#	鏡映直角正12面体
#
#	全ての面の内角が直角であるような、正12面体は、3次元双曲型空間内に存在する。
#	次の12の行列は、それぞれ直角正12面体の、12の面を鏡映面とする鏡映変換であって、
#	3次元双曲型空間を、隙間無く直角正12面体で埋め尽くす、タイル張りを生成する。
#
#	行列要素は、全て、体 Q[ξ] の元である。ここに、ξ とは、4次の既約方程式
#	ξ⁴ - 2ξ³ - 12ξ² - 12ξ - 4 のひとつの根であって、黄金比 φ ≈ 1.61803... によって、
#	ξ = φ + √(3 + 5φ) ≈ 4.94822... という関係で与えられている。
#	実際に、行列要素として現れる数は、次の4つである:
#
#		     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...
#

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