Pyramid

:See also: Egyptian pyramids, Mesoamerican pyramids, Nubian pyramids.

Related Topics:
Egyptian pyramids - Mesoamerican pyramids - Nubian pyramids

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An n-sided pyramid is a polyhedron formed by connecting an n-sided polygonal base and a point, called the apex, by n triangular faces (n≥3). In other words, it is a conic solid with polygonal base. When unspecified the base is usually assumed to be square. For a triangular pyramid each face can serve as base, with the opposite vertex as apex. One of the Platonic solids, the tetrahedron, is a triangular pyramid. The square and pentagonal pyramids can also be constructed with all faces regular, and so count among the Johnson solids. All pyramids are self-dual. The volume of a pyramid is V = rac{1}{3} Ah where A is the area of the base and h the height from the base to the apex.

Related Topics:
Polyhedron - Polygon - Apex - Triangular - Conic solid - Platonic solid - Tetrahedron - Johnson solid - Dual

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The geometric centre of a square-sided regular pyramid is located on the symmetry axis, one quarter of the way from the base to the apex.

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If the base is regular and the apex is above the center, the symmetry group of the n-sided pyramid is Cnv of order 2n, except in the case of a regular tetrahedron, which has the larger symmetry group Td of order 24, which has four versions of C3v as subgroups.

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The rotation group is Cn of order n, except in the case of a regular tetrahedron, which has the larger rotation group T of order 12, which has four versions of C3 as subgroups.

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