# 帶鏡像的直角十二面體 # # 直角十二面體存在於三維的雙曲空間中。 # 利用下面的代表沿著它的十二個面的反射的矩陣, # 可以平鋪一個雙曲3-維空間。 # # 矩陣的每一項都是域Q[ξ]的元素,其中 # ξ是不可約的度為4的多項式 # ξ⁴ - 2ξ³ - 12ξ² - 12ξ - 4 的根。 # 利用黃金分割率 φ ≈ 1.61803..., # ξ = φ + √(3 + 5φ) ≈ 4.94822... # 因此矩陣的特殊項 # # 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