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#  庞加莱(Poincaré)十二面体空间
#
#  二次二十面体群作用于3维球面所得到的商空间就是著名庞加莱十二面体空间。
#  群的矩阵元素属于域Q[φ],其中 φ = (1 + √5)/2 ≈ 1.6180339887...
#  是黄金分割率并且是不可约多项式 φ² - φ - 1 的根。

  0.80901699437494742410 -0.50000000000000000000  0.00000000000000000000 -0.30901699437494742410
  0.50000000000000000000  0.80901699437494742410  0.30901699437494742410  0.00000000000000000000
  0.00000000000000000000 -0.30901699437494742410  0.80901699437494742410  0.50000000000000000000
  0.30901699437494742410  0.00000000000000000000 -0.50000000000000000000  0.80901699437494742410

  0.80901699437494742410 -0.30901699437494742410  0.50000000000000000000  0.00000000000000000000
  0.30901699437494742410  0.80901699437494742410  0.00000000000000000000  0.50000000000000000000
 -0.50000000000000000000  0.00000000000000000000  0.80901699437494742410  0.30901699437494742410
  0.00000000000000000000 -0.50000000000000000000 -0.30901699437494742410  0.80901699437494742410