46 relations: Alternation (geometry), Antiprism, Bipyramid, Convex set, Coxeter–Dynkin diagram, Dihedral angle, Dodecahedron, Dual polyhedron, Edge (geometry), Elongated triangular gyrobicupola, Elongated triangular orthobicupola, Equilateral triangle, Face (geometry), Geometry, Golden ratio, Great icosahedron, Great stellated dodecahedron, Gyroelongated triangular cupola, Hilbert's third problem, Icosahedral symmetry, Isohedral figure, Isosceles triangle, Johnson solid, Kepler–Poinsot polyhedron, Metabiaugmented dodecahedron, Net (polyhedron), Parabiaugmented dodecahedron, Pentagram, Platonic solid, Polyhedron, Prism, Pyramid, Regular icosahedron, Rhombic icosahedron, Rhombic triacontahedron, Right angle, Schläfli symbol, Stellation, Tetrahedral symmetry, The Fifty-Nine Icosahedra, Trapezohedron, Triangular hebesphenorotunda, Truncated octahedron, Vertex (geometry), Zonohedron, 600-cell.

## 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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## 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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## Bipyramid

An n-gonal bipyramid or dipyramid is a polyhedron formed by joining an n-gonal pyramid and its mirror image base-to-base.

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## Convex set

In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.

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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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## Dihedral angle

A dihedral angle is the angle between two intersecting planes.

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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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## Edge (geometry)

In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.

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## Elongated triangular gyrobicupola

In geometry, the elongated triangular gyrobicupola is one of the Johnson solids (J36).

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## Elongated triangular orthobicupola

In geometry, the elongated triangular orthobicupola is one of the Johnson solids (J35).

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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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## 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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## Golden ratio

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

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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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## Gyroelongated triangular cupola

In geometry, the gyroelongated triangular cupola is one of the Johnson solids (J22).

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## Hilbert's third problem

The third on Hilbert's list of mathematical problems, presented in 1900, was the first to be solved.

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## Icosahedral symmetry

A regular icosahedron has 60 rotational (or orientation-preserving) symmetries, and a symmetry order of 120 including transformations that combine a reflection and a rotation.

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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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## Isosceles triangle

In geometry, an isosceles triangle is a triangle that has two sides of equal length.

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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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## Kepler–Poinsot polyhedron

In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra.

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## Metabiaugmented dodecahedron

In geometry, the metabiaugmented dodecahedron is one of the Johnson solids (J60).

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## Net (polyhedron)

In geometry a net of a polyhedron is an arrangement of edge-joined polygons in the plane which can be folded (along edges) to become the faces of the polyhedron.

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## Parabiaugmented dodecahedron

In geometry, the parabiaugmented dodecahedron is one of the Johnson solids (J59).

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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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## 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

In optics, a prism is a transparent optical element with flat, polished surfaces that refract light.

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## Pyramid

A pyramid (from πυραμίς) is a structure whose outer surfaces are triangular and converge to a single point at the top, making the shape roughly a pyramid in the geometric sense.

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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 icosahedron

A rhombic icosahedron is a polyhedron shaped like an oblate sphere.

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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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## Right angle

In geometry and trigonometry, a right angle is an angle of exactly 90° (degrees), corresponding to a quarter 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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## 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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## Tetrahedral symmetry

A regular tetrahedron, an example of a solid with full tetrahedral symmetry A regular tetrahedron has 12 rotational (or orientation-preserving) symmetries, and a symmetry order of 24 including transformations that combine a reflection and a rotation.

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## The Fifty-Nine Icosahedra

The Fifty-Nine Icosahedra is a book written and illustrated by H. S. M. Coxeter, P. Du Val, H. T. Flather and J. F. Petrie.

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## Trapezohedron

The n-gonal trapezohedron, antidipyramid, antibipyramid or deltohedron is the dual polyhedron of an n-gonal antiprism.

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## Triangular hebesphenorotunda

In geometry, the triangular hebesphenorotunda is one of the Johnson solids (J92).

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## Truncated octahedron

In geometry, the truncated octahedron is an Archimedean solid.

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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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## Zonohedron

A zonohedron is a convex polyhedron with point symmetry, every face of which is a polygon with point symmetry.

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## 600-cell

In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.

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## Redirects here:

20-face, 20-hedron, Birectified Dodecahedron, Eicosahedron, Great stellatriakis icosahedron, Gyroelongated pentagonal bipyramid, Gyroelongated pentagonal dipyramid, Icosahedra, Icosasphere, Icosihedron, Icosohedran, Icosohedron, Isocahedron, Pseudo-icosahedron, Pseudoicosahedra, Pseudoicosahedron, Pyritohedral icosahedron, Snub tetratetrahedron, Vertices of an icosahedron.