Binary Polyhedral Groups
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Home > Art, Film & Photography > Binary Polyhedral Groups: Binary Icosahedral Group, Binary Tetrahedral Group, Binary Octahedral Group, Binary Cyclic Group
Binary Polyhedral Groups: Binary Icosahedral Group, Binary Tetrahedral Group, Binary Octahedral Group, Binary Cyclic Group

Binary Polyhedral Groups: Binary Icosahedral Group, Binary Tetrahedral Group, Binary Octahedral Group, Binary Cyclic Group


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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: Binary Icosahedral Group, Binary Tetrahedral Group, Binary Octahedral Group, Binary Cyclic Group, Binary Polyhedral Group, Binary Dihedral Group. Not illustrated. Excerpt: In mathematics, the binary icosahedral group is a certain nonabelian group of order 120. It is an extension of the icosahedral group I of order 60 by a cyclic group of order 2, and is the preimage of the icosahedral group under the 2:1 covering homomorphism of the special orthogonal group by the spin group. It follows that the binary icosahedral group is discrete subgroup of Spin(3) of order 120. It should not be confused with the full icosahedral group, which is a different group of order 120, and is rather a subgroup of the orthogonal group O(3). The binary icosahedral group is most easily described concretely as a discrete subgroup of the unit quaternions, under the isomorphism where Sp(1) is the multiplicative group of unit quaternions. (For a description of this homomorphism see the article on quaternions and spatial rotations.) Explicitly, the binary icosahedral group is given as the union of the 24 Hurwitz units {1, i, j, k, (1 i j k)}with all 96 quaternions obtained from (0 i j k)by an even permutation of coordinates (all possible sign combinations). Here = (1+5) is the golden ratio. All told there are 120 elements. They all have absolute value 1 and therefore lie in the unit quaternion group Sp(1). The convex hull of these 120 elements in 4-dimensional space form a convex regular 4-polytope called the 600-cell. The binary icosahedral group, denoted by 2I, is the universal perfect central extension of the icosahedral group, and thus is quasisimple: it is a perfect central extension of a simple group. Explicitly, it fits into the short exact seq... More: http: //booksllc.net/?id=3195145


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Product Details
  • ISBN-13: 9781158278039
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • No of Pages: 46
  • Spine Width: 3 mm
  • Weight: 82 gr
  • ISBN-10: 1158278039
  • Publisher Date: 19 Jun 2010
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Binary Icosahedral Group, Binary Tetrahedral Group, Binary Octahedral Group, Binary Cyclic Group
  • Width: 229 mm


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