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77 relations: Alternated octagonal tiling, Alternated order-4 hexagonal tiling, Catalan solid, Checkerboard, Chiral polytope, Convex polytope, Coxeter–Dynkin diagram, Cube, Cubic honeycomb, Cuboctahedron, Ditrigonal dodecadodecahedron, Ditrigonal polyhedron, Dodecadodecahedron, Dodecahedron, Dual polyhedron, Face (geometry), Geometry, Great ditrigonal icosidodecahedron, Great dodecahedron, Great icosahedron, Great icosidodecahedron, Great stellated dodecahedron, Harold Scott MacDonald Coxeter, Hexagonal tiling, Icosahedron, Icosidodecahedron, Isogonal figure, Isohedral figure, Isotoxal figure, Johannes Kepler, Kepler–Poinsot polyhedron, Michael S. Longuet-Higgins, Octahedron, Order-4 apeirogonal tiling, Order-4 hexagonal tiling, Order-4 pentagonal tiling, Order-5 cubic honeycomb, Order-6 apeirogonal tiling, Order-6 cubic honeycomb, Order-6 hexagonal tiling, Order-6 pentagonal tiling, Order-6 square tiling, Order-8 hexagonal tiling, Order-8 pentagonal tiling, Order-8 square tiling, Order-8 triangular tiling, Rectification (geometry), Regular polygon, Regular polyhedron, Regular Polytopes (book), ..., Rhombic dodecahedron, Rhombic triacontahedron, Rhombille tiling, Rhombus, Schläfli symbol, Semiregular polyhedron, Small ditrigonal icosidodecahedron, Small stellated dodecahedron, Square tiling, Star polyhedron, Stellated octahedron, Tessellation, Tesseract, Tetrahedral-octahedral honeycomb, Tetrahedron, Triangular tiling, Triapeirogonal tiling, Triheptagonal tiling, Trihexagonal tiling, Truncation (geometry), Uniform tilings in hyperbolic plane, Vertex (geometry), Vertex configuration, Vertex figure, Wythoff construction, Wythoff symbol, 16-cell. Expand index (27 more) »
Alternated octagonal tiling
In geometry, the tritetragonal tiling or alternated octagonal tiling is a uniform tiling of the hyperbolic plane.
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Alternated order-4 hexagonal tiling
In geometry, the alternated order-4 hexagonal tiling or ditetragonal tritetratrigonal tiling is a uniform tiling of the hyperbolic plane.
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Catalan solid
In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid.
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Checkerboard
A checkerboard (American English) or chequerboard (British English; see spelling differences) is a board of chequered pattern on which English draughts (checkers) is played.
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Chiral polytope
In mathematics, there are two competing definitions for a chiral polytope.
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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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Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
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Cubic honeycomb
The cubic honeycomb or cubic cellulation is the only regular space-filling tessellation (or honeycomb) in Euclidean 3-space, made up of cubic cells.
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Cuboctahedron
In geometry, a cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces.
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Ditrigonal dodecadodecahedron
In geometry, the ditrigonal dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U41.
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Ditrigonal polyhedron
In geometry, there are seven uniform and uniform dual polyhedra named as ditrigonal.
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Dodecadodecahedron
In geometry, the dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U36.
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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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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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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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Great ditrigonal icosidodecahedron
In geometry, the great ditrigonal icosidodecahedron is a nonconvex uniform polyhedron, indexed as U47.
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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 icosidodecahedron
In geometry, the great icosidodecahedron is a nonconvex uniform polyhedron, indexed as U54.
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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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Hexagonal tiling
In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which three hexagons meet at each vertex.
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Icosahedron
In geometry, an icosahedron is a polyhedron with 20 faces.
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Icosidodecahedron
In geometry, an icosidodecahedron is a polyhedron with twenty (icosi) triangular faces and twelve (dodeca) pentagonal faces.
