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# 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. [1]

## Box

Box (plural: boxes) describes a variety of containers and receptacles for permanent use as storage, or for temporary use, often for transporting contents.

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## Congruence (geometry)

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

## 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.

## 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

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

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## Cupboard

The term cupboard was originally used to describe an open-shelved side table for displaying dishware, more specifically plates, cups and saucers.

## Dihedral group

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

## 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.

## Euler brick

In mathematics, an Euler brick, named after Leonhard Euler, is a rectangular cuboid whose edges and face diagonals all have integer lengths.

## Euler characteristic

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

## 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.

## Frustum

In geometry, a frustum (plural: frusta or frustums) is the portion of a solid (normally a cone or pyramid) that lies between one or two parallel planes cutting it.

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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.

## Hexahedron

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

## Honeycomb (geometry)

In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps.

## Hyperrectangle

In geometry, an n-orthotopeCoxeter, 1973 (also called a hyperrectangle or a box) is the generalization of a rectangle for higher dimensions, formally defined as the Cartesian product of intervals.

## 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.

## List of finite spherical symmetry groups

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

## 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.

## Parallelepiped

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

## Plesiohedron

In geometry, a plesiohedron is a special kind of space-filling polyhedron, defined as the Voronoi cell of a symmetric Delone set.

## Polyhedral graph

In geometric graph theory, a branch of mathematics, a polyhedral graph is the undirected graph formed from the vertices and edges of a convex polyhedron.

## 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.

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

## Rectangle

In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles.

## Right angle

In geometry and trigonometry, a right angle is an angle of exactly 90° (degrees), corresponding to a quarter turn.

## Room

A room is any distinguishable space within a structure.

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## 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.

## Square pyramid

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

## Sugar

Sugar is the generic name for sweet-tasting, soluble carbohydrates, many of which are used in food.

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## Surface area

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

## Trapezohedron

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

## Vertex (geometry)

In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.

## 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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## 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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