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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. [1]

111 relations: Analytic geometry, Antipodal point, Area, Cartesian coordinate system, Circumscribed sphere, Compass-and-straightedge construction, Compound of five cubes, Compound of three cubes, Conformal map, Constructible number, Convex uniform honeycomb, Coxeter element, Coxeter group, Coxeter–Dynkin diagram, Cube (algebra), Cube (film), Cube root, Cubic honeycomb, Cuboctahedron, Cuboid, Diamond cubic, Dihedral angle, Dihedral group, Dihedral symmetry in three dimensions, Distance-regular graph, Distance-transitive graph, Dodecahedron, Doubling the cube, Dual polyhedron, Euclidean space, Face diagonal, Facet (geometry), Forum Geometricorum, Geometry, Gerardus Heymans, Graph (discrete mathematics), Greek mathematics, Hamiltonian path, Hamming graph, Hemicube (geometry), Hexahedron, Hypercube, Hypercube graph, Inscribed sphere, Isogonal figure, K-vertex-connected graph, Kaaba, Line segment, List of finite spherical symmetry groups, Locus (mathematics), ... Expand index (61 more) »

## Analytic geometry

In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system.

## Antipodal point

In mathematics, the antipodal point of a point on the surface of a sphere is the point which is diametrically opposite to it — so situated that a line drawn from the one to the other passes through the center of the sphere and forms a true diameter.

## Area

Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.

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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.

## 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.

## Compass-and-straightedge construction

Compass-and-straightedge construction, also known as ruler-and-compass construction or classical construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass.

## Compound of five cubes

The compound of five cubes is one of the five regular polyhedral compounds.

## Compound of three cubes

This uniform polyhedron compound is a symmetric arrangement of 3 cubes, considered as square prisms.

## Conformal map

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

## Constructible number

In geometry and algebra, a real number is constructible if and only if, given a line segment of unit length, a line segment of length || can be constructed with compass and straightedge in a finite number of steps.

## Convex uniform honeycomb

In geometry, a convex uniform honeycomb is a uniform tessellation which fills three-dimensional Euclidean space with non-overlapping convex uniform polyhedral cells.

## Coxeter element

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

## 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).

## 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).

## Cube (algebra)

In arithmetic and algebra, the cube of a number is its third power: the result of the number multiplied by itself twice: It is also the number multiplied by its square: This is also the volume formula for a geometric cube with sides of length, giving rise to the name.

## Cube (film)

Cube is a 1997 Canadian science-fiction horror film directed and co-written by Vincenzo Natali.

## Cube root

In mathematics, a cube root of a number x is a number y such that y3.

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## Cubic honeycomb

The cubic honeycomb or cubic cellulation is the only regular space-filling tessellation (or honeycomb) in Euclidean 3-space, made up of cubic cells.

## Cuboctahedron

In geometry, a cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces.

## Cuboid

In geometry, a cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube.

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## Diamond cubic

The diamond cubic crystal structure is a repeating pattern of 8 atoms that certain materials may adopt as they solidify.

## Dihedral angle

A dihedral angle is the angle between two intersecting planes.

## Dihedral group

In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections.

## Dihedral symmetry in three dimensions

In geometry, dihedral symmetry in three dimensions is one of three infinite sequences of point groups in three dimensions which have a symmetry group that as abstract group is a dihedral group Dihn (n ≥ 2).

## Distance-regular graph

In mathematics, a distance-regular graph is a regular graph such that for any two vertices v and w, the number of vertices at distance j from v and at distance k from w depends only upon j, k, and i.

## Distance-transitive graph

In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any other two vertices x and y at the same distance, there is an automorphism of the graph that carries v to x and w to y.

## Dodecahedron

In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces.

## Doubling the cube

Doubling the cube, also known as the Delian problem, is an ancient geometric problem.

## 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.

## Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

## Face diagonal

In geometry, a face diagonal of a polyhedron is a diagonal on one of the faces, in contrast to a space diagonal passing through the interior of the polyhedron.

