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Stellation

Index 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. [1]

68 relations: Archimedean solid, Arthur Cayley, Chirality (mathematics), Coprime integers, Cube, Cuboctahedron, Digon, Dimension, Divisor, Dodecahedron, Dual polyhedron, Duality (mathematics), Enneagram (geometry), Facet (geometry), Faceting, Final stellation of the icosahedron, Geometry, Gravitation (M. C. Escher), Great dodecahedron, Great grand stellated 120-cell, Great icosahedron, Great stellated dodecahedron, Harold Scott MacDonald Coxeter, Hemipolyhedron, Heptagon, Heptagram, Hexagon, Hexagram, Hyperplane, Icosahedron, Icosidodecahedron, Italian Renaissance, J. C. P. Miller, Johannes Kepler, John Horton Conway, Kepler–Poinsot polyhedron, List of Wenninger polyhedron models, Lithography, M. C. Escher, Magnus Wenninger, Mathematics and art, Nonagon, Octagon, Octagram, Octahedron, Paolo Uccello, Pentagon, Pentagram, Polygon, Polyhedron, ..., Polytope, Polytope compound, Regular 4-polytope, Rhombic dodecahedron, Rhombic triacontahedron, Schläfli symbol, Small stellated dodecahedron, Square, St Mark's Basilica, Star polygon, Stellated octahedron, Stellation diagram, Tetrahedron, The Fifty-Nine Icosahedra, Triakis tetrahedron, Venice Biennale, 120-cell, 4-polytope. Expand index (18 more) »

Archimedean solid

In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes.

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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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Chirality (mathematics)

In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone.

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Coprime integers

In number theory, two integers and are said to be relatively prime, mutually prime, or coprime (also written co-prime) if the only positive integer (factor) that divides both of them is 1.

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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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Digon

In geometry, a digon is a polygon with two sides (edges) and two vertices.

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Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

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Divisor

In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder.

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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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Duality (mathematics)

In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A. Such involutions sometimes have fixed points, so that the dual of A is A itself.

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Enneagram (geometry)

In geometry, an enneagram is a nine-pointed plane figure.

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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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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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Final stellation of the icosahedron

In geometry, the complete or final stellation of the icosahedron is the outermost stellation of the icosahedron, and is "complete" and "final" because it includes all of the cells in the icosahedron's stellation diagram.

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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 grand stellated 120-cell

In geometry, the great grand stellated 120-cell or great grand stellated polydodecahedron is a regular star 4-polytope with Schläfli symbol, one of 10 regular Schläfli-Hess 4-polytopes.

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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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Hemipolyhedron

In geometry, a hemipolyhedron is a uniform star polyhedron some of whose faces pass through its center.

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Heptagon

In geometry, a heptagon is a seven-sided polygon or 7-gon.

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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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Hexagon

In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.

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Hexagram

A hexagram (Greek) or sexagram (Latin) is a six-pointed geometric star figure with the Schläfli symbol, 2, or.

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Hyperplane

In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.

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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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Italian Renaissance

The Italian Renaissance (Rinascimento) was the earliest manifestation of the general European Renaissance, a period of great cultural change and achievement that began in Italy during the 14th century (Trecento) and lasted until the 17th century (Seicento), marking the transition between Medieval and Modern Europe.

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J. C. P. Miller

Jeffrey Charles Percy Miller (31 August 1906 – 24 April 1981) was an English mathematician and computing pioneer.

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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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Kepler–Poinsot polyhedron

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

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List of Wenninger polyhedron models

This is an indexed list of the uniform and stellated polyhedra from the book Polyhedron Models, by Magnus Wenninger.

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Lithography

Lithography is a method of printing originally based on the immiscibility of oil and water.

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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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Magnus Wenninger

Father Magnus J. Wenninger OSB (October 31, 1919Banchoff (2002)– February 17, 2017) was an American mathematician who worked on constructing polyhedron models, and wrote the first book on their construction.

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Mathematics and art

Mathematics and art are related in a variety of ways.

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Nonagon

In geometry, a nonagon or enneagon is a nine-sided polygon or 9-gon.

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Octagon

In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is an eight-sided polygon or 8-gon.

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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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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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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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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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Polytope

In elementary geometry, a polytope is a geometric object with "flat" sides.

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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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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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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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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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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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Stellated octahedron

The stellated octahedron is the only stellation of the octahedron.

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Stellation diagram

In geometry, a stellation diagram or stellation pattern is a two-dimensional diagram in the plane of some face of a polyhedron, showing lines where other face planes intersect with this one.

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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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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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Triakis tetrahedron

In geometry, a triakis tetrahedron (or kistetrahedron) is an Archimedean dual solid, or a Catalan solid.

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Venice Biennale

The Venice Biennale (La Biennale di Venezia; in English also called the "Venice Biennial") refers to an arts organization based in Venice and the name of the original and principal biennial exhibition the organization organizes.

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120-cell

In geometry, the 120-cell is the convex regular 4-polytope with Schläfli symbol.

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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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Redirects here:

Compound polygon, Miller's rules, Polytope stellations, Stellated, Stellated polyhedra.

References

[1] https://en.wikipedia.org/wiki/Stellation

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