94 relations: Antiprism, Archimedean solid, Bitruncation, Cairo pentagonal tiling, Cantellation (geometry), Catalan solid, Chamfer (geometry), Commutative property, Cube, Cuboctahedron, Cupola (geometry), Deltoidal hexecontahedron, Deltoidal icositetrahedron, Disdyakis dodecahedron, Disdyakis triacontahedron, Dodecahedron, Dual polyhedron, Eisenstein integer, Euclidean domain, Expansion (geometry), Gaussian integer, Geodesic polyhedron, George W. Hart, Goldberg polyhedron, Goldberg–Coxeter construction, Graph embedding, Gyroelongated bipyramid, Hexagonal tiling, Icosahedron, Icosidodecahedron, Identity function, Identity matrix, Isogonal figure, Isohedral figure, Johannes Kepler, John Horton Conway, Johnson solid, Kleetope, List of convex uniform tilings, List of geodesic polyhedra and Goldberg polyhedra, List of regular polytopes and compounds, Medial graph, Michel Deza, Midsphere, Octahedron, Omnitruncation, Operation (mathematics), Pentagonal antiprism, Pentagonal hexecontahedron, Pentagonal icositetrahedron, ..., Pentakis dodecahedron, Platonic solid, Polyhedral graph, Polyhedron, Prism (geometry), Pyramid (geometry), Rectification (geometry), Regular dodecahedron, Regular icosahedron, Rhombic dodecahedron, Rhombic triacontahedron, Rhombicosidodecahedron, Rhombicuboctahedron, Rhombille tiling, Rhombitrihexagonal tiling, Snub (geometry), Snub cube, Snub dodecahedron, Snub square tiling, Snub trihexagonal tiling, Square tiling, Symmetrohedron, Tetrahedron, Tetrakis hexahedron, Tetrakis square tiling, Toroidal polyhedron, Triakis icosahedron, Triakis octahedron, Triakis tetrahedron, Triangular tiling, Trihexagonal tiling, Truncated cube, Truncated cuboctahedron, Truncated dodecahedron, Truncated hexagonal tiling, Truncated icosahedron, Truncated icosidodecahedron, Truncated octahedron, Truncated square tiling, Truncated tetrahedron, Truncated trapezohedron, Truncated trihexagonal tiling, Truncation (geometry), Zonohedron. Expand index (44 more) »
Antiprism
In geometry, an n-sided antiprism is a polyhedron composed of two parallel copies of some particular n-sided polygon, connected by an alternating band of triangles.
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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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Cairo pentagonal tiling
In geometry, the Cairo pentagonal tiling is a dual semiregular tiling of the Euclidean plane.
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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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Catalan solid
In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid.
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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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Commutative property
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.
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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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Cuboctahedron
In geometry, a cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces.
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Cupola (geometry)
In geometry, a cupola is a solid formed by joining two polygons, one (the base) with twice as many edges as the other, by an alternating band of isosceles triangles and rectangles.
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Deltoidal hexecontahedron
In geometry, a deltoidal hexecontahedron (also sometimes called a trapezoidal hexecontahedron, a strombic hexecontahedron, or a tetragonal hexacontahedron) is a Catalan solid which is the dual polyhedron of the rhombicosidodecahedron, an Archimedean solid.
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Deltoidal icositetrahedron
In geometry, a deltoidal icositetrahedron (also a trapezoidal icositetrahedron, tetragonal icosikaitetrahedron,, tetragonal trisoctahedron and strombic icositetrahedron) is a Catalan solid.
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Disdyakis dodecahedron
In geometry, a disdyakis dodecahedron, (also hexoctahedron, hexakis octahedron, octakis cube, octakis hexahedron, kisrhombic dodecahedron), is a Catalan solid with 48 faces and the dual to the Archimedean truncated cuboctahedron.