## 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.

## Forum Geometricorum

Forum Geometricorum: A Journal on Classical Euclidean Geometry (often abbreviated Forum Geom.) is a peer-reviewed open-access academic journal that specializes in mathematical research papers on Euclidean geometry.

## 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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## Gerardus Heymans

Gerardus Heymans (17 April 1857, Ferwert &ndash; 18 February 1930, Groningen) was a Dutch philosopher, psychologist, a follower of Gustav Fechner's idea of psychic monism, and from 1890 to 1927 a Professor at Groningen University.

## Graph (discrete mathematics)

In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".

## Greek mathematics

Greek mathematics refers to mathematics texts and advances written in Greek, developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean.

## 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.

## Hamming graph

Hamming graphs are a special class of graphs named after Richard Hamming and used in several branches of mathematics and computer science.

## Hemicube (geometry)

In abstract geometry, a hemicube is an abstract regular polyhedron, containing half the faces of a cube.

## Hexahedron

A hexahedron (plural: hexahedra) is any polyhedron with six faces.

## Hypercube

In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.

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## Hypercube graph

In graph theory, the hypercube graph is the graph formed from the vertices and edges of an -dimensional hypercube.

## Inscribed sphere

In geometry, the inscribed sphere or insphere of a convex polyhedron is a sphere that is contained within the polyhedron and tangent to each of the polyhedron's faces.

## 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.

## K-vertex-connected graph

In graph theory, a connected graph G is said to be k-vertex-connected (or k-connected) if it has more than k vertices and remains connected whenever fewer than k vertices are removed.

## Kaaba

The Kaaba (ٱلْـكَـعْـبَـة, "The Cube"), also referred as al-Kaʿbah al-Musharrafah (ٱلْـكَـعْـبَـة الْـمُـشَـرًّفَـة, the Holy Ka'bah), is a building at the center of Islam's most important mosque, that is Al-Masjid Al-Ḥarām (ٱلْـمَـسْـجِـد الْـحَـرَام, The Sacred Mosque), in the Hejazi city of Mecca, Saudi Arabia.

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## Line segment

In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.

## List of finite spherical symmetry groups

Finite spherical symmetry groups are also called point groups in three dimensions.

## Locus (mathematics)

In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.

## 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.

## Necker cube

The Necker cube is an optical illusion first published as a rhomboid in 1832 by Swiss crystallographer Louis Albert Necker.

## 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.

## Octagon

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

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## Octahedral symmetry

A regular octahedron has 24 rotational (or orientation-preserving) symmetries, and a symmetry order of 48 including transformations that combine a reflection and a rotation.

## Octahedron

In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.

## OLAP cube

In database engineering in computing, OLAP cube is a term that typically refers to a multi-dimensional array of data.

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## Orthographic projection

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

## Parallel computing

Parallel computing is a type of computation in which many calculations or the execution of processes are carried out concurrently.

## Parallelepiped

In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning).

## Pierre Wantzel

Pierre Laurent Wantzel (5 June 1814 in Paris – 21 May 1848 in Paris) was a French mathematician who proved that several ancient geometric problems were impossible to solve using only compass and straightedge.

## Planar graph

In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints.

## Platonic graph

In the mathematical field of graph theory, a Platonic graph is a graph that has one of the Platonic solids as its skeleton.

## Platonic solid

In three-dimensional space, a Platonic solid is a regular, convex polyhedron.

## Point (geometry)

In modern mathematics, a point refers usually to an element of some set called a space.

## Polytope compound

A polyhedral compound is a figure that is composed of several polyhedra sharing a common centre.

## Prince Rupert's cube

In geometry, Prince Rupert's cube (named after Prince Rupert of the Rhine) is the largest cube that can pass through a hole cut through a unit cube, i.e. through a cube whose sides have length 1, without splitting the cube into two pieces.

## Prism (geometry)

In geometry, a prism is a polyhedron comprising an n-sided polygonal base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces (necessarily all parallelograms) joining corresponding sides of the two bases.

## Projection (linear algebra)

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

## Projective polyhedron

In geometry, a (globally) projective polyhedron is a tessellation of the real projective plane.

