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In Hermann–Mauguin notation, space groups are named by a symbol combining the point group identifier with the uppercase letters describing the lattice type. Translations within the lattice in the form of screw axes and glide planes are also noted, giving a complete crystallographic space group. These are the Bravais lattices in three dimensions:
In n dimensions, an affine space group, or Bieberbach group, ... 31 1 Frieze groups: 7 31 2 Wallpaper groups 17 80 3 0 Three-dimensional point groups: 32 122 1 ...
In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, ... 31: Fundamental domain
In geometry, a point group in four dimensions is an isometry group in four dimensions that leaves the origin fixed, ... (Du Val #31 (I/C 2;I/C 2), Conway ...
Size: 46.56 kpc (152,000 ... named the Andromeda Nebula and is cataloged as Messier 31, M31, ... to be more massive than G1 and the largest cluster of the Local Group
Advanced Persistent Threat Group 31 (APT31) is a collective of Chinese state-sponsored intelligence officers, contract hackers and attendant staff that engage in hacking activities and "malicious ...
The other is the quaternion group for p = 2 and a group of exponent p for p > 2. Order p 4 : The classification is complicated, and gets much harder as the exponent of p increases. Most groups of small order have a Sylow p subgroup P with a normal p -complement N for some prime p dividing the order, so can be classified in terms of the possible ...
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