69 relations: Andreas Speiser, Arthur Moritz Schoenflies, Asterisk, Bullet (typography), Cartesian product, Chaim Goodman-Strauss, Coxeter notation, Cross-cap, Digon, Dimension, Emphasis (typography), Euclidean space, Euler characteristic, Fibrifold, Flag of Hong Kong, Frieze group, Geometry, Gyration, Hermann–Mauguin notation, Hyperbolic geometry, Infinite-order apeirogonal tiling, Infinite-order square tiling, Infinity, Integer, John Horton Conway, One-dimensional symmetry group, Orbifold, Order-3 apeirogonal tiling, Order-4 apeirogonal tiling, Order-4 heptagonal tiling, Order-4 hexagonal tiling, Order-4 octagonal tiling, Order-4 pentagonal tiling, Order-6 square tiling, Order-8 square tiling, Orientability, Paul Niggli, Pentagon, Poincaré disk model, Point groups in three dimensions, Rhombitetraapeirogonal tiling, Rhombitetrahexagonal tiling, Rotation, Snowflake, Space group, Sphere, Symmetry, Symmetry group, Tetraapeirogonal tiling, Tetrahexagonal tiling, ..., Tetraoctagonal tiling, Triangle group, Truncated infinite-order triangular tiling, Truncated order-4 hexagonal tiling, Truncated order-4 pentagonal tiling, Truncated order-6 hexagonal tiling, Truncated order-6 square tiling, Truncated order-8 triangular tiling, Truncated tetraapeirogonal tiling, Truncated tetrahexagonal tiling, Truncated tetraoctagonal tiling, Truncated tetrapentagonal tiling, Truncated triapeirogonal tiling, Truncated trioctagonal tiling, Two-dimensional space, Uniform tiling symmetry mutations, Wallpaper group, William Thurston, 3-7 kisrhombille. Expand index (19 more) »
Andreas Speiser
Andreas Speiser (June 10, 1885 – October 12, 1970) was a Swiss Mathematician and Philosopher of science.
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Arthur Moritz Schoenflies
Arthur Moritz Schoenflies (17 April 1853 – 27 May 1928), sometimes written as Schönflies, was a German mathematician, known for his contributions to the application of group theory to crystallography, and for work in topology.
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Asterisk
An asterisk (*); from Late Latin asteriscus, from Ancient Greek ἀστερίσκος, asteriskos, "little star") is a typographical symbol or glyph. It is so called because it resembles a conventional image of a star. Computer scientists and mathematicians often vocalize it as star (as, for example, in the A* search algorithm or C*-algebra). In English, an asterisk is usually five-pointed in sans-serif typefaces, six-pointed in serif typefaces, and six- or eight-pointed when handwritten. It is often used to censor offensive words, and on the Internet, to indicate a correction to a previous message. The asterisk is derived from the need of the printers of family trees in feudal times for a symbol to indicate date of birth. The original shape was seven-armed, each arm like a teardrop shooting from the center. In computer science, the asterisk is commonly used as a wildcard character, or to denote pointers, repetition, or multiplication.
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Bullet (typography)
In typography, a bullet (•) is a typographical symbol or glyph used to introduce items in a list.
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Cartesian product
In set theory (and, usually, in other parts of mathematics), a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.
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Chaim Goodman-Strauss
Chaim Goodman-Strauss (born June 1967 in Austin TX) is an American mathematician who works in convex geometry, especially aperiodic tiling.
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Coxeter notation
In geometry, Coxeter notation (also Coxeter symbol) is a system of classifying symmetry groups, describing the angles between with fundamental reflections of a Coxeter group in a bracketed notation expressing the structure of a Coxeter-Dynkin diagram, with modifiers to indicate certain subgroups.
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Cross-cap
In mathematics, a cross-cap is a two-dimensional surface in 3-space that is one-sided and the continuous image of a Möbius strip that intersects itself in an interval.
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Digon
In geometry, a digon is a polygon with two sides (edges) and two vertices.
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Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
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Emphasis (typography)
In typography, emphasis is the strengthening of words in a text with a font in a different style from the rest of the text, to highlight them.
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Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
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Euler characteristic
In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.
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Fibrifold
In mathematics, a fibrifold is (roughly) a fiber space whose fibers and base spaces are orbifolds.
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Flag of Hong Kong
The flag of Hong Kong features a white, stylised, five-petal Hong Kong orchid tree (''Bauhinia blakeana'') flower in the centre of a red field.
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Frieze group
In mathematics, a frieze or frieze pattern is a design on a two-dimensional surface that is repetitive in one direction.
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Geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
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Gyration
In geometry, a gyration is a rotation in a discrete subgroup of symmetries of the Euclidean plane such that the subgroup does not also contain a reflection symmetry whose axis passes through the center of rotational symmetry.
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Hermann–Mauguin notation
In geometry, Hermann–Mauguin notation is used to represent the symmetry elements in point groups, plane groups and space groups.
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Hyperbolic geometry
In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.
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Infinite-order apeirogonal tiling
In geometry, the infinite-order apeirogonal tiling is a regular tiling of the hyperbolic plane.
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Infinite-order square tiling
In geometry, the infinite-order square tiling is a regular tiling of the hyperbolic plane.
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Infinity
Infinity (symbol) is a concept describing something without any bound or larger than any natural number.
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Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
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John Horton Conway
John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.
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One-dimensional symmetry group
A one-dimensional symmetry group is a mathematical group that describes symmetries in one dimension (1D).
