Surface Area of a Cuboid and a Cube

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Surface Area of a Cuboid and a Cube
Surface Area of a Cuboid and a Cube
In geometry, a Cuboid is a solid figure bounded by six faces, forming a convex polyhedron. There are
two competing (but incompatible) definitions of a cuboid in mathematical literature. In the more
general definition of a cuboid, the only additional requirement is that these six faces each be a
quadrilateral, and that the undirected graph formed by the vertices and edges of the polyhedron should
be isomorphic to the graph of a cube.Alternatively, the word "cuboid" is sometimes used to refer to a
shape of this type in which each of the faces is a rectangle (and so each pair of adjacent faces meets in a
right angle); this more restrictive type of cuboid is also known as a right cuboid, rectangular box,
rectangular hexahedron, right rectangular prism, or rectangular parallelepiped.
In a rectangular cuboid, all angles are right angles, and opposite faces of a cuboid are equal. It is also a
right rectangular prism. The term "rectangular or oblong prism" is ambiguous. Also the term
rectangular parallelepiped or orthogonal parallelepiped is used. The square cuboid, square box, or right
square prism (also ambiguously called square prism) is a special case of the cuboid in which at least
two faces are squares. The cube is a special case of the square cuboid in which all six faces are squares.
If the dimensions of a cuboid are a, b and c, then its volume is abc and
Its surface area is 2ab + 2ac + 2bc.

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In geometry, a Cube is a three-dimensional solid object bounded by six square faces, facets or sides,
with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the
five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and of trigonal
trapezohedron. The cube is dual to the octahedron. It has cubical symmetry (also called octahedral
symmetry). It is special by being a cuboid and a rhombohedron. A cube has eleven nets (one shown
above): that is, there are eleven ways to flatten a hollow cube by cutting seven edges.[2] To color the
cube so that no two adjacent faces have the same color, one would need at least three colors. The cube
is the cell of the only regular tiling of three-dimensional Euclidean space. It is also unique among the
Platonic solids in having faces with an even number of sides and, consequently, it is the only member
of that group that is a zonohedron (every face has point symmetry). The cube can be cut into six
identical square pyramids. If these square pyramids are then attached to the faces of a second cube, a
rhombic dodecahedron is obtained (with pairs of coplanar triangles combined into rhombic faces.)
The surface area of the Cube = 6*a2 whare a is the length of the a side..
The vertices of a cube can be grouped into two groups of four, each forming a regular tetrahedron;
more generally this is referred to as a demicube. These two together form a regular compound, the
stella octangula. The intersection of the two forms a regular octahedron. The symmetries of a regular
tetrahedron correspond to those of a cube which map each tetrahedron to itself; the other symmetries of
the cube map the two to each other. One such regular tetrahedron has a volume of 12 of that of the
cube. The remaining space consists of four equal irregular tetrahedra with a volume of 16 of that of the
cube, each. The rectified cube is the cuboctahedron. If smaller corners are cut off we get a polyhedron
with six octagonal faces and eight triangular ones. In particular we can get regular octagons (truncated
cube). The rhombicuboctahedron is obtained by cutting off both corners and edges to the correct
amount. A cube can be inscribed in a 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 compound of five cubes. If two opposite corners of a cube are truncated at the
depth of the three vertices directly connected to them, an irregular octahedron is obtained. Eight of
these irregular octahedra can be attached to the triangular faces of a regular octahedron to obtain the
cuboctahedron.