返回

#  带镜像的直角十二面体
#
#  直角十二面体存在于三维的双曲空间中。
#  利用下面的代表沿着它的十二个面的反射的矩阵,
#  可以平铺一个双曲3-维空间。
#
#  矩阵的每一项都是域Q[ξ]的元素,其中
#  ξ是不可约的度为4的多项式
#  ξ⁴ - 2ξ³ - 12ξ² - 12ξ - 4 的根。
#  利用黄金分割率 φ ≈ 1.61803...,
#  ξ = φ + √(3 + 5φ) ≈ 4.94822...
#  因此矩阵的特殊项
#
#  	     φ     = -(1/4)ξ³ +      ξ² + (3/2)ξ     ≈ 1.61803...
#  	   φ + 1   = -(1/4)ξ³ +      ξ² + (3/2)ξ + 1 ≈ 2.61803...
#  	√( φ² - 1) = -(1/4)ξ³ + (1/2)ξ² + (7/2)ξ + 2 ≈ 1.27201...
#  	√(2φ² - 1) =  (1/2)ξ³ - (3/2)ξ² -   4  ξ - 2 ≈ 2.05817...

 -1.61803398874989484820  1.61803398874989484820  0.00000000000000000000 -2.05817102727149225032
  1.61803398874989484820  0.00000000000000000000  0.00000000000000000000  1.27201964951406896425
  0.00000000000000000000  0.00000000000000000000  1.00000000000000000000  0.00000000000000000000
  2.05817102727149225032 -1.27201964951406896425  0.00000000000000000000  2.61803398874989484820

 -1.61803398874989484820 -1.61803398874989484820  0.00000000000000000000 -2.05817102727149225032
 -1.61803398874989484820  0.00000000000000000000  0.00000000000000000000 -1.27201964951406896425
  0.00000000000000000000  0.00000000000000000000  1.00000000000000000000  0.00000000000000000000
  2.05817102727149225032  1.27201964951406896425  0.00000000000000000000  2.61803398874989484820

 -1.61803398874989484820 -1.61803398874989484820  0.00000000000000000000  2.05817102727149225032
 -1.61803398874989484820  0.00000000000000000000  0.00000000000000000000  1.27201964951406896425
  0.00000000000000000000  0.00000000000000000000  1.00000000000000000000  0.00000000000000000000
 -2.05817102727149225032 -1.27201964951406896425  0.00000000000000000000  2.61803398874989484820

 -1.61803398874989484820  1.61803398874989484820  0.00000000000000000000  2.05817102727149225032
  1.61803398874989484820  0.00000000000000000000  0.00000000000000000000 -1.27201964951406896425
  0.00000000000000000000  0.00000000000000000000  1.00000000000000000000  0.00000000000000000000
 -2.05817102727149225032  1.27201964951406896425  0.00000000000000000000  2.61803398874989484820

  0.00000000000000000000  0.00000000000000000000  1.61803398874989484820  1.27201964951406896425
  0.00000000000000000000  1.00000000000000000000  0.00000000000000000000  0.00000000000000000000
  1.61803398874989484820  0.00000000000000000000 -1.61803398874989484820 -2.05817102727149225032
 -1.27201964951406896425  0.00000000000000000000  2.05817102727149225032  2.61803398874989484820

  0.00000000000000000000  0.00000000000000000000 -1.61803398874989484820 -1.27201964951406896425
  0.00000000000000000000  1.00000000000000000000  0.00000000000000000000  0.00000000000000000000
 -1.61803398874989484820  0.00000000000000000000 -1.61803398874989484820 -2.05817102727149225032
  1.27201964951406896425  0.00000000000000000000  2.05817102727149225032  2.61803398874989484820

  0.00000000000000000000  0.00000000000000000000 -1.61803398874989484820  1.27201964951406896425
  0.00000000000000000000  1.00000000000000000000  0.00000000000000000000  0.00000000000000000000
 -1.61803398874989484820  0.00000000000000000000 -1.61803398874989484820  2.05817102727149225032
 -1.27201964951406896425  0.00000000000000000000 -2.05817102727149225032  2.61803398874989484820

  0.00000000000000000000  0.00000000000000000000  1.61803398874989484820 -1.27201964951406896425
  0.00000000000000000000  1.00000000000000000000  0.00000000000000000000  0.00000000000000000000
  1.61803398874989484820  0.00000000000000000000 -1.61803398874989484820  2.05817102727149225032
  1.27201964951406896425  0.00000000000000000000 -2.05817102727149225032  2.61803398874989484820

  1.00000000000000000000  0.00000000000000000000  0.00000000000000000000  0.00000000000000000000
  0.00000000000000000000 -1.61803398874989484820  1.61803398874989484820 -2.05817102727149225032
  0.00000000000000000000  1.61803398874989484820  0.00000000000000000000  1.27201964951406896425
  0.00000000000000000000  2.05817102727149225032 -1.27201964951406896425  2.61803398874989484820

  1.00000000000000000000  0.00000000000000000000  0.00000000000000000000  0.00000000000000000000
  0.00000000000000000000 -1.61803398874989484820 -1.61803398874989484820 -2.05817102727149225032
  0.00000000000000000000 -1.61803398874989484820  0.00000000000000000000 -1.27201964951406896425
  0.00000000000000000000  2.05817102727149225032  1.27201964951406896425  2.61803398874989484820

  1.00000000000000000000  0.00000000000000000000  0.00000000000000000000  0.00000000000000000000
  0.00000000000000000000 -1.61803398874989484820 -1.61803398874989484820  2.05817102727149225032
  0.00000000000000000000 -1.61803398874989484820  0.00000000000000000000  1.27201964951406896425
  0.00000000000000000000 -2.05817102727149225032 -1.27201964951406896425  2.61803398874989484820

  1.00000000000000000000  0.00000000000000000000  0.00000000000000000000  0.00000000000000000000
  0.00000000000000000000 -1.61803398874989484820  1.61803398874989484820  2.05817102727149225032
  0.00000000000000000000  1.61803398874989484820  0.00000000000000000000 -1.27201964951406896425
  0.00000000000000000000 -2.05817102727149225032  1.27201964951406896425  2.61803398874989484820