
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...
15 KB (936 words) - 06:09, 27 January 2025
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...
32 KB (2,666 words) - 10:07, 13 July 2025
In geometry, a regular skew apeirohedron is an infinite regular skew polyhedron. They have either skew regular faces or skew regular vertex figures. In...
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looked at skew vertex figures which created new 4-dimensional regular polyhedra, and much later Branko Grünbaum looked at regular skew faces. Infinite regular...
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List of regular polytopes (redirect from List of regular polygons)
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...
101 KB (5,453 words) - 12:31, 18 July 2025
Regular polyhedron (section Regular skew apeirohedra)
are regular skew polygons, vertices zig-zagging between two planes. Finite regular skew polyhedra exist in 4-space. These finite regular skew polyhedra...
32 KB (3,128 words) - 14:50, 8 June 2025
Regular polytope (redirect from Infinite polytope)
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...
43 KB (5,355 words) - 03:56, 5 July 2025
John Flinders Petrie (section The Petrie polygon)
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...
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Polyhedron Stereoscopy (3-D imaging) 3-manifold Axis of rotation Knots Skew lines Skew polygon Volume 4 dimensions Spacetime Fourth spatial dimension Convex regular...
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bifrustum Hexagonal truncated trapezohedron Hill tetrahedron Holyhedron Infinite skew polyhedron Jessen's icosahedron Near-miss Johnson solid Parallelepiped...
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any dimension bivectors can be identified with skew-symmetric matrices, so the product between a skew-symmetric matrix and vector is equivalent to the...
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Polytope (section Infinite polytopes)
because they have infinitely many cells. Among these, there are regular forms including the regular skew polyhedra and the infinite series of tilings...
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Polyhedron (redirect from Null polygon)
with infinitely many faces. Examples of apeirohedra include: tilings or tessellations of the plane, and sponge-like structures called infinite skew polyhedra...
96 KB (10,656 words) - 01:16, 15 July 2025
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...
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self-intersecting and topologically self-dual. Projective polyhedron Skew apeirohedron (infinite skew polyhedron) Spherical polyhedron Toroidal graph Whiteley (1979);...
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Quadrilateral (redirect from Skew quadrilateral)
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...
50 KB (7,041 words) - 04:14, 21 July 2025
Angle (section Polygon-related angles)
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...
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dimensions Regular polytope, a generalization of a regular polygon to higher dimensions Regular skew polyhedron Axiom of Regularity, also called the Axiom...
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polyhedra, and faces are regular polygons. There are 47 non-prismatic convex uniform 4-polytopes. There are two infinite sets of convex prismatic forms...
135 KB (4,386 words) - 00:41, 14 July 2025
24-cell (section Related complex polygons)
have a common center. The 24-cell's Petrie polygon is a skew dodecagon {12} and also (orthogonally) a skew dodecagram {12/5} which zig-zags 90° left and...
237 KB (30,663 words) - 21:18, 18 July 2025
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...
28 KB (3,095 words) - 22:12, 28 April 2025
Square (category Constructible polygons)
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...
84 KB (9,050 words) - 06:05, 21 July 2025