55 relations: Alternation (geometry), Archimedean solid, Bitruncation, Cantellation (geometry), Chamfer (geometry), Conway polyhedron notation, Coxeter group, Coxeter–Dynkin diagram, Cube, Cubic honeycomb, Cuboctahedron, Decagon, Dual polygon, Dual polyhedron, Elongated bipyramid, Euclidean tilings by convex regular polygons, Facet (geometry), Geometry, Harold Scott MacDonald Coxeter, Heptagram, Icosahedron, Icosidodecahedron, Johannes Kepler, Johnson solid, Norman Johnson (mathematician), Octagram, Octahedron, Pentagon, Pentagram, Platonic solid, Polygon, Polytope, Rectification (geometry), Regular polygon, Regular polyhedron, Regular polytope, Regular Polytopes (book), Runcination, Schläfli symbol, Snub cube, Square, Star polygon, Stellated truncated hexahedron, Tetradecagon, Tetrahedrally diminished dodecahedron, Tetrahedron, Tridiminished icosahedron, Truncated cube, Truncated cuboctahedron, Truncated icosidodecahedron, ..., Truncated octahedron, Uniform 4-polytope, Uniform polyhedron, Uniform polytope, Uniform star polyhedron. Expand index (5 more) »
Alternation (geometry)
In geometry, an alternation or partial truncation, is an operation on a polygon, polyhedron, tiling, or higher dimensional polytope that removes alternate vertices.
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Archimedean solid
In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes.
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Bitruncation
In geometry, a bitruncation is an operation on regular polytopes.
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Cantellation (geometry)
In geometry, a cantellation is an operation in any dimension that bevels a regular polytope at its edges and vertices, creating a new facet in place of each edge and vertex.
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Chamfer (geometry)
In geometry, chamfering or edge-truncation is a topological operator that modifies one polyhedron into another.
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Conway polyhedron notation
In geometry, Conway polyhedron notation, invented by John Horton Conway and promoted by George W. Hart, is used to describe polyhedra based on a seed polyhedron modified by various prefix operations.
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Coxeter group
In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors).
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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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Decagon
In geometry, a decagon is a ten-sided polygon or 10-gon.
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Dual polygon
In geometry, polygons are associated into pairs called duals, where the vertices of one correspond to the edges of the other.
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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 bipyramid
In geometry, the elongated bipyramids are an infinite set of polyhedra, constructed by elongating an n-gonal bipyramid (by inserting an n-gonal prism between its congruent halves).
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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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Facet (geometry)
In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.
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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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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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Heptagram
A heptagram, septagram, septegram or septogram is a seven-point star drawn with seven straight strokes.
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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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Johannes Kepler
Johannes Kepler (December 27, 1571 – November 15, 1630) was a German mathematician, astronomer, and astrologer.
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Johnson solid
In geometry, a Johnson solid is a strictly convex polyhedron, which is not uniform (i.e., not a Platonic solid, Archimedean solid, prism, or antiprism), and each face of which is a regular polygon.
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Norman Johnson (mathematician)
Norman Woodason Johnson (November 12, 1930 – July 13, 2017) was a mathematician, previously at Wheaton College, Norton, Massachusetts.
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Octagram
In geometry, an octagram is an eight-angled star polygon.
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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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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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Polygon
In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.
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Polytope
In elementary geometry, a polytope is a geometric object with "flat" sides.
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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 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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Regular Polytopes (book)
Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter.
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Runcination
In geometry, runcination is an operation that cuts a regular polytope (or honeycomb) simultaneously along the faces, edges and vertices, creating new facets in place of the original face, edge, and vertex centers.
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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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Snub cube
In geometry, the snub cube, or snub cuboctahedron, is an Archimedean solid with 38 faces: 6 squares and 32 equilateral triangles.
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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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Star polygon
In geometry, a star polygon is a type of non-convex polygon.
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Stellated truncated hexahedron
In geometry, the stellated truncated hexahedron (or quasitruncated hexahedron) is a uniform star polyhedron, indexed as U19.
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Tetradecagon
In geometry, a tetradecagon or tetrakaidecagon or 14-gon is a fourteen-sided polygon.
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Tetrahedrally diminished dodecahedron
In geometry, a tetrahedrally diminished dodecahedron (also tetrahedrally stellated icosahedron) is a topologically self-dual polyhedron made of 16 vertices, 30 edges, and 16 faces (4 equilateral triangles and 12 identical quadrilaterals).
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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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Tridiminished icosahedron
In geometry, the tridiminished icosahedron is one of the Johnson solids (J63).
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Truncated cube
In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid.
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Truncated cuboctahedron
In geometry, the truncated cuboctahedron is an Archimedean solid, named by Kepler as a truncation of a cuboctahedron.
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Truncated icosidodecahedron
In geometry, the truncated icosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed by two or more types of regular polygon faces.
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Truncated octahedron
In geometry, the truncated octahedron is an Archimedean solid.
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Uniform 4-polytope
In geometry, a uniform 4-polytope (or uniform polychoron) is a 4-polytope which is vertex-transitive and whose cells are uniform polyhedra, and faces are regular polygons.
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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 polytope
A uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets.
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Uniform star polyhedron
In geometry, a uniform star polyhedron is a self-intersecting uniform polyhedron.
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Quasitruncation, Quasitruncation (geometry), Truncated polyhedra, Truncated polyhedron, Truncated tiling.
References
[1] https://en.wikipedia.org/wiki/Truncation_(geometry)