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54 relations: Algorithm, American Mathematical Monthly, Aperiodic tiling, Automorphism, École normale supérieure de Lyon, Binary tiling, Cairo pentagonal tiling, Chirality (mathematics), Convex polygon, Dodecahedron, Dual polyhedron, Elongated triangular tiling, Equilateral triangle, Euclidean tilings by convex regular polygons, Geometry, Group action, Hexagon, Internal and external angles, Isogonal figure, Isohedral figure, Jennifer McLoud-Mann, List of convex uniform tilings, List of Martin Gardner Mathematical Games columns, Marjorie Rice, Martin Gardner, Matematicheskii Sbornik, Mathematics Magazine, Orbifold notation, Order-4 pentagonal tiling, Order-5 pentagonal tiling, Order-6 pentagonal tiling, Order-8 pentagonal tiling, Parallelogram, Pentagon, Primitive cell, Quanta Magazine, Regular dodecahedron, Rep-tile, Rotational symmetry, Schläfli symbol, Scientific American, Snub trihexagonal tiling, Sphere, Sphinx tiling, Square, Tessellation, The Guardian, Turn (geometry), Two-dimensional space, Uniform tiling, ..., Uniform tilings in hyperbolic plane, University of Washington Bothell, Vertex configuration, Wallpaper group. Expand index (4 more) »
Algorithm
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
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American Mathematical Monthly
The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.
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Aperiodic tiling
An aperiodic tiling is a non-periodic tiling with the additional property that it does not contain arbitrarily large periodic patches.
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Automorphism
In mathematics, an automorphism is an isomorphism from a mathematical object to itself.
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École normale supérieure de Lyon
The École normale supérieure de Lyon (also known as ENS Lyon, ENSL or Normale Sup' Lyon) is a highly selective grande école located in Lyon, France.
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Binary tiling
In geometry, the binary tiling (sometimes called the Böröczky tiling) is a tiling of the hyperbolic plane, resembling a quadtree over the Poincaré half-plane model of the hyperbolic plane.
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Cairo pentagonal tiling
In geometry, the Cairo pentagonal tiling is a dual semiregular tiling of the Euclidean plane.
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Chirality (mathematics)
In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone.
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Convex polygon
A convex polygon is a simple polygon (not self-intersecting) in which no line segment between two points on the boundary ever goes outside the polygon.
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Dodecahedron
In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces.
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Dual polyhedron
In geometry, any polyhedron is associated with a second dual figure, where the vertices of one correspond to the faces of the other and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other.
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Elongated triangular tiling
In geometry, the elongated triangular tiling is a semiregular tiling of the Euclidean plane.
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Equilateral triangle
In geometry, an equilateral triangle is a triangle in which all three sides are equal.
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Euclidean tilings by convex regular polygons
Euclidean plane tilings by convex regular polygons have been widely used since antiquity.
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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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Group action
In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.
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Hexagon
In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.
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Internal and external angles
In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint.
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Isogonal figure
In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.
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Isohedral figure
In geometry, a polytope of dimension 3 (a polyhedron) or higher is isohedral or face-transitive when all its faces are the same.
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Jennifer McLoud-Mann
Jennifer McLoud-Mann is a Native American mathematician known for her 2015 discovery, with Casey Mann and undergraduate student David Von Derau, of the 15th and last class of convex pentagons to tile the plane.
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List of convex uniform tilings
This table shows the 11 convex uniform tilings (regular and semiregular) of the Euclidean plane, and their dual tilings.
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List of Martin Gardner Mathematical Games columns
Over a period of 24 years (January 1957 – December 1980), Martin Gardner wrote 288 consecutive "Mathematical Games" columns for Scientific American magazine.
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Marjorie Rice
Marjorie Rice (née Jeuck, February 16, 1923 – July 2, 2017) was an American amateur mathematician most famous for her discoveries in geometry.
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Martin Gardner
Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer, with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literature—especially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton.
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Matematicheskii Sbornik
Matematicheskii Sbornik (Математический сборник, abbreviated Mat. Sb.) is a peer reviewed Russian mathematical journal founded by the Moscow Mathematical Society in 1866.
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Mathematics Magazine
Mathematics Magazine is a refereed bimonthly publication of the Mathematical Association of America.
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Orbifold notation
In geometry, orbifold notation (or orbifold signature) is a system, invented by William Thurston and popularized by the mathematician John Conway, for representing types of symmetry groups in two-dimensional spaces of constant curvature.
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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-5 pentagonal tiling
In geometry, the order-5 pentagonal tiling is a regular tiling of the hyperbolic plane.
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Order-6 pentagonal tiling
In geometry, the order-6 pentagonal tiling is a regular tiling of the hyperbolic plane.
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Order-8 pentagonal tiling
In geometry, the order-8 pentagonal tiling is a regular tiling of the hyperbolic plane.
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Parallelogram
In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides.
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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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Primitive cell
In geometry, crystallography, mineralogy, and solid state physics, a primitive cell is a minimum volume cell (a unit cell) corresponding to a single lattice point of a structure with discrete translational symmetry.
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Quanta Magazine
Quanta Magazine is an editorially independent online publication of the Simons Foundation covering developments in mathematics, theoretical physics, theoretical computer science and the basic life sciences.
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Regular dodecahedron
A regular dodecahedron or pentagonal dodecahedron is a dodecahedron that is regular, which is composed of twelve regular pentagonal faces, three meeting at each vertex.
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Rep-tile
In the geometry of tessellations, a rep-tile or reptile is a shape that can be dissected into smaller copies of the same shape.
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Rotational symmetry
Rotational symmetry, also known as radial symmetry in biology, is the property a shape has when it looks the same after some rotation by a partial turn.
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Schläfli symbol
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
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Scientific American
Scientific American (informally abbreviated SciAm) is an American popular science magazine.
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Snub trihexagonal tiling
In geometry, the snub hexagonal tiling (or snub trihexagonal tiling) is a semiregular tiling of the Euclidean plane.
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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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Sphinx tiling
In geometry, the sphinx tiling is a tessellation of the plane using the "sphinx", a pentagonal hexiamond formed by gluing six equilateral triangles together.
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Square
In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.
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Tessellation
A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.
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The Guardian
The Guardian is a British daily newspaper.
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Turn (geometry)
A turn is a unit of plane angle measurement equal to 2pi radians, 360 degrees or 400 gradians.
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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
In geometry, a uniform tiling is a tessellation of the plane by regular polygon faces with the restriction of being vertex-transitive.
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Uniform tilings in hyperbolic plane
In hyperbolic geometry, a uniform (regular, quasiregular or semiregular) hyperbolic tiling is an edge-to-edge filling of the hyperbolic plane which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other).
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University of Washington Bothell
The University of Washington Bothell (UW Bothell) is a four-year undergraduate and graduate campus in northeast King County, one of the three campuses of the public University of Washington.
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Vertex configuration
In geometry, a vertex configuration by Walter Steurer, Sofia Deloudi, (2009) pp.
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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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Redirects here:
Hirschhorn tiling, Pentagon tiling, Pentagonal Tiling.
References
[1] https://en.wikipedia.org/wiki/Pentagonal_tiling
