#	Mirrored Right-Angled Dodecahedron
#
#	A dodecahedron with all right angles lives in 3-dimensional
#	hyperbolic space.  The following matrices, representing
#	reflections across each of its twelve faces, generate
#	a tiling of hyperbolic 3-space.
#
#	The matrix entries live in the field Q[ξ], where
#	ξ is a root of the irreducible quartic polynomial
#	ξ⁴ - 2ξ³ - 12ξ² - 12ξ - 4.
#	In terms of the golden ratio φ ≈ 1.61803...,
#	ξ = φ + √(3 + 5φ) ≈ 4.94822...
#	The specific matrix entries are
#
#		     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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