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Polygonal chain whose vertices are not all coplanar
In geometry, a skew polygon is a closed polygonal chain in Euclidean space. It is a figure similar to a polygon except its vertices are not all coplanar
Skew_polygon
Shape with equal angles and equal sides
a regular polygon in orthogonal projection. In the infinite limit regular skew polygons become skew apeirogons. A non-convex regular polygon is a regular
Regular_polygon
Non-planar polygon with infinitely many sides
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_polygon
Plane figure bounded by line segments
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
Polygon
Skew polygon derived from a polytope
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
Petrie_polygon
Infinite regular skew polyhedron
figures. In 1926 John Flinders Petrie took the concept of regular skew polygons, polygons whose vertices are not all in the same plane, and extended it to
Regular_skew_apeirohedron
Topics referred to by the same term
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
Skew
Infinite polyhedron with non-planar faces
surface. Skew apeirohedra have also been called polyhedral sponges. Many are directly related to a convex uniform honeycomb, being the polygonal surface
Skew_apeirohedron
Polygon with 24 edges
quasitruncations: t{12/11}={24/11}, and t{12/7}={24/7}. A skew icositetragon is a skew polygon with 24 vertices and edges but not existing on the same plane
Icositetragon
Polygon with 12 edges
is a skew polygon 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
Dodecagon
are infinitely many regular skew polygons. Skew polygons can be created via the blending operation. The blend of two polygons P and Q, written P#Q, can
List_of_regular_polytopes
Polygon shape with eight sides
squares and rhombs are used in the Ammann–Beenker tilings. A skew octagon is a skew polygon with eight vertices and edges but not existing on the same plane
Octagon
Shape with ten sides
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
Decagon
Shape with six sides
triangular antiprism) have regular skew hexagons as petrie polygons. The regular skew hexagon is the Petrie polygon for these higher dimensional regular
Hexagon
Four-sided polygon
ordinary quadrilaterals to non-planar figures is called a skew quadrilateral, a four-sided skew polygon. Formulas to compute its dihedral angles from the edge
Quadrilateral
Polygon with 16 edges
up to 16-fold rotations and chiral forms in reflection. A skew hexadecagon is a skew polygon with 24 vertices and edges but not existing on the same plane
Hexadecagon
Polygon with equally angled vertices
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
Equiangular_polygon
Connected series of line segments
distinction between a polygonal area and a polygonal chain. A space closed polygonal chain is also known as a skew "polygon". A polygonal chain is called monotone
Polygonal_chain
Polyhedron with non-planar faces
Flinders Petrie generalized the concept of regular skew polygons (nonplanar polygons) to regular skew polyhedra. Coxeter offered a modified Schläfli symbol
Regular_skew_polyhedron
Polyhedron with regular congruent polygons as faces
are regular skew polygons, vertices zig-zagging between two planes. Finite regular skew polyhedra exist in 4-space. These finite regular skew polyhedra
Regular_polyhedron
Topics referred to by the same term
Skew square may refer to: Skewsquare, a plane quadrilateral whose edge midpoints form a square A three-dimensional skew polygon with four equal edge lengths
Skew_square
Developer of 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
John_Flinders_Petrie
Pattern like a row of Ws joined together
a "zigzag line" form by using seismograph. Serpentine shape Infinite skew polygon Liberman, Anatoly (2009). Word Origins...And How We Know Them: Etymology
Zigzag
Four-dimensional analog of the dodecahedron
tesseract, they form zig-zag Petrie polygons instead. The 120-cell's Petrie polygon is a triacontagon {30} zig-zag skew polygon. Since the 120-cell has a circumference
120-cell
Geometric property of objects being in the same plane
or less. A skew polygon is a polygon whose vertices are not coplanar. Such a polygon must have at least four vertices; there are no skew triangles. A
Coplanarity
2-D shapes in which sides intersect
rectangle with two equal opposite sides and two diagonals of a square. Skew polygon Coxeter, H.S.M., M. S. Longuet-Higgins and J.C.P Miller, Uniform Polyhedra
Crossed_polygon
Property of a mathematical space
Polyhedron Stereoscopy (3-D imaging) 3-manifold Axis of rotation Knots Skew lines Skew polygon Volume 4 dimensions Spacetime Fourth spatial dimension Convex regular
Dimension
Form of an object
