1Real embedded number field: 2min_poly (q^2 - 5) embedding [2.2360679774997896964091736687312762354406183596115257242708972 +/- 6.03e-62] 3 47 lattice points in polytope 520 vertices of polyhedron 60 extreme rays of recession cone 712 support hyperplanes of polyhedron (homogenized) 8 9embedding dimension = 4 10affine dimension of the polyhedron = 3 (maximal) 11rank of recession cone = 0 (polyhedron is polytope) 12 13size of triangulation = 32 14resulting sum of |det|s = (-1056*q+2400 ~ 38.712216) 15 16dehomogenization: 170 0 0 1 18 19 20volume (lattice normalized) = (-1056*q+2400 ~ 38.712216) 21volume (Euclidean) = 6.45203596004 22 23*********************************************************************** 24 257 lattice points in polytope: 26 -1 0 0 1 27 0 -1 0 1 28 0 0 -1 1 29 0 0 0 1 30 0 0 1 1 31 0 1 0 1 32 1 0 0 1 33 3420 vertices of polyhedron: 35 (-q+1 ~ -1.2360680) (-2*q+4 ~ -0.47213595) 0 1 36 (-q+1 ~ -1.2360680) (2*q-4 ~ 0.47213595) 0 1 37 (q-3 ~ -0.76393202) (q-3 ~ -0.76393202) (q-3 ~ -0.76393202) 1 38 (q-3 ~ -0.76393202) (q-3 ~ -0.76393202) (-q+3 ~ 0.76393202) 1 39 (q-3 ~ -0.76393202) (-q+3 ~ 0.76393202) (q-3 ~ -0.76393202) 1 40 (q-3 ~ -0.76393202) (-q+3 ~ 0.76393202) (-q+3 ~ 0.76393202) 1 41 (-2*q+4 ~ -0.47213595) 0 (-q+1 ~ -1.2360680) 1 42 (-2*q+4 ~ -0.47213595) 0 (q-1 ~ 1.2360680) 1 43 0 (-q+1 ~ -1.2360680) (-2*q+4 ~ -0.47213595) 1 44 0 (-q+1 ~ -1.2360680) (2*q-4 ~ 0.47213595) 1 45 0 (q-1 ~ 1.2360680) (-2*q+4 ~ -0.47213595) 1 46 0 (q-1 ~ 1.2360680) (2*q-4 ~ 0.47213595) 1 47 (2*q-4 ~ 0.47213595) 0 (-q+1 ~ -1.2360680) 1 48 (2*q-4 ~ 0.47213595) 0 (q-1 ~ 1.2360680) 1 49 (-q+3 ~ 0.76393202) (q-3 ~ -0.76393202) (q-3 ~ -0.76393202) 1 50 (-q+3 ~ 0.76393202) (q-3 ~ -0.76393202) (-q+3 ~ 0.76393202) 1 51 (-q+3 ~ 0.76393202) (-q+3 ~ 0.76393202) (q-3 ~ -0.76393202) 1 52 (-q+3 ~ 0.76393202) (-q+3 ~ 0.76393202) (-q+3 ~ 0.76393202) 1 53 (q-1 ~ 1.2360680) (-2*q+4 ~ -0.47213595) 0 1 54 (q-1 ~ 1.2360680) (2*q-4 ~ 0.47213595) 0 1 55 560 extreme rays of recession cone: 57 5812 support hyperplanes of polyhedron (homogenized): 59 (-1/4*q-1/4 ~ -0.80901699) 0 (-1/2 ~ -0.50000000) 1 60 (-1/4*q-1/4 ~ -0.80901699) 0 (1/2 ~ 0.50000000) 1 61 (-1/2 ~ -0.50000000) (-1/4*q-1/4 ~ -0.80901699) 0 1 62 (-1/2 ~ -0.50000000) (1/4*q+1/4 ~ 0.80901699) 0 1 63 0 (-1/2 ~ -0.50000000) (-1/4*q-1/4 ~ -0.80901699) 1 64 0 (-1/2 ~ -0.50000000) (1/4*q+1/4 ~ 0.80901699) 1 65 0 (1/2 ~ 0.50000000) (-1/4*q-1/4 ~ -0.80901699) 1 66 0 (1/2 ~ 0.50000000) (1/4*q+1/4 ~ 0.80901699) 1 67 (1/2 ~ 0.50000000) (-1/4*q-1/4 ~ -0.80901699) 0 1 68 (1/2 ~ 0.50000000) (1/4*q+1/4 ~ 0.80901699) 0 1 69 (1/4*q+1/4 ~ 0.80901699) 0 (-1/2 ~ -0.50000000) 1 70 (1/4*q+1/4 ~ 0.80901699) 0 (1/2 ~ 0.50000000) 1 71 72