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Small stellated dodecahedron

Index Small stellated dodecahedron

In geometry, the small stellated dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol. [1]

42 relations: Arthur Cayley, Branch point, Branched covering, Bring's curve, Cambridge University Press, Compound of small stellated dodecahedron and great dodecahedron, Convex polytope, Coxeter–Dynkin diagram, Degeneracy (mathematics), Dodecadodecahedron, Dodecahedron, Euler's formula, Felix Klein, Genus (mathematics), Geometry, Gravitation (M. C. Escher), Great complex icosidodecahedron, Great dodecahedron, Great icosahedron, Icosahedron, Isosceles triangle, Kepler–Poinsot polyhedron, Lithography, Louis Poinsot, M. C. Escher, Mosaic, Net (polyhedron), Paolo Uccello, Pentagon, Pentagram, Pentakis dodecahedron, Riemann sphere, Riemann surface, Schläfli symbol, Spherical polyhedron, St Mark's Basilica, Stellation, Symmetric group, Truncated great dodecahedron, Truncation (geometry), Venice, Vertex arrangement.

Arthur Cayley

Arthur Cayley F.R.S. (16 August 1821 – 26 January 1895) was a British mathematician.

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Branch point

In the mathematical field of complex analysis, a branch point of a multi-valued function (usually referred to as a "multifunction" in the context of complex analysis) is a point such that the function is discontinuous when going around an arbitrarily small circuit around this point.

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Branched covering

In mathematics, a branched covering is a map that is almost a covering map, except on a small set.

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Bring's curve

In mathematics, Bring's curve (also called Bring's surface) is the curve given by the equations It was named by after Erland Samuel Bring who studied a similar construction in 1786 in a Promotionschrift submitted to the University of Lund.

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Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

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Compound of small stellated dodecahedron and great dodecahedron

The compound of small stellated dodecahedron and great dodecahedron is a polyhedron compound where the great dodecahedron is interior to its dual, the small stellated dodecahedron.

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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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Degeneracy (mathematics)

In mathematics, a degenerate case is a limiting case in which an element of a class of objects is qualitatively different from the rest of the class and hence belongs to another, usually simpler, class.

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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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Euler's formula

Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function.

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Felix Klein

Christian Felix Klein (25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group theory.

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Genus (mathematics)

In mathematics, genus (plural genera) has a few different, but closely related, meanings.

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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 complex icosidodecahedron

In geometry, the great complex icosidodecahedron is a degenerate uniform star polyhedron.

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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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Icosahedron

In geometry, an icosahedron is a polyhedron with 20 faces.

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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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Kepler–Poinsot polyhedron

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

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Lithography

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

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Louis Poinsot

Louis Poinsot (3 January 1777 – 5 December 1859) was a French mathematician and physicist.

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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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Mosaic

A mosaic is a piece of art or image made from the assemblage of small pieces of colored glass, stone, or other materials.

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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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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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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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Riemann sphere

In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane, the complex plane plus a point at infinity.

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Riemann surface

In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold.

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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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Spherical polyhedron

In mathematics, a spherical polyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded regions called spherical polygons.

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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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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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Symmetric group

In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.

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Truncated great dodecahedron

In geometry, the truncated great dodecahedron is a nonconvex uniform polyhedron, indexed as U37.

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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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Venice

Venice (Venezia,; Venesia) is a city in northeastern Italy and the capital of the Veneto region.

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Vertex arrangement

In geometry, a vertex arrangement is a set of points in space described by their relative positions.

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Redirects here:

Lesser stellated dodecahedron, Sissid, Small Stellated Dodecahedron.

References

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

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