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- Q6640332 subject Q7035965.
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- Q6640332 abstract "Spherical symmetry groups are also called point groups in three dimensions; however, this article is limited to the finite symmetries. There are five fundamental symmetry classes which have triangular fundamental domains: dihedral, cyclic, tetrahedral, octahedral, and icosahedral symmetry.This article lists the groups by Schoenflies notation, Coxeter notation, orbifold notation, and order. John Conway uses a variation of the Schoenflies notation, based on the groups' quaternion algebraic structure, labeled by one or two upper case letters, and whole number subscripts. The group order is defined as the subscript, unless the order is doubled for symbols with a plus or minus, "±", prefix, which implies a central inversion.Hermann–Mauguin notation (International notation) is also given. The crystallography groups, 32 in total, are a subset with element orders 2, 3, 4 and 6.".
- Q6640332 thumbnail Sphere_symmetry_group_c1.png?width=300.
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- Q6640332 comment "Spherical symmetry groups are also called point groups in three dimensions; however, this article is limited to the finite symmetries. There are five fundamental symmetry classes which have triangular fundamental domains: dihedral, cyclic, tetrahedral, octahedral, and icosahedral symmetry.This article lists the groups by Schoenflies notation, Coxeter notation, orbifold notation, and order.".
- Q6640332 label "List of spherical symmetry groups".
- Q6640332 depiction Sphere_symmetry_group_c1.png.