of shapes with metaphorical names Lists of shapes Shape factor Size Skew polygon Solid geometry Region (mathematics) Kendall, D.G. (1984). "Shape Manifolds
Shape
Flat-sided three-dimensional shape
regular skew apeirohedra originated from the extension of regular skew polygons. These polygons are known for non-planar vertices. John Flinders Petrie, who
Polyhedron
Aspect of topological graph theory
Petrie dual to a regular polyhedron produces a regular map. The number of skew h-gonal faces is g/2h, where g is the group order, and h is the coxeter number
Petrie_dual
Type of closed polygonal chain
closed polygonal chain in three-dimensional space (a skew polygon) that is topologically equal to the unknot but cannot be deformed to a simple polygon when
Stuck_unknot
Polyhedron formed by joining mirroring pyramids base-to-base
type of a right symmetric di-n-gonal bipyramid, with a regular zigzag skew polygon base. A regular right symmetric di-n-gonal scalenohedron has n two-fold
Bipyramid
Polygon able to tessellate edge-to-edge, without rotation
In geometry, a parallelogon is a polygon with parallel opposite sides (hence the name) that can tile a plane by translation (rotation is not permitted)
Parallelogon
Prism with a 3-sided base
rotates around the prism's centerline and breaks the square faces into skew polygons. Each square face can be re-triangulated with two triangles to form
Triangular_prism
Polygon with 18 edges
t{9/2}={18/2}=2{9}. A regular skew octadecagon is the Petrie polygon for a number of higher-dimensional polytopes, shown in these skew orthogonal projections
Octadecagon
Polygon with 14 edges
solutions, q=1..6, are polygons. Regular skew tetradecagons exist as Petrie polygon for many higher-dimensional polytopes, shown in these skew orthogonal projections
Tetradecagon
Polyhedron with parallel bases connected by triangles
antiprism Grand antiprism, a four-dimensional polytope Skew polygon, a three-dimensional polygon whose convex hull is an antiprism Kepler, Johannes (1619)
Antiprism
compound polygons, this notation reduces to {nk}[k{n/m}]{nk}: for example, the hexagram may be written thus as {6}[2{3}]{6}. Regular skew polygons also create
List of regular polytope compounds
List_of_regular_polytope_compounds
Polyhedral compound
generate a compound regular skew polygon, with 3 skew squares. Each tetrahedron contains one skew square. This regular compound polygon containing the same symmetry
Compound_of_three_tetrahedra
Polygon with an infinite number of sides
apeiron 'infinite, boundless' and γωνία gonia 'angle') or infinite polygon is a polygon with an infinite number of sides. Apeirogons are the rank-2 case
Apeirogon
French mathematician (1875–1941)
The next five dealt with surfaces applicable to a plane, the area of skew polygons, surface integrals of minimum area with a given bound, and the final
Henri_Lebesgue
Canadian geometer (1907–2003)
concept of regular skew polygons—where the vertices are not in the same plane—to three-dimensional polyhedra. He found two regular skew apeirohedra, constructed
H._S._M._Coxeter
American hip hop recording artist
Pharrell-ish but lower on the octave scale." Last.fm describes Polygon as "an eclectic mix of indie skewed hip hop and world music. He walks to his own beat and
Johnny_Polygon
Non-convex polyhedron with no triangulation
continuously. This rotation causes the square faces of the triangle to become skew polygons, each of which can be re-triangulated with two triangles to form either
Schönhardt_polyhedron
Polytope or tiling whose vertices are identical
In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries
Isogonal_figure
Polygon with 17 edges
regular heptadecagon is the Petrie polygon for one higher-dimensional regular convex polytope, projected in a skew orthogonal projection: Arthur Jones
Heptadecagon
symmetry orientations between the two color sets. The 3{3}3 polygon can be seen in a regular skew polyhedral net inside a 16-cell, with 8 vertices, 24 edges
Möbius–Kantor_polygon
examples. Vertex the ridge or (n−2)-face of the polygon Edge the facet or (n−1)-face of the polygon Vertex the peak or (n−3)-face of the polyhedron Edge
List of polygons, polyhedra and polytopes
List_of_polygons,_polyhedra_and_polytopes
Cartesian product of two polytopes
constructed from two regular polygons of the same edge length is a uniform duoprism. A duoprism made of n-polygons and m-polygons is named by prefixing 'duoprism'
Duoprism
Regular skew polyhedron Abstract polytope 11-cell 57-cell Convex polygon Concave polygon Constructible polygon Cyclic polygon Equiangular polygon Equilateral
List_of_mathematical_shapes
Mathematical operation on vectors in 3D space
any dimension bivectors can be identified with skew-symmetric matrices, so the product between a skew-symmetric matrix and vector is equivalent to the
Cross_product
Geospatial vector data format