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Disdyakis triacontahedron
In geometry, a disdyakis triacontahedron, hexakis icosahedron, decakis dodecahedron or kisrhombic triacontahedron is a Catalan solid with 120 faces and the dual to the Archimedean truncated icosidodecahedron.
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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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Eisenstein integer
In mathematics, Eisenstein integers (named after Gotthold Eisenstein), occasionally also known as Eulerian integers (after Leonhard Euler), are complex numbers of the form where and are integers and is a primitive (hence non-real) cube root of unity.
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Euclidean domain
In mathematics, more specifically in ring theory, a Euclidean domain (also called a Euclidean ring) is an integral domain that can be endowed with a Euclidean function which allows a suitable generalization of the Euclidean division of the integers.
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Expansion (geometry)
In geometry, expansion is a polytope operation where facets are separated and moved radially apart, and new facets are formed at separated elements (vertices, edges, etc.). Equivalently this operation can be imagined by keeping facets in the same position but reducing their size.
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Gaussian integer
In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers.
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Geodesic polyhedron
A geodesic polyhedron is a convex polyhedron made from triangles that approximates a sphere.
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George W. Hart
George William Hart (born 1955) is an American geometer who expresses himself both artistically and academically.
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Goldberg polyhedron
A Goldberg polyhedron is a convex polyhedron made from hexagons and pentagons.
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Goldberg–Coxeter construction
The Goldberg–Coxeter construction or Goldberg–Coxeter operation (GC construction or GC operation) is a graph operation defined on regular polyhedral graphs with degree 3 or 4.
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Graph embedding
In topological graph theory, an embedding (also spelled imbedding) of a graph G on a surface \Sigma is a representation of G on \Sigma in which points of \Sigma are associated with vertices and simple arcs (homeomorphic images of) are associated with edges in such a way that.
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Gyroelongated bipyramid
In geometry, the gyroelongated bipyramids are an infinite set of polyhedra, constructed by elongating an n-gonal bipyramid by inserting an n-gonal antiprism between its congruent halves.
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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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Identity function
Graph of the identity function on the real numbers In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument.
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Identity matrix
In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.
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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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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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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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Kleetope
In geometry and polyhedral combinatorics, the Kleetope of a polyhedron or higher-dimensional convex polytope is another polyhedron or polytope formed by replacing each facet of with a shallow pyramid.
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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 geodesic polyhedra and Goldberg polyhedra
This is a list of selected geodesic polyhedra and Goldberg polyhedra, two infinite classes of polyhedra.
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List of regular polytopes and compounds
This page lists the regular polytopes and regular polytope compounds in Euclidean, spherical and hyperbolic spaces.
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Medial graph
In the mathematical discipline of graph theory, the medial graph of plane graph G is another graph M(G) that represents the adjacencies between edges in the faces of G. Medial graphs were introduced in 1922 by Ernst Steinitz to study combinatorial properties of convex polyhedra, although the inverse construction was already used by Peter Tait in 1877 in his foundational study of knots and links.
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Michel Deza
Michel Marie Deza (27 April 1939.-23 November 2016) was a Soviet and French mathematician, specializing in combinatorics, discrete geometry and graph theory.
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Midsphere
In geometry, the midsphere or intersphere of a polyhedron is a sphere which is tangent to every edge of the polyhedron.
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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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Omnitruncation
In geometry, an omnitruncation is an operation applied to a regular polytope (or honeycomb) in a Wythoff construction that creates a maximum number of facets.
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Operation (mathematics)
In mathematics, an operation is a calculation from zero or more input values (called operands) to an output value.
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Pentagonal antiprism
In geometry, the pentagonal antiprism is the third in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.
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Pentagonal hexecontahedron
In geometry, a pentagonal hexecontahedron is a Catalan solid, dual of the snub dodecahedron.
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Pentagonal icositetrahedron
In geometry, a pentagonal icositetrahedron or pentagonal icosikaitetrahedron is a Catalan solid which is the dual of the snub cube.
