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Balls exist in any dimension and are generically called n-balls or hyperballs, where n is the number of dimensions. The same reasoning can be generalized to n-balls using the general equations for volume and surface area, which are:
A right prism is a prism in which the joining edges and faces are perpendicular to the base faces. [5] This applies if and only if all the joining faces are rectangular. The dual of a right n-prism is a right n-bipyramid. A right prism (with rectangular sides) with regular n-gon bases has Schläfli symbol { }×{n}.
By definition, this makes it a right rectangular prism. Rectangular cuboids may be referred to colloquially as "boxes" (after the physical object). If two opposite faces become squares, the resulting one may obtain another special case of rectangular prism, known as square rectangular cuboid. [b] They can be represented as the prism graph.
Right rhombic prism: it has two rhombic faces and four congruent rectangular faces. Note: the fully rhombic special case, with two rhombic faces and four congruent square faces ( a = b = c ) {\displaystyle (a=b=c)} , has the same name, and the same symmetry group (D 2h , order 8).
A sphere of radius r has surface area 4πr 2.. The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. [1] The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with ...
The formula for the volume of a pyramidal square frustum was introduced by the ancient Egyptian mathematics in what is called the Moscow Mathematical Papyrus, written in the 13th dynasty (c. 1850 BC): = (+ +), where a and b are the base and top side lengths, and h is the height.
A prism of which the base is a parallelogram; Rhombohedron: A parallelepiped where all edges are the same length; A cube, except that its faces are not squares but rhombi; Cuboid: A convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube [4]
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