A pyramid (of the Greek grc pyramis ) with N east coasts a Polyhedral formed by connecting a polygonal base of N with dimensions to a point, called the apex, by N triangular faces ( N ≥ 3). In other words, it is a conical Solide with a polygonal base.

They are the Greeks who introduced the name of “pyramid”, comparing the Pyramides of Egypt with one their ptisseries of similar form called “ pyramis ” or “ pyramous ”.

When that is not specified, the base is supposed to be square. For a triangular pyramid each face can be used as a basis, with the top opposed for apex. The regular Tetrahedron , one of the solid of Plato, is a triangular pyramid. The square and pentagonal pyramids can also be built with all the regular faces, and consequently are solid of Johnson. All the pyramids are auto- duaux.

The pyramids are subclasses of the Prismatoïde S.

Volume

The Volume of a pyramid is $V\; =\; \backslash \; frac\; \{1\}\; \{3\}\; Ah$ where has is the surface of the base and H the height of the base to the apex. This is valid for any localization of the apex, provided that H is measured as the distance Perpendiculaire starting from the plan which contains the base.

Surface of surface

The surface of the surface of a regular pyramid is $A\; =\; A\_b\; +\; \backslash \; frac\; \{PS\}\; \{2\}$ where $A\_b$ is the surface of the base, p is the périmère base and S is the height of the slope along the bisectrix of a face (IE the length starting from the medium of an unspecified edge of the base to the apex).

Pyramids with polygonal faces

If all the faces are regular polygons, the base of the pyramid can be a regular polygon of 3,4 or 5 with dimensions:

The geometrical center of a square pyramid is localized on the axis of symmetry, with a quarter of the base towards the apex.

Symmetry

If the base is regular and the apex is above the center, the Groupe of symmetry of a pyramid with N east coasts C_nv of a nature 2 N , except in the case of a regular tetrahedron, which has the larger group of symmetry T_d of order 24, which has four versions of C_3v for sub-groups. The Groupe of rotation is C_n of order N , except in the case of a regular tetrahedron, which has the larger group of rotation T of order 12, which has four versions of C₃ for sub-groups.

Symbolic system

The pyramidal form would be magic, and would increase certain qualities in it, at a precise place.

See also: Fields of form

See too

• Bipyramide
• trigonal Pyramid (chemistry)

External bonds

• uniform polyhedrons
• triangular Pyramid, square Pyramid and pentagonal Pyramid in rotation on the site Maths Is Fun
• Polyhedral actually virtual the encyclopedia of the Model polyhedrons
• vrml (George Binder) <3> <4> <5>
• Owners out of paper of pyramids

Random links:

DirectX | Festival of Angouleme 1996 | Lamina | Prarolo | Jonathon Power