Three dimensions

A cube (or hexahedron) is a A Platonic solid is a convex polyhedron whose faces all use the same regular polygon and such that the same number of faces meet at all its vertices. Compare with the Kepler-Poinsot solids, which are not convex, and the Archimedean and Johnson solids, which while made of regular polygons... Platonic solid composed of six square faces, with three meeting at each vertex. The cube is a special kind of square In geometry, a prism is a polyhedron made of two parallel copies of some polygonal base joined by faces that are rectangles or parallelograms. In the case these joining faces are rectangular, the object is said to be a right prism. The rectangular prism, or cuboid, and square prism are... prism, of rectangular A parallelepiped (alternately, parallelopiped, parallelepipedon or parallelopipedon) is a 3-dimensional polyhedron with six parallelograms for faces. The word is also sometimes used for the higher-dimensional analogues. Properties All opposite faces are parallel and since each face has point symmetry, it is a zonohedron. The volume of a parallelepiped... parallelepiped and of triangular The trapezohedra are the Dual polyhedrons of the antiprisms. None of the faces are trapezoids, so the name is misleading. A trapezohedron is also known as a deltohedron. A deltohedron should not be confused with a deltahedron (spelled with an a). Categories: Polyhedra | Stub ... trapezohedron, and is dual to the An octahedron (plural: octahedra) is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight faces each of which is an equilateral triangle four of which meet at each vertex. The regular octahedron is a special kind of triangular antiprism and of square bipyramid, and... octahedron. Canonical coordinates for the vertices of a cube centered at the origin are (±1,±1,±1), while the interior of the same consists of all points (x₀, x₁, x₂) with -1 < x_i < 1.

Flattened polyhedron, source is image:makepoly.c, File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. Click on date to download the file or see the image uploaded on that date. (del) (cur) 23:52, 4 Nov 2004 . . Cyp...

The area A and the volume V of a cube of edge length a are:

A = 6a²

V = a³

Note that a cube construction will always create the largest Volume (also called capacity) is a quantification of how much space an object occupies. The SI unit for volume is the cubic metre (American spelling meter). The volume of a solid object is a numerical value given to describe the three-dimensional concept of how much space it occupies. One... volume possible per amount of material available (e.g. paper, cardboard, sheet metal, etc.) provided a flat six-sided face is a requirement. (The proof requires For other uses of the term calculus see calculus (disambiguation) Calculus is a central branch of mathematics, developed from algebra and geometry, and built on two major complementary ideas. One concept is called differential calculus. It studies rates of change, which are usually illustrated by the slope of a line... calculus, and assumes Dimension (from Latin measured out) is, in essence, the number of degrees of freedom available for movement in a space. (In common usage, the dimensions of an object are the measurements that define its shape and size. That usage is related to, but different from, what this article is about... 2D squares can be created with no waste.) A similar object having a In geometry, a rectangle is a defined as a quadrilateral polygon in which all four angles are right angles. From this definition, it follows that a rectangle has two pairs of opposite sides of equal length; that is, a rectangle is a parallelogram. A square is a special kind of... rectangular shape will always have a lesser volume than a cube for the same liner measurement (length + width + height).

A cube can be inscribed in a A dodecahedron is a Platonic solid composed of twelve pentagonal faces, with three meeting at each vertex. It has twenty vertices and thirty edges. Its dual polyhedron is the icosahedron. Canonical coordinates for the vertices of a dodecahedron centered at the origin are {(0,±1/φ,±φ), (±1/φ,±φ... dodecahedron so that each vertex of the cube is a vertex of the dodecahedron and each edge is a diagonal of one of the dodecahedron's faces; taking all such cubes gives rise to the regular Stella octangula, a polyhedral compound A polyhedral compound is a polyhedron which is itself composed of several other polyhedra sharing a common centre, the three-dimensional analogs of polygonal compounds such as the hexagram. The best known is the compound of two tetrahedra called the stella octangula, discovered by Kepler... compound of five cubes. The compound of two A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or equilateral, and is one of the Platonic solids. The area A and the volume V of a regular... tetrahedra is made from the cube in like fashion. The cube is unique among the Platonic solids for being able to tile space regularly, and finds many uses because of this. For instance, This article deals with sugar as food and as an important, widely traded commodity; the word also has other uses; see Sugar (disambiguation) A sugar is a form of carbohydrate; the most commonly used sugar is a white crystalline solid, sucrose; used to alter the flavor and properties (mouthfeel, perservation... sugar is frequently pressed into cubes containing a convenient amount to sweeten beverages, and the familiar six-sided Rolling dice Dice (the plural of the word die, probably from the Latin dare: to give) are, in general, small polyhedral objects with the faces marked with numbers or other symbols, thrown in order to choose one of the faces randomly. The most common dice are small cubes 1-2... die is cube shaped.

Expo 67, cubes in a room Interior of Man the Producer Pavilion, Restrictions on access: Nil File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. Click on date to download the file or see the image uploaded on that...

Expo 67, cubes in a room Interior of Man the Producer Pavilion, Restrictions on access: Nil File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. Click on date to download the file or see the image uploaded on that...

Room of cubes at Expo 67

If each edge of a cube is replaced by a one The ohm is the SI derived unit of electrical resistance (derived from the ampere and the watt). Its symbol is the Greek capital letter omega (Ω) (Ω) (Ω may also work, but this Unicode symbol is intended only for use with certain Oriental languages). The ohm is named for Georg... ohm An ideal resistor is a component with an electrical resistance that remains constant regardless of the applied voltage or current flowing through the device. While real world resistors cannot attain this perfect goal, they are designed to present little variation in electrical resistance when subjected to changing temperature and other... resistor, the resistance between opposite vertices is 5/6 ohms, and that between adjacent vertices 7/12 ohms.

Four dimensions

In the four-dimensional geometry, the analogue of a cube has a special name - a In geometry, the tesseract, or hypercube, is a regular, convex polychoron with eight cubical cells. It can be thought of as a 4-dimensional analogue of the cube. Roughly speaking, the tesseract is to the cube as the cube is to the square. Generalizations of the cube to dimensions greater... tesseract or In geometry, the tesseract, or hypercube, is a regular, convex polychoron with eight cubical cells. It can be thought of as a 4-dimensional analogue of the cube. Roughly speaking, the tesseract is to the cube as the cube is to the square. Generalizations of the cube to dimensions greater... hypercube.

Arbitrary dimensions

In an n-dimensional space the analog of the figure is called n-dimensional cube, or simply cube, if it doesn't lead to a confusion.

See also

• A unit cube is a 3-dimensional geometric figure that consists of a cube in which all of its dimensions are 1 unit long. Its volume is 1 cubic unit, and its total surface area is 6 cubic units. Categories: Math stubs ... Unit cube

External links

• The Uniform Polyhedra (http://www.mathconsult.ch/showroom/unipoly/)
• Virtual Reality Polyhedra (http://www.georgehart.com/virtual-polyhedra/vp.html) The Encyclopedia of Polyhedra
• Paper Models of Polyhedra (http://www.korthalsaltes.com/) Many links