Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: In geometry, a tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids. The tetrahedron is the only convex polyhedron that has four faces. The tetrahedron is the three-dimensional case of the more general concept of a simplex. The tetrahedron is one kind of pyramid, which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point. In the case of a tetrahedron the base is a triangle (any of the four faces can be considered the base), so a tetrahedron is also known as a triangular pyramid. Like all convex polyhedra, a tetrahedron can be folded from a single sheet of paper. It has two nets. For any tetrahedron there exists a sphere (the circumsphere) such that the tetrahedron's vertices lie on the sphere. For a regular tetrahedron of edge length : Note that with respect to the base plane the slope of a face () is twice that of an edge (), corresponding to the fact that the horizontal distance covered from the base to the apex along an edge is twice that along the median of a face. In other words, if C is the centroid of the base, the distance from C to a vertex of the base is twice that from C to the midpoint of an edge of the base. This follows from the fact that the medians of a triangle intersect at its centroid, and this point divides each of them in two segments, one of which is twice as long as the other (see proof). The volume of a tetrahedron is given by the pyramid volume formula: where is the area of the base and h the height from the base to the apex. This applies for each of the four choices of the base, so the ... More: http://booksllc.net/?id=30606
Author Publisher Books LLC Publication Date 2010-05-31 Binding Paperback ISBN 1156226333 Number Of Pages 44 Sales Rank 99999999
