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Truncated icosahedron

Index 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. [1]

72 relations: Albrecht Dürer, Allotropy, Archimedean graph, Archimedean solid, Archimedes, Ball (association football), Buckminster Fuller, Buckminsterfullerene, Cartesian coordinate system, Circumscribed sphere, Conformal map, Convex hull, Coxeter element, Cubic graph, De divina proportione, Euler characteristic, Face (geometry), Fat Man, Final stellation of the icosahedron, Fullerene, Geodesic dome, Geometry, George W. Hart, Goldberg polyhedron, Golden ratio, Graph theory, Great dodecicosidodecahedron, Great rhombidodecahedron, Hamiltonian path, Hexagon, Icosahedron, Icosidodecadodecahedron, Isogonal figure, Isohedral figure, Johannes Kepler, Leonardo da Vinci, Luca Pacioli, Mathematics, N-skeleton, Nanometre, Nonconvex great rhombicosidodecahedron, Nuclear weapon, Order-5 dodecahedral honeycomb, Orthographic projection, Oxford University Press, Parity of a permutation, Pentagon, Pontiac, Pontiac Firebird, Pontiac Grand Prix, ..., Projection (linear algebra), Radius, Radome, Regular graph, Regular polygon, Rhombicosahedron, Rhombidodecadodecahedron, Schlegel diagram, Small snub icosicosidodecahedron, Sparkleball, Spherical polyhedron, Stereographic projection, Trinity (nuclear test), Truncated great dodecahedron, Truncated order-7 triangular tiling, Truncation (geometry), Uniform star polyhedron, Vertex (graph theory), Weather station, Zero-symmetric graph, 1970 FIFA World Cup, 2006 FIFA World Cup. Expand index (22 more) »

Albrecht Dürer

Albrecht Dürer (21 May 1471 – 6 April 1528)Müller, Peter O. (1993) Substantiv-Derivation in Den Schriften Albrecht Dürers, Walter de Gruyter.

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Allotropy

Allotropy or allotropism is the property of some chemical elements to exist in two or more different forms, in the same physical state, known as allotropes of these elements.

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Archimedean graph

In the mathematical field of graph theory, an Archimedean graph is a graph that forms the skeleton of one of the Archimedean solids.

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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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Archimedes

Archimedes of Syracuse (Ἀρχιμήδης) was a Greek mathematician, physicist, engineer, inventor, and astronomer.

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Ball (association football)

A football, soccer ball, or association football ball is the ball used in the sport of association football.

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Buckminster Fuller

Richard Buckminster "Bucky" Fuller (July 12, 1895 – July 1, 1983) was an American architect, systems theorist, author, designer, inventor and futurist.

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Buckminsterfullerene

Buckminsterfullerene is a type of fullerene with the formula C60.

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Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.

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Circumscribed sphere

In geometry, a circumscribed sphere of a polyhedron is a sphere that contains the polyhedron and touches each of the polyhedron's vertices.

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Conformal map

In mathematics, a conformal map is a function that preserves angles locally.

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Convex hull

In mathematics, the convex hull or convex envelope or convex closure of a set X of points in the Euclidean plane or in a Euclidean space (or, more generally, in an affine space over the reals) is the smallest convex set that contains X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around X., p. 3.

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Coxeter element

In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.

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Cubic graph

In the mathematical field of graph theory, a cubic graph is a graph in which all vertices have degree three.

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De divina proportione

De divina proportione (On the Divine Proportion) is a book on mathematics written by Luca Pacioli and illustrated by Leonardo da Vinci, composed around 1498 in Milan and first printed in 1509.

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Euler characteristic

In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.

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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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Fat Man

"Fat Man" was the codename for the atomic bomb that was detonated over the Japanese city of Nagasaki by the United States on 9 August 1945.

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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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Fullerene

A fullerene is a molecule of carbon in the form of a hollow sphere, ellipsoid, tube, and many other shapes.

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Geodesic dome

A geodesic dome is a hemispherical thin-shell structure (lattice-shell) based on a geodesic 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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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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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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Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

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Great dodecicosidodecahedron

In geometry, the great dodecicosidodecahedron is a nonconvex uniform polyhedron, indexed as U61.

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Great rhombidodecahedron

In geometry, the great rhombidodecahedron is a nonconvex uniform polyhedron, indexed as U73.

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Hamiltonian path

In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once.

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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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Icosahedron

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

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Icosidodecadodecahedron

In geometry, the icosidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U44.

