Regular Polyhedra
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Home > Art, Film & Photography > Regular Polyhedra: Kepler-Poinsot Polyhedra, Platonic Solids, Tetrahedron, Icosahedron, Octahedron, Dodecahedron, Cube
Regular Polyhedra: Kepler-Poinsot Polyhedra, Platonic Solids, Tetrahedron, Icosahedron, Octahedron, Dodecahedron, Cube

Regular Polyhedra: Kepler-Poinsot Polyhedra, Platonic Solids, Tetrahedron, Icosahedron, Octahedron, Dodecahedron, Cube


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About the Book

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 23. Chapters: Kepler-Poinsot polyhedra, Platonic solids, Tetrahedron, Icosahedron, Octahedron, Dodecahedron, Cube, Kepler-Poinsot polyhedron, Small stellated dodecahedron, Harmonices Mundi, Great stellated dodecahedron, Great icosahedron, Great dodecahedron, Platonic hydrocarbon, Prince Rupert's cube. 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 Euclidean 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's surface. 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 ...


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Product Details
  • ISBN-13: 9781157925583
  • Publisher: Books LLC, Wiki Series
  • Publisher Imprint: Books LLC, Wiki Series
  • Height: 246 mm
  • No of Pages: 24
  • Spine Width: 1 mm
  • Weight: 64 gr
  • ISBN-10: 1157925588
  • Publisher Date: 09 Jul 2011
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Kepler-Poinsot Polyhedra, Platonic Solids, Tetrahedron, Icosahedron, Octahedron, Dodecahedron, Cube
  • Width: 189 mm


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