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