shapefile format can spatially describe vector features: points, lines, and polygons, representing, for example, water wells, rivers, and lakes. Each item usually
Shapefile
Mathematical idealization of the trace left by a moving point
three-dimensional; a skew curve is a space curve which lies in no plane (for example, a helix). These definitions of plane, space and skew curves apply also
Curve
Shape with four equal sides and angles
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
Square
Partition of a toroidal surface into polygons
collections of polygons that meet at their edges and vertices, forming a manifold as they do. That is, each edge should be shared by exactly two polygons, and at
Toroidal_polyhedron
Four-dimensional analog of the icosahedron
triacontagram, a skew 30-gram spiral of 30 edge-bonded triangular faces, that is the Petrie polygon of the 600-cell. The dual of the 30-cell ring (the skew 30-gon
600-cell
(Chapter 5: Regular Skew Polyhedra in three and four dimensions and their topological analogues) Coxeter, H. S. M. Regular Skew Polyhedra in Three and
3-4_duoprism
Upcoming video game
technically be $100, but it's had its cake and ate it too as pre-orders are 'skewing more to the premium edition'". PC Gamer. Archived from the original on
Grand_Theft_Auto_VI
Four-dimensional analog of the octahedron
of the 16-cell's distinct isoclinic rotations. Each eight-edge helix is a skew octagram {8/3} that winds three times around the 16-cell and visits every
16-cell
Generalization of a polytope in real space
polygon is a truncation of a regular polygon. A quasiregular polygon contains alternate edges of the regular polygons and . The quasiregular polygon has
Complex_polytope
Theorem in geometry
even for a skew quadrilateral, and is planar whether the quadrilateral is planar or not. The theorem can be generalized to the midpoint polygon of an arbitrary
Varignon's_theorem
Relationship between two lines that meet at a right angle
the origin to a plane in three-dimensional space Nearest distance between skew lines, for the perpendicular distance between two non-parallel lines in three-dimensional
Perpendicular
Geometric shape formed from squares
Guttmann, Anthony J. (2000). "Statistics of lattice animals (polyominoes) and polygons". Journal of Physics A: Mathematical and General. 33 (29): L257–L263.
Polyomino
Any of 4 regular star polyhedra
compounds with the same edge radius. They also show that the Petrie polygons are skew. Two relationships described in the article below are also easily
Kepler–Poinsot_polyhedron
Type of polyhedron with many holes
edges with quadrilateral-shaped struts. Coxeter later discovered the regular skew polyhedron. Felix Klein discovered the three genera. Together with Robert
Leonardo_polyhedron
Part of a straight line that is bounded by two distinct end points
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
Line_segment
Vector graphics editor
with geometric transformations, such as moving, rotating, scaling, and skewing. Inkscape began in 2003 as a code fork of the Sodipodi project. Sodipodi
Inkscape
Figure formed by two rays meeting at a common point
between two planes (or curved surfaces) from their normal vectors and between skew lines from their vector equations. To define angles in an abstract real inner
Angle
is a 4-polytope that can be constructed using Cartesian product of two polygons. In the case of 3-3 duoprism is the simplest among them, and it can be
3-3_duoprism
Convex polytope, the n-dimensional analogue of a square and a cube
32,24,8,1). An n-cube can be projected inside a regular 2n-gonal polygon by a skew orthogonal projection, shown here from the line segment to the 10-cube
Hypercube
Polytope with highest degree of symmetry
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 edges are the same length
Regular_polytope
5-dimensional hypercube
other elements. The 5-cube is 5th in a series of hypercube: The regular skew polyhedron {4,5| 4} can be realized within the 5-cube, with its 32 vertices
5-cube
Straight path on a curved surface or a Riemannian manifold
Y − ∇ ¯ X Y {\displaystyle D(X,Y)=\nabla _{X}Y-{\bar {\nabla }}_{X}Y} is skew-symmetric, then ∇ {\displaystyle \nabla } and ∇ ¯ {\displaystyle {\bar {\nabla
Geodesic
Pornographic video game mod
clothing or other nudity-blocking elements of their design. Nude mods usually skew towards a male audience, and are often controversial with game developers
Nude_mod
Uniform 6-polytope
regular skew icosahedron {3, 5} with the same symmetries as the icosahedron itself, but at different angles. He dubbed this the regular skew icosahedron
6-demicube
English filmmaker (born 1971)
E. or any of those brilliant super-spy concepts, but seen through that skewed perspective we brought to superheroes in 'Kick-Ass.' It feels very, very
Matthew_Vaughn
Graph operation
