The Lattice cubic P (classical holotype)

An entry from the Catalogue of Lattices, which is a joint project of
Neil J. A. Sloane, AT&T Labs-Research (njas@research.att.com) and
Gabriele Nebe, University of Ulm (nebe@mathematik.uni-ulm.de)

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIM
GRAM
DET
GROUP_NAME
GROUP_ORDER
REFERENCES
NOTES
BASIS
TRIANGULAR_BASIS
PROPERTIES
LAST_LINE

• NAME
  cubic P (classical holotype)
  
• DIM
  3
  
• GRAM
  3 3
  1 0 0
  0 1 0
  0 0 1
  
• DET
  1
  
• GROUP_NAME
  *432 = +-O_24
  Also O_h = m3{bar}m = [3,4] = 2xS_4
  
• GROUP_ORDER
  48
  
• REFERENCES
  Kittel, Intro to Solid State Physics p. 14.
  Wells, Structural Inorganic Chemistry p. 43.
  
• NOTES
  The simple cubic lattice Z3 = I3.
  One of the Bravais lattices.
  Holotype = smallest determinant of any classically integral lattice
  of this type.
  
• BASIS
  3 3
  .100000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .100000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .100000000000E+01
  
• TRIANGULAR_BASIS
  3 3
  .100000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .100000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .100000000000E+01
  
• PROPERTIES
  INTEGRAL =1
  
• LAST_LINE
  
  

INDEX FILE | ABBREVIATIONS

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