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Orbifold
In the mathematical disciplines of topology, geometry, and geometric group theory, an orbifold (for "orbit-manifold") is a generalization of a manifold.
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Order-3 apeirogonal tiling
In geometry, the order-3 apeirogonal tiling is a regular tiling of the hyperbolic plane.
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Order-4 apeirogonal tiling
In geometry, the order-4 apeirogonal tiling is a regular tiling of the hyperbolic plane.
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Order-4 heptagonal tiling
In geometry, the order-4 heptagonal tiling is a regular tiling of the hyperbolic plane.
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Order-4 hexagonal tiling
In geometry, the order-4 hexagonal tiling is a regular tiling of the hyperbolic plane.
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Order-4 octagonal tiling
In geometry, the order-4 octagonal tiling is a regular tiling of the hyperbolic plane.
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Order-4 pentagonal tiling
In geometry, the order-4 pentagonal tiling is a regular tiling of the hyperbolic plane.
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Order-6 square tiling
In geometry, the order-6 square tiling is a regular tiling of the hyperbolic plane.
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Order-8 square tiling
In geometry, the order-8 square tiling is a regular tiling of the hyperbolic plane.
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Orientability
In mathematics, orientability is a property of surfaces in Euclidean space that measures whether it is possible to make a consistent choice of surface normal vector at every point.
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Paul Niggli
Niggli was born in Zofingen and studied at the Swiss Federal Institute of Technology (ETH) in Zurich and the University of Zurich, where he obtained a doctorate.
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Pentagon
In geometry, a pentagon (from the Greek πέντε pente and γωνία gonia, meaning five and angle) is any five-sided polygon or 5-gon.
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Poincaré disk model
In geometry, the Poincaré disk model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which the points of the geometry are inside the unit disk, and the straight lines consist of all segments of circles contained within that disk that are orthogonal to the boundary of the disk, plus all diameters of the disk.
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Point groups in three dimensions
In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere.
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Rhombitetraapeirogonal tiling
In geometry, the rhombitetraapeirogonal tiling is a uniform tiling of the hyperbolic plane.
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Rhombitetrahexagonal tiling
In geometry, the rhombitetrahexagonal tiling is a uniform tiling of the hyperbolic plane.
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Rotation
A rotation is a circular movement of an object around a center (or point) of rotation.
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Snowflake
A snowflake is a single ice crystal that has achieved a sufficient size, and may have amalgamated with others, then falls through the Earth's atmosphere as snow.
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Space group
In mathematics, physics and chemistry, a space group is the symmetry group of a configuration in space, usually in three dimensions.
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Sphere
A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").
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Symmetry
Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance.
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Symmetry group
In group theory, the symmetry group of an object (image, signal, etc.) is the group of all transformations under which the object is invariant with composition as the group operation.
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Tetraapeirogonal tiling
In geometry, the tetraapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of r.
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Tetrahexagonal tiling
In geometry, the tetrahexagonal tiling is a uniform tiling of the hyperbolic plane.
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Tetraoctagonal tiling
In geometry, the tetraoctagonal tiling is a uniform tiling of the hyperbolic plane.
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Triangle group
In mathematics, a triangle group is a group that can be realized geometrically by sequences of reflections across the sides of a triangle.
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Truncated infinite-order triangular tiling
In geometry, the truncated infinite-order triangular tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of t.
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Truncated order-4 hexagonal tiling
In geometry, the truncated order-4 hexagonal tiling is a uniform tiling of the hyperbolic plane.
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Truncated order-4 pentagonal tiling
In geometry, the truncated order-4 pentagonal tiling is a uniform tiling of the hyperbolic plane.
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Truncated order-6 hexagonal tiling
In geometry, the truncated order-6 hexagonal tiling is a uniform tiling of the hyperbolic plane.
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Truncated order-6 square tiling
In geometry, the truncated order-6 square tiling is a uniform tiling of the hyperbolic plane.
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Truncated order-8 triangular tiling
In geometry, the Truncated order-8 triangular tiling is a semiregular tiling of the hyperbolic plane.
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Truncated tetraapeirogonal tiling
In geometry, the truncated tetrapeirogonal tiling is a semiregular tiling of the hyperbolic plane.
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Truncated tetrahexagonal tiling
In geometry, the truncated tetrahexagonal tiling is a semiregular tiling of the hyperbolic plane.
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Truncated tetraoctagonal tiling
In geometry, the truncated tetraoctagonal tiling is a semiregular tiling of the hyperbolic plane.
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Truncated tetrapentagonal tiling
In geometry, the truncated tetrapentagonal tiling is a uniform tiling of the hyperbolic plane.
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Truncated triapeirogonal tiling
In geometry, the truncated triapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of tr.
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Truncated trioctagonal tiling
In geometry, the truncated trioctagonal tiling is a semiregular tiling of the hyperbolic plane.
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Two-dimensional space
Two-dimensional space or bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point).
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Uniform tiling symmetry mutations
In geometry, a symmetry mutation is a mapping of fundamental domains between two symmetry groups.
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Wallpaper group
A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern.
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William Thurston
William Paul Thurston (October 30, 1946August 21, 2012) was an American mathematician.
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3-7 kisrhombille
In geometry, the 3-7 kisrhombille tiling is a semiregular dual tiling of the hyperbolic plane.
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Redirects here:
Conway orbifold notation, Conway's orbifold notation, Conway-Thurston orbifold notation, Hyperbolic symmetry, I22 symmetry, Ii symmetry, Orbifold signature.
References
[1] https://en.wikipedia.org/wiki/Orbifold_notation