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Home > Art, Film & Photography > Platonic Solids: Platonic Solid, Tetrahedron, Icosahedron, Octahedron, Dodecahedron, Cube, Harmonices Mundi
Platonic Solids: Platonic Solid, Tetrahedron, Icosahedron, Octahedron, Dodecahedron, Cube, Harmonices Mundi

Platonic Solids: Platonic Solid, Tetrahedron, Icosahedron, Octahedron, Dodecahedron, Cube, Harmonices Mundi


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About the Book

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. Chapters: Platonic Solid, Tetrahedron, Icosahedron, Octahedron, Dodecahedron, Cube, Harmonices Mundi, Platonic Hydrocarbon. Excerpt: Regular Hexahedron In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids . It is a special kind of square prism, of rectangular parallelepiped and of trigonal trapezohedron . The cube is dual to the octahedron . It has cubical symmetry (also called octahedral symmetry ). A cube is the three-dimensional case of the more general concept of a hypercube . It has 11 nets . If one were to colour the cube so that no two adjacent faces had the same colour, one would need 3 colours. If the original cube has edge length 1, its dual octahedron has edge length . Cartesian coordinates For a cube centered at the origin, with edges parallel to the axes and with an edge length of 2, the Cartesian coordinates of the vertices are ( 1, 1, 1) while the interior consists of all points ( x 0, x 1, x 2) with 1 x i 1. Formulae For a cube of edge length a, surface area: 6 a As the volume of a cube is the third power of its sides a a a, third powers are called cubes, by analogy with squares and second powers. A cube has the largest volume among cuboids (rectangular boxes) with a given surface area . Also, a cube has the largest volume among cuboids with the same total linear size (length ] width + height). Uniform colorings and symmetry The cube has 3 uniform colorings, named by the colors of the square faces around each vertex: 111, 112, 123. The cube has 3 classes of symmetry, which can be represented by vertex-transitive coloring the faces. The highest octahedral symmetry Oh has all the faces th...


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Product Details
  • ISBN-13: 9781155679686
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • No of Pages: 72
  • Spine Width: 4 mm
  • Weight: 118 gr
  • ISBN-10: 1155679687
  • Publisher Date: 06 May 2010
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Platonic Solid, Tetrahedron, Icosahedron, Octahedron, Dodecahedron, Cube, Harmonices Mundi
  • Width: 229 mm


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