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120-cell

Index 120-cell

In geometry, the 120-cell is the convex regular 4-polytope with Schläfli symbol. [1]

58 relations: Antarctic Circle, Arctic Circle, Clifford torus, Complex polytope, Configuration (polytope), Convex set, Coxeter element, Coxeter group, Decagon, Dihedral angle, Dodecahedron, Dual polyhedron, Equilateral triangle, Face (geometry), Geometry, Golden ratio, Harold Scott MacDonald Coxeter, Hexagonal tiling honeycomb, Hopf fibration, Hyperbolic manifold, Icosahedral pyramid, Icosidodecahedron, Isogonal figure, Isohedral figure, Isotoxal figure, John Horton Conway, Michael Guy, Norman Johnson (mathematician), Order-5 120-cell honeycomb, Orthographic projection, Parity of a permutation, Pentagon, Permutation, Perspective (graphical), Polyhedral combinatorics, Proceedings of the American Mathematical Society, Projection (linear algebra), Rectified 120-cell, Regular 4-polytope, Regular Polytopes (book), Schläfli symbol, Schlegel diagram, Snub 24-cell, Stereographic projection, Tesseract, Tetrahedron, Torsion of a curve, Triacontagon, Triangular bipyramid, Tropic of Cancer, ..., Tropic of Capricorn, Vertex figure, 24-cell, 3-sphere, 4-polytope, 5-cell, 57-cell, 600-cell. Expand index (8 more) »

Antarctic Circle

The Antarctic Circle is the most southerly of the five major circles of latitude that mark maps of the Earth.

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Arctic Circle

The Arctic Circle is the most northerly of the five major circles of latitude as shown on maps of Earth.

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Clifford torus

In geometric topology, the Clifford torus is the simplest and most symmetric Euclidean space embedding of the cartesian product of two circles S1a and S1b.

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Complex polytope

In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imaginary one.

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Configuration (polytope)

In geometry, H. S. M. Coxeter called a regular polytope a special kind of configuration.

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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 element

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

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Coxeter group

In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors).

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Decagon

In geometry, a decagon is a ten-sided polygon or 10-gon.

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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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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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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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Hexagonal tiling honeycomb

In the field of hyperbolic geometry, the hexagonal tiling honeycomb arises one of 11 regular paracompact honeycombs in 3-dimensional hyperbolic space.

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Hopf fibration

In the mathematical field of differential topology, the Hopf fibration (also known as the Hopf bundle or Hopf map) describes a 3-sphere (a hypersphere in four-dimensional space) in terms of circles and an ordinary sphere.

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Hyperbolic manifold

In mathematics, a hyperbolic manifold is a space where every point looks locally like hyperbolic space of some dimension.

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Icosahedral pyramid

The icosahedral pyramid is a four-dimensional convex polytope, bounded by one icosahedron as its base and by 20 triangular pyramid cells which meet at its apex.

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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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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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Isotoxal figure

In geometry, a polytope (for example, a polygon or a polyhedron), or a tiling, is isotoxal or edge-transitive if its symmetries act transitively on its edges.

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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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Michael Guy

Michael J. T. Guy (born c.1942) is a British computer scientist and mathematician.

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Norman Johnson (mathematician)

Norman Woodason Johnson (November 12, 1930 – July 13, 2017) was a mathematician, previously at Wheaton College, Norton, Massachusetts.

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Order-5 120-cell honeycomb

In the geometry of hyperbolic 4-space, the order-5 120-cell honeycomb is one of five compact regular space-filling tessellations (or honeycombs).

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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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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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Permutation

In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.

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Perspective (graphical)

Perspective (from perspicere "to see through") in the graphic arts is an approximate representation, generally on a flat surface (such as paper), of an image as it is seen by the eye.

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Polyhedral combinatorics

Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higher-dimensional convex polytopes.

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Proceedings of the American Mathematical Society

Proceedings of the American Mathematical Society is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society.

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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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Rectified 120-cell

In geometry, a rectified 120-cell is a uniform 4-polytope formed as the rectification of the regular 120-cell.

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Regular 4-polytope

In mathematics, a regular 4-polytope is a regular four-dimensional polytope.

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Regular Polytopes (book)

Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter.

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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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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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Snub 24-cell

In geometry, the snub 24-cell or snub disicositetrachoron is a convex uniform 4-polytope composed of 120 regular tetrahedral and 24 icosahedral cells.

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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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Tesseract

In geometry, the tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square.

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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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Torsion of a curve

In the elementary differential geometry of curves in three dimensions, the torsion of a curve measures how sharply it is twisting out of the plane of curvature.

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Triacontagon

In geometry, a triacontagon or 30-gon is a thirty-sided polygon.

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Triangular bipyramid

In geometry, the triangular bipyramid (or dipyramid) is a type of hexahedron, being the first in the infinite set of face-transitive bipyramids.

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Tropic of Cancer

The Tropic of Cancer, also referred to as the Northern Tropic, is the most northerly circle of latitude on Earth at which the Sun can be directly overhead.

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Tropic of Capricorn

The Tropic of Capricorn (or the Southern Tropic) is the circle of latitude that contains the subsolar point on the December (or southern) solstice.

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Vertex figure

In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.

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24-cell

In geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.

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3-sphere

In mathematics, a 3-sphere, or glome, is a higher-dimensional analogue of a sphere.

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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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5-cell

In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.

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57-cell

In mathematics, the 57-cell (pentacontakaiheptachoron) is a self-dual abstract regular 4-polytope (four-dimensional polytope).

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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:

120 cell, 5,3,3, Davis 120-cell, Dodecacontachoron, Dodecaplex, Hecatonicosachoron, Hi (geometry), Hyperdodecahedron.

References

[1] https://en.wikipedia.org/wiki/120-cell

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