52 relations: Alexander's Star, Arthur Cayley, Augustin-Louis Cauchy, Chaim Goodman-Strauss, Convex polygon, Convex polytope, Coxeter–Dynkin diagram, Density (polytope), Dissection problem, Dodecahedron, Dual polyhedron, Euler characteristic, Face (geometry), Faceting, Geometry, Gravitation (M. C. Escher), Great dodecahedron, Great icosahedron, Great stellated dodecahedron, Harold Scott MacDonald Coxeter, Icosahedron, Isosceles triangle, Johannes Kepler, John Horton Conway, Joseph Bertrand, Louis Poinsot, M. C. Escher, Oslo Airport, Gardermoen, Paolo Uccello, Pentagon, Pentagram, Platonic solid, Polytope compound, Regular 4-polytope, Regular polyhedron, Regular polytope, Schläfli symbol, Small stellated dodecahedron, St Mark's Basilica, Star polygon, Star polyhedron, Stellation, Symmetry group, Uniform polyhedron, Uniform star polyhedron, Vebjørn Sand, Venice, Vertex arrangement, Vertex configuration, Vertex figure, ..., Wenzel Jamnitzer, 4-polytope. Expand index (2 more) »
Alexander's Star
Alexander's Star is a puzzle similar to the Rubik's Cube, in the shape of a great dodecahedron.
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Arthur Cayley
Arthur Cayley F.R.S. (16 August 1821 – 26 January 1895) was a British mathematician.
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Augustin-Louis Cauchy
Baron Augustin-Louis Cauchy FRS FRSE (21 August 178923 May 1857) was a French mathematician, engineer and physicist who made pioneering contributions to several branches of mathematics, including: mathematical analysis and continuum mechanics.
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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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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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Convex polytope
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn.
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Coxeter–Dynkin diagram
In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes).
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Density (polytope)
In geometry, the density of a polytope represents the number of windings of a polytope, particularly a uniform or regular polytope, around its center.
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Dissection problem
In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged into a new figure of equal content.
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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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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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Face (geometry)
In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by flat faces is a polyhedron.
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Faceting
Stella octangula as a faceting of the cube In geometry, faceting (also spelled facetting) is the process of removing parts of a polygon, polyhedron or polytope, without creating any new vertices.
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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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Gravitation (M. C. Escher)
Gravitation (also known as Gravity) is a mixed media work by the Dutch artist M. C. Escher completed in June 1952.
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Great dodecahedron
In geometry, the great dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol and Coxeter–Dynkin diagram of.
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Great icosahedron
In geometry, the great icosahedron is one of four Kepler-Poinsot polyhedra (nonconvex regular polyhedra), with Schläfli symbol and Coxeter-Dynkin diagram of.
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Great stellated dodecahedron
In geometry, the great stellated dodecahedron is a Kepler-Poinsot polyhedron, with Schläfli symbol.
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Harold Scott MacDonald Coxeter
Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.
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Icosahedron
In geometry, an icosahedron is a polyhedron with 20 faces.
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Isosceles triangle
In geometry, an isosceles triangle is a triangle that has two sides of equal length.
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Johannes Kepler
Johannes Kepler (December 27, 1571 – November 15, 1630) was a German mathematician, astronomer, and astrologer.
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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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Joseph Bertrand
Joseph Louis François Bertrand (11 March 1822 – 5 April 1900) was a French mathematician who worked in the fields of number theory, differential geometry, probability theory, economics and thermodynamics.
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Louis Poinsot
Louis Poinsot (3 January 1777 – 5 December 1859) was a French mathematician and physicist.
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M. C. Escher
Maurits Cornelis Escher (17 June 1898 – 27 March 1972) was a Dutch graphic artist who made mathematically-inspired woodcuts, lithographs, and mezzotints.
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Oslo Airport, Gardermoen
Oslo Airport (Oslo Lufthavn) is the main international airport serving Oslo, Norway, the capital and most populous city in the country.
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Paolo Uccello
Paolo Uccello (1397 – 10 December 1475), born Paolo di Dono, was an Italian painter and mathematician who was notable for his pioneering work on visual perspective in art.
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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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Pentagram
A pentagram (sometimes known as a pentalpha or pentangle or a star pentagon) is the shape of a five-pointed star drawn with five straight strokes.
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Platonic solid
In three-dimensional space, a Platonic solid is a regular, convex polyhedron.
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Polytope compound
A polyhedral compound is a figure that is composed of several polyhedra sharing a common centre.
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Regular 4-polytope
In mathematics, a regular 4-polytope is a regular four-dimensional polytope.
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Regular polyhedron
A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags.
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Regular polytope
In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.
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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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Small stellated dodecahedron
In geometry, the small stellated dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol.
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St Mark's Basilica
The Patriarchal Cathedral Basilica of Saint Mark (Basilica Cattedrale Patriarcale di San Marco), commonly known as Saint Mark's Basilica (Basilica di San Marco; Baxéłega de San Marco), is the cathedral church of the Roman Catholic Archdiocese of Venice, northern Italy.
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Star polygon
In geometry, a star polygon is a type of non-convex polygon.
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Star polyhedron
In geometry, a star polyhedron is a polyhedron which has some repetitive quality of nonconvexity giving it a star-like visual quality.
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Stellation
In geometry, stellation is the process of extending a polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in n dimensions to form a new figure.
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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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Uniform polyhedron
A uniform polyhedron is a polyhedron 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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Uniform star polyhedron
In geometry, a uniform star polyhedron is a self-intersecting uniform polyhedron.
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Vebjørn Sand
Vebjørn Sand (born March 11, 1966 in Bærum) is a Norwegian painter and artist.
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Venice
Venice (Venezia,; Venesia) is a city in northeastern Italy and the capital of the Veneto region.
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Vertex arrangement
In geometry, a vertex arrangement is a set of points in space described by their relative positions.
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Vertex configuration
In geometry, a vertex configuration by Walter Steurer, Sofia Deloudi, (2009) pp.
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Vertex figure
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.
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Wenzel Jamnitzer
Wenzel Jamnitzer (sometimes Jamitzer, or Wenzel Gemniczer) (1507/1508 – 19 December 1585) was a Northern Mannerist goldsmith, artist, and printmaker in etching, who worked in Nuremberg.
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4-polytope
In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope.
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Kepler Poinsot solids, Kepler Solid, Kepler solid, Kepler-Poinsot, Kepler-Poinsot polyhedra, Kepler-Poinsot polyhedron, Kepler-Poinsot solid, Kepler-Poinsot solids, Kepler-poinsot solid, Kepler–Poinsot polyhedra, Kepler–Poinsot solid, Nonconvex Platonic solids, Poinsot solid.
References
[1] https://en.wikipedia.org/wiki/Kepler–Poinsot_polyhedron