## Proto-Indo-European language

Proto-Indo-European (PIE) is the linguistic reconstruction of the hypothetical common ancestor of the Indo-European languages, the most widely spoken language family in the world.

In Euclidean plane geometry, a quadrilateral is a polygon with four edges (or sides) and four vertices or corners.

The radian (SI symbol rad) is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics.

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## Rectification (geometry)

In Euclidean geometry, rectification or complete-truncation is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points.

## Rectified 24-cell

In geometry, the rectified 24-cell or rectified icositetrachoron is a uniform 4-dimensional polytope (or uniform 4-polytope), which is bounded by 48 cells: 24 cubes, and 24 cuboctahedra.

## 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.

## Regular polyhedron

A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags.

## Rhombic dodecahedron

In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces.

## Rhombicuboctahedron

In geometry, the rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid with eight triangular and eighteen square faces.

## Rhombohedron

In geometry, a rhombohedron is a three-dimensional figure like a cube, except that its faces are not squares but rhombi.

## Rhombus

In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a simple (non-self-intersecting) quadrilateral whose four sides all have the same length.

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## Rubik's Cube

Rubik's Cube is a 3-D combination puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik.

## Runcinated tesseracts

In four-dimensional geometry, a runcinated tesseract (or runcinated 16-cell) is a convex uniform 4-polytope, being a runcination (a 3rd order truncation) of the regular tesseract.

## Schläfli symbol

In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.

## Space diagonal

In geometry a space diagonal (also interior diagonal or body diagonal) of a polyhedron is a line connecting two vertices that are not on the same face.

## 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.

## 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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## Square (algebra)

In mathematics, a square is the result of multiplying a number by itself.

## Square pyramid

In geometry, a square pyramid is a pyramid having a square base.

## Stellated octahedron

The stellated octahedron is the only stellation of the octahedron.

## Stereographic projection

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

## Surface area

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

## Symmetric graph

In the mathematical field of graph theory, a graph G is symmetric (or arc-transitive) if, given any two pairs of adjacent vertices u1—v1 and u2—v2 of G, there is an automorphism such that In other words, a graph is symmetric if its automorphism group acts transitively upon ordered pairs of adjacent vertices (that is, upon edges considered as having a direction).

## 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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## Tetrahedral-octahedral honeycomb

The tetrahedral-octahedral honeycomb, alternated cubic honeycomb is a quasiregular space-filling tessellation (or honeycomb) in Euclidean 3-space.

## 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.

## The Cube (game show)

The Cube is a British game show that aired on ITV from 22 August 2009 to 8 August 2015 and was hosted by Phillip Schofield.

## Three-dimensional space

Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point).

## Trapezohedron

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

## Triangular prismatic honeycomb

The triangular prismatic honeycomb or triangular prismatic cellulation is a space-filling tessellation (or honeycomb) in Euclidean 3-space.

## Trigonal trapezohedron

In geometry, a trigonal trapezohedron or trigonal deltohedron is a three-dimensional figure formed by six congruent rhombi.

## Truncated 24-cells

In geometry, a truncated 24-cell is a uniform 4-polytope (4-dimensional uniform polytope) formed as the truncation of the regular 24-cell.

## Truncated cube

In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid.

## Uniform 4-polytope

In geometry, a uniform 4-polytope (or uniform polychoron) is a 4-polytope which is vertex-transitive and whose cells are uniform polyhedra, and faces are regular polygons.

## Unit cube

A unit cube, more formally a cube of side 1, is a cube whose sides are 1 unit long.

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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.

## Vertex figure

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

## Volume

Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.

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## Wythoff symbol

In geometry, the Wythoff symbol represents a Wythoff construction of a uniform polyhedron or plane tiling, from a Schwarz triangle.

## Yoshimoto Cube

The Yoshimoto Cube is a polyhedral mechanical puzzle toy invented in 1971 by, who discovered that two stellated rhombic dodecahedra could be pieced together into a cube when he was finding different ways he could split a cube equally in half.

## Zonohedron

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

## References

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