mathematics, the binary icosahedral group 2I or ⟨2,3,5⟩ is a certain nonabelian group of order 120. It is an extension of the icosahedral group I or (2,3,5)...

icosahedral group (subject of this article, also known as H3) 2I, the binary icosahedral group They correspond to the following short exact sequences (the latter...

For example the binary icosahedral group covers the icosahedral group, an alternating group of degree 5, and the binary tetrahedral group covers the tetrahedral...

fundamental group of a homology sphere, then G is superperfect. The smallest finite, non-trivial superperfect group is the binary icosahedral group (the fundamental...

Binary dihedral group, ⟨2,2,n⟩, order 4n Binary octahedral group, 2O = ⟨2,3,4⟩, order 48 Binary icosahedral group, 2I = ⟨2,3,5⟩, order 120 Coxeter, Complex...

binary icosahedral group of order 120. The icosian ring: all finite sums of the 120 unit icosians. The 120 unit icosians, which form the icosian group, are...

is known as the binary dihedral group. The connection with the binary cyclic group C2n, the cyclic group Cn, and the dihedral group Dihn of order 2n...

polyhedral group (l,m,n). For instance, the preimage of the icosahedral group (2,3,5) is the binary icosahedral group, ⟨2,3,5⟩. The binary polyhedral groups are:...

double cover of the alternating group A5, or equivalently the binary icosahedral group. They can also be used to give a construction of an exotic map...

order 48 binary icosahedral group, ⟨2,3,5⟩, order 120 Coxeter, H. S. M. (1959), "Symmetrical definitions for the binary polyhedral groups", Proc. Sympos...

perfect group need not be simple; for example, the special linear group over the field with 5 elements, SL(2,5) (or the binary icosahedral group, which...

finite fundamental group. Its fundamental group is known as the binary icosahedral group and has order 120. Since the fundamental group of the 3-sphere is...

group binary cyclic group, ⟨n⟩, index 2n binary dihedral group, ⟨2,2,n⟩, index 4n binary tetrahedral group, 2T=⟨2,3,3⟩, index 24 binary icosahedral group...

3, and 4. The fundamental group is a product of a cyclic group of order m coprime to 30 with the binary icosahedral group (order 120) which has the presentation...

as it is the quotient of the 3-sphere by the binary icosahedral group, which is very close to icosahedral symmetry, the symmetry of a soccer ball. This...

prefix binary. For instance, the preimage of the icosahedral group is the binary icosahedral group. The versors' group is isomorphic to SU(2), the group of...

alternating group A5 agrees with the chiral icosahedral group (itself an exceptional object), and the double cover of the alternating group A5 is the binary icosahedral...

3-sphere itself) with a finite fundamental group. Its fundamental group is known as the binary icosahedral group and has order 120. This shows the Poincaré...

Nintendo DS storage devices Base 2i, or Quater-imaginary base The binary icosahedral group 2I SSH 2I (WA), now U.S. Route 97 in Washington The 2i's Coffee...

Mebius. The binary icosahedral group is isomorphic to SL(2,5). The full symmetry group of the 600-cell is the Weyl group of H4. This is a group of order...

multiply as the binary octahedral group. Another subgroup is formed by 120 icosians which multiply in the manner of the binary icosahedral group. A hyperbolic...

the figure on the right. Specifically, with quaternions from the binary Icosahedral group ( p , q ) ∈ I h {\displaystyle (p,q)\in I_{h}} , where q = p ¯...

Zassenhaus's paper. The binary tetrahedral, octahedral and icosahedral groups are central extensions of the rotational symmetry groups of the platonic solids;...

U1(H): the binary cyclic groups, binary dihedral groups, binary tetrahedral group, binary octahedral group, and binary icosahedral group. Hoggar, S.G...

the cyclic groups, the binary dihedral groups, the binary tetrahedral group, the binary octahedral group, and the binary icosahedral group; and for SO(3)...

PMID 10035936. Day, Charles (2001-02-01). "Binary Quasicrystals Discovered That Are Stable and Icosahedral". Physics Today. 54 (2): 17–18. Bibcode:2001PhT...

{Z} )=H_{2}(G;\mathbf {Z} )=0} . The converse is not true: the binary icosahedral group is superperfect (hence perfect) but not acyclic. Aspherical space...

explains the name dihedral group (in analogy to tetrahedral, octahedral and icosahedral group, referring to the proper symmetry groups of a regular tetrahedron...

tetrahedron has chiral symmetry. Octahedral symmetry Icosahedral symmetry Binary tetrahedral group Koca et al. 2016. Peter R. Cromwell, Polyhedra (1997)...

{\displaystyle a^{-1}} . Formally, a group is an ordered pair of a set and a binary operation on this set that satisfies the group axioms. The set is called the...