| 31. | The set of all rotations forms a Lie subgroup isomorphic to the ordinary rotation group SO ( 3 ).
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| 32. | The rotation group SO ( 3 ) can be described as a subgroup of direct isometries of Euclidean "'R "'3.
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| 33. | In norm quaternions, is also simply connected, so it is the covering group of the rotation group SO ( 3 ).
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| 34. | The 5D rotation group SO ( 5 ) and all higher rotation groups contain subgroups isomorphic to O ( 4 ).
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| 35. | The set of all appropriate matrices together with the operation of matrix multiplication is the rotation group SO ( 3 ).
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| 36. | Noticing that there are 8 corners and 12 edges, and that all the rotation groups are abelian, gives the above structure.
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| 37. | For example, in the rotation group SO ( 3 ) the maximal tori are given by rotations about a fixed axis.
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| 38. | The 5D rotation group SO ( 5 ) and all higher rotation groups contain subgroups isomorphic to O ( 4 ).
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| 39. | One is rotation group, or more generally of double cover of the generalized special orthogonal group on spaces with metric signature.
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| 40. | The rotation group of an object is equal to its full symmetry group if and only if the object is chiral.
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