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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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Isotoxal figure
In geometry, a polytope (for example, a polygon or a polyhedron), or a tiling, is isotoxal or edge-transitive if its symmetries act transitively on its edges.
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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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Kepler–Poinsot polyhedron
In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra.
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Michael S. Longuet-Higgins
Michael Selwyn Longuet-Higgins FRS (December 8, 1925 – February 26, 2016) was a mathematician and oceanographer at the Department of Applied Mathematics and Theoretical Physics (DAMTP), Cambridge University, England and Institute for Nonlinear Science, University of California, San Diego, USA.
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Octahedron
In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.
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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 hexagonal tiling
In geometry, the order-4 hexagonal 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-5 cubic honeycomb
The order-5 cubic honeycomb is one of four compact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space.
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Order-6 apeirogonal tiling
In geometry, the order-6 apeirogonal tiling is a regular tiling of the hyperbolic plane.
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Order-6 cubic honeycomb
The order-6 cubic honeycomb is a paracompact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space.
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Order-6 hexagonal tiling
In geometry, the order-6 hexagonal 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-6 square tiling
In geometry, the order-6 square tiling is a regular tiling of the hyperbolic plane.
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Order-8 hexagonal tiling
In geometry, the order-8 hexagonal 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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Order-8 square tiling
In geometry, the order-8 square tiling is a regular tiling of the hyperbolic plane.
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Order-8 triangular tiling
In geometry, the order-8 triangular tiling is a regular tiling of the hyperbolic plane.
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Rectification (geometry)
In Euclidean geometry, rectification or complete-truncation is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points.
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Regular polygon
In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).
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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 Polytopes (book)
Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter.
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Rhombic dodecahedron
In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces.
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Rhombic triacontahedron
In geometry, the rhombic triacontahedron, sometimes simply called the triacontahedron as it is the most common thirty-faced polyhedron, is a convex polyhedron with 30 rhombic faces.
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Rhombille tiling
In geometry, the rhombille tiling, also known as tumbling blocks, reversible cubes, or the dice lattice, is a tessellation of identical 60° rhombi on the Euclidean plane.
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Rhombus
In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a simple (non-self-intersecting) quadrilateral whose four sides all have the same length.
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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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Semiregular polyhedron
The term semiregular polyhedron (or semiregular polytope) is used variously by different authors.
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Small ditrigonal icosidodecahedron
In geometry, the small ditrigonal icosidodecahedron is a nonconvex uniform polyhedron, indexed as U30.
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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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Square tiling
In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane.
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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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Stellated octahedron
The stellated octahedron is the only stellation of the octahedron.
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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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Tesseract
In geometry, the tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square.
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Tetrahedral-octahedral honeycomb
The tetrahedral-octahedral honeycomb, alternated cubic honeycomb is a quasiregular space-filling tessellation (or honeycomb) in Euclidean 3-space.
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Tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.
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Triangular tiling
In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane.
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Triapeirogonal tiling
In geometry, the triapeirogonal tiling (or trigonal-horocyclic tiling) is a uniform tiling of the hyperbolic plane with a Schläfli symbol of r.
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Triheptagonal tiling
In geometry, the triheptagonal tiling is a semiregular tiling of the hyperbolic plane, representing a rectified Order-3 heptagonal tiling.
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Trihexagonal tiling
In geometry, the trihexagonal tiling is one of 11 uniform tilings of the Euclidean plane by regular polygons.
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Truncation (geometry)
In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex.
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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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Vertex (geometry)
In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.
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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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Wythoff construction
In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling.
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Wythoff symbol
In geometry, the Wythoff symbol represents a Wythoff construction of a uniform polyhedron or plane tiling, from a Schwarz triangle.
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16-cell
In four-dimensional geometry, a 16-cell is a regular convex 4-polytope.
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Quasiregular honeycomb, Quasiregular polygon, Quasiregular polyhedra, Quasiregular polytope, Quasiregular tiling.
References
[1] https://en.wikipedia.org/wiki/Quasiregular_polyhedron
