# 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