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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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Leonardo da Vinci

Leonardo di ser Piero da Vinci (15 April 14522 May 1519), more commonly Leonardo da Vinci or simply Leonardo, was an Italian polymath of the Renaissance, whose areas of interest included invention, painting, sculpting, architecture, science, music, mathematics, engineering, literature, anatomy, geology, astronomy, botany, writing, history, and cartography.

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Luca Pacioli

Fra Luca Bartolomeo de Pacioli (sometimes Paccioli or Paciolo; 1447–1517) was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and a seminal contributor to the field now known as accounting.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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N-skeleton

In mathematics, particularly in algebraic topology, the of a topological space X presented as a simplicial complex (resp. CW complex) refers to the subspace Xn that is the union of the simplices of X (resp. cells of X) of dimensions In other words, given an inductive definition of a complex, the is obtained by stopping at the.

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Nanometre

The nanometre (International spelling as used by the International Bureau of Weights and Measures; SI symbol: nm) or nanometer (American spelling) is a unit of length in the metric system, equal to one billionth (short scale) of a metre (m).

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Nonconvex great rhombicosidodecahedron

In geometry, the nonconvex great rhombicosidodecahedron is a nonconvex uniform polyhedron, indexed as U67.

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Nuclear weapon

A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either fission (fission bomb) or from a combination of fission and fusion reactions (thermonuclear bomb).

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Order-5 dodecahedral honeycomb

No description.

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Orthographic projection

Orthographic projection (sometimes orthogonal projection), is a means of representing three-dimensional objects in two dimensions.

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Oxford University Press

Oxford University Press (OUP) is the largest university press in the world, and the second oldest after Cambridge University Press.

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Parity of a permutation

In mathematics, when X is a finite set of at least two elements, the permutations of X (i.e. the bijective functions from X to X) fall into two classes of equal size: the even permutations and the odd permutations.

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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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Pontiac

Pontiac is a now-defunct car brand that was owned, made, and sold by General Motors.

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Pontiac Firebird

The Pontiac Firebird is an American automobile built by Pontiac from the 1967 to the 2002 model years.

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Pontiac Grand Prix

The Grand Prix was a line of all terrain automobiles produced by the Pontiac Division of General Motors from 1962 through 2002 for coupes and 1988-2008 for sedans.

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Projection (linear algebra)

In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.

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Radius

In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.

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Radome

A radome (which is a portmanteau of radar and dome) is a structural, weatherproof enclosure that protects a radar antenna.

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Regular graph

In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency.

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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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Rhombicosahedron

In geometry, the rhombicosahedron is a nonconvex uniform polyhedron, indexed as U56.

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Rhombidodecadodecahedron

In geometry, the rhombidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U38.

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Schlegel diagram

In geometry, a Schlegel diagram is a projection of a polytope from R^d into R^ through a point beyond one of its facets or faces.

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Small snub icosicosidodecahedron

In geometry, the small snub icosicosidodecahedron or snub disicosidodecahedron is a uniform star polyhedron, indexed as U32.

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Sparkleball

A sparkleball is an ornament handmade out of Christmas lights and plastic cups.

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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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Stereographic projection

In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.

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Trinity (nuclear test)

Trinity was the code name of the first detonation of a nuclear weapon.

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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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Truncated order-7 triangular tiling

In geometry, the Order-7 truncated triangular tiling, sometimes called the hyperbolic soccerball, is a semiregular tiling of the hyperbolic 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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Uniform star polyhedron

In geometry, a uniform star polyhedron is a self-intersecting uniform polyhedron.

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Vertex (graph theory)

In mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices).

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Weather station

A weather station is a facility, either on land or sea, with instruments and equipment for measuring atmospheric conditions to provide information for weather forecasts and to study the weather and climate.

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Zero-symmetric graph

In the mathematical field of graph theory, a zero-symmetric graph is a connected graph in which all vertices are symmetric to each other, each vertex has exactly three incident edges, and these three edges are not symmetric to each other.

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1970 FIFA World Cup

The 1970 FIFA World Cup was the ninth FIFA World Cup, the quadrennial international football championship for men's national teams.

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2006 FIFA World Cup

The 2006 FIFA World Cup was the 18th FIFA World Cup, the quadrennial international football world championship tournament.

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Redirects here:

Bitruncated dodecahedron, Ti (geometry), Truncated Icosahedron, Truncated icosahedral graph.

References

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

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