# Poincaré Dodecahedral Space # # The quotient of the 3-sphere by the binary icosahedral group # is the famous Poincaré dodecahedral space. # The matrix elements lie in the field Q[φ], where # φ is the golden ratio. The golden ratio is a root # of the irreducible polynomial φ² - φ - 1, # with numerical value φ = (1 + √5)/2 ≈ 1.6180339887... 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