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Pentakis dodecahedron
In geometry, a pentakis dodecahedron or kisdodecahedron is a dodecahedron with a pentagonal pyramid covering each face; that is, it is the Kleetope of the dodecahedron.
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Platonic solid
In three-dimensional space, a Platonic solid is a regular, convex polyhedron.
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Polyhedral graph
In geometric graph theory, a branch of mathematics, a polyhedral graph is the undirected graph formed from the vertices and edges of a convex polyhedron.
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Polyhedron
In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices.
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Prism (geometry)
In geometry, a prism is a polyhedron comprising an n-sided polygonal base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces (necessarily all parallelograms) joining corresponding sides of the two bases.
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Pyramid (geometry)
In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex.
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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 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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Regular icosahedron
In geometry, a regular icosahedron is a convex polyhedron with 20 faces, 30 edges and 12 vertices.
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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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Rhombicosidodecahedron
In geometry, the rhombicosidodecahedron, or small rhombicosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces.
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Rhombicuboctahedron
In geometry, the rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid with eight triangular and eighteen square 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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Rhombitrihexagonal tiling
In geometry, the rhombitrihexagonal tiling is a semiregular tiling of the Euclidean plane.
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Snub (geometry)
In geometry, a snub is an operation applied to a polyhedron.
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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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Snub dodecahedron
In geometry, the snub dodecahedron, or snub 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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Snub square tiling
In geometry, the snub square tiling is a semiregular tiling of the Euclidean plane.
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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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Square tiling
In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane.
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Symmetrohedron
In geometry, a symmetrohedron is a high-symmetry polyhedron containing convex regular polyhedron on symmetry axes with gaps on the convex hull filled by irregular polyhedra.
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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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Tetrakis hexahedron
In geometry, a tetrakis hexahedron (also known as a tetrahexahedron, hextetrahedron, tetrakis cube, and kiscube) is a Catalan solid.
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Tetrakis square tiling
In geometry, the tetrakis square tiling is a tiling of the Euclidean plane.
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Toroidal polyhedron
In geometry, a toroidal polyhedron is a polyhedron which is also a toroid (a g-holed torus), having a topological genus of 1 or greater.
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Triakis icosahedron
In geometry, the triakis icosahedron (or kisicosahedron) is an Archimedean dual solid, or a Catalan solid.
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Triakis octahedron
In geometry, a triakis octahedron (or trigonal trisoctahedron or kisoctahedron) is an Archimedean dual solid, or a Catalan solid.
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Triakis tetrahedron
In geometry, a triakis tetrahedron (or kistetrahedron) is an Archimedean dual solid, or a Catalan solid.
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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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Trihexagonal tiling
In geometry, the trihexagonal tiling is one of 11 uniform tilings of the Euclidean plane by regular polygons.
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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 dodecahedron
In geometry, the truncated dodecahedron is an Archimedean solid.
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Truncated hexagonal tiling
In geometry, the truncated hexagonal tiling is a semiregular tiling of the Euclidean plane.
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Truncated icosahedron
In geometry, the truncated icosahedron is an Archimedean solid, one of 13 convex isogonal nonprismatic solids whose faces are two or more types of regular polygons.
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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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Truncated square tiling
In geometry, the truncated square tiling is a semiregular tiling by regular polygons of the Euclidean plane with one square and two octagons on each vertex.
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Truncated tetrahedron
In geometry, the truncated tetrahedron is an Archimedean solid.
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Truncated trapezohedron
An n-gonal truncated trapezohedron is a polyhedron formed by a n-gonal trapezohedron with n-gonal pyramids truncated from its two polar axis vertices.
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Truncated trihexagonal tiling
In geometry, the truncated trihexagonal tiling is one of eight semiregular tilings of the Euclidean plane.
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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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Zonohedron
A zonohedron is a convex polyhedron with point symmetry, every face of which is a polygon with point symmetry.
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References
[1] https://en.wikipedia.org/wiki/Conway_polyhedron_notation