polyhedron with a lattice of triangular, square, or hexagonal polygons, possibly skewed with regards to the original face: it is an extension of concepts
Goldberg–Coxeter_construction
spiral Syntractrix Tractrix Trochoid Bézier curve Loess curve Lowess Ogee Polygonal curve Maurer rose Reuleaux triangle Stadium Splines B-spline Nonuniform
List_of_curves
Geometric object with flat sides
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
Polytope
Set of edges without common vertices
{\displaystyle G} is k {\displaystyle k} if and only if (a) there is a real skew-symmetric matrix A {\displaystyle A} with graph G {\displaystyle G} and eigenvalues
Matching_(graph_theory)
2018 video game
Byford from The Verge described the pacing as "excellent," noting that it "skewed less toward combat than ever" with "fewer forced gun battles". Several critics
Shadow_of_the_Tomb_Raider
Topics referred to by the same term
dimensions Regular polytope, a generalization of a regular polygon to higher dimensions Regular skew polyhedron Axiom of Regularity, also called the Axiom
Regular
Line through four points of a curve
by a formula derived by Arthur Cayley. Quadrisecants of arrangements of skew lines touch subsets of four lines from the arrangement. They are associated
Quadrisecant
coincide with the vertices of an inscribed cantellated tesseract. The regular skew polyhedron, {4,8|3}, exists in 4-space with 8 square around each vertex,
Runcinated_24-cells
Quadric surface with one axis of symmetry and no center of symmetry
paraboloid is a doubly ruled surface: it contains two families of mutually skew lines. The lines in each family are parallel to a common plane, but not to
Paraboloid
2025 single by Huntrix
Andy Dudman – strings recording Rob Mathes – strings arranging Hillary Skewes – strings contracting Oren Yaacoby – music editing Sandra Park – vocals
Golden_(Huntrix_song)
order of a subgroup order by removing one mirror at a time. The regular skew polyhedron, {6,4|3}, exists in 4-space with 4 hexagonal around each vertex
Truncated_5-cell
American science fiction television series
One series that was being planned as part of this deal was a "younger-skewing" project set at Starfleet Academy. It was being developed by Stephanie
Star_Trek:_Starfleet_Academy
Class of 4-dimensional polytopes
vertex-transitive and whose cells are uniform polyhedra, and faces are regular polygons. There are 47 non-prismatic convex uniform 4-polytopes. There are two infinite
Uniform_4-polytope
2000 animated musical comedy film
Radford explained, "We originally thought it would be rated PG-13 and so we skewed it to that group... But then we thought we could not exclude the younger
The_Road_to_El_Dorado
Class of commutative rings
is sometimes assumed to be skew-symmetric, so that bx,y = –by,x for all x and y. More generally the matrix might be skew-symmetrizable, meaning there
Cluster_algebra
Professional League of Legends esports league
LCS finals". polygon. 24 April 2017. "SK Telecom T1 vs. G2 Esports 2017 live blog: Scores, highlights, and news from the MSI final". polygon. 22 May 2017
League of Legends EMEA Championship
League_of_Legends_EMEA_Championship
Fantasy role-playing game
"actual play media circumvents D&D's insulated or exclusionary aspects, skewing away from 'basement dwelling nerds' in favor of a networked, global fandom
Dungeons_&_Dragons
Step in the design cycle of devices
skew analysis is necessary. Global skew is the skew between any two clocked pins, without considering any logic relationship. Local skew is the skew between
Physical_design_(electronics)
2021 film by Justin Lin
diverse (with 37% Hispanic, 35% Caucasian, 16% Black and 8% Asian) and skewed to both younger (51% under the age of 25) and male (57%) crowds. In its
F9_(film)
Signature title sequence style of numbered Star Wars films
designed a logotype, consisting of block-capital letters filled with stars and skewed towards a vanishing point to follow the same perspective as the opening
Star_Wars_opening_crawl
Japanese video game franchise
within Japan has an average age of 32 years, and a male-to-female ratio that skews 40:60. Japanese website 4Gamer.net referred to the series as one of Japan's
Megami_Tensei
Marvel Studios film
film that Disney revealed Premier Access revenue for, with the revenue skewing heavily towards the United States with $55 million. Analytics company Samba
Black_Widow_(2021_film)
Video game franchise
while understating the repercussions", leaving audiences with a heavily skewed version of reality. He felt this did the most harm by portraying military
Call_of_Duty
2020 video game
there would be similarities to the God of War games, but felt those games "skew very heavily towards the mythology", whereas Ubisoft wanted Valhalla to be
Assassin's_Creed_Valhalla
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