Quantum Marginal Problems¶
The following are solutions to a number of pure-state quantum marginal problem. See, e.g., Klyachko (2004) or Walter (2014)) for an introduction to the subject. Mathematically, these are given by the Kronecker polytopes \(C(d_1,d_2,d_3,\dots)\), i.e., the moment polytopes for the action of some \(\times_i GL(d_i)\) on \(\bigotimes_i \mathbb C^{d_i}\).
#import logging
#reload(logging)
#logging.basicConfig(format='%(asctime)s %(levelname)s:%(message)s', level=logging.DEBUG, datefmt='%I:%M:%S')
from moment_polytopes import *
\(C(4,4,4)\)¶
qmp.pretty((4, 4, 4), algorithm='mathematica')
C(4,4,4)
========
Facets
------
# H_A H_B H_C z Remarks
--- --------------- --------------- --------------- --- ---------
1 (-5, -1, 3, 3) (-5, 3, 3, -1) (5, 1, -3, -3) 5 *
2 (-5, -1, 3, 3) (1, -3, -3, 5) (3, 3, -1, -5) 5
3 (-5, 3, -1, 3) (-5, 3, -1, 3) (5, 1, -3, -3) 5 *
4 (-5, 3, -1, 3) (-5, 3, 3, -1) (5, -3, 1, -3) 5 *
5 (-5, 3, -1, 3) (-3, 1, -3, 5) (3, 3, -1, -5) 5 *
6 (-5, 3, -1, 3) (-3, 5, 1, -3) (3, -5, 3, -1) 5 *
7 (-5, 3, -1, 3) (1, -3, -3, 5) (3, -1, 3, -5) 5
8 (-5, 3, -1, 3) (1, -3, 5, -3) (3, -1, -5, 3) 5
9 (-5, 3, 3, -1) (-5, 3, 3, -1) (5, -3, -3, 1) 5 *
10 (-5, 3, 3, -1) (-3, -3, 1, 5) (3, 3, -1, -5) 5 *
11 (-5, 3, 3, -1) (-3, -3, 5, 1) (3, 3, -5, -1) 5 *
12 (-5, 3, 3, -1) (-3, 1, -3, 5) (3, -1, 3, -5) 5 *
13 (-5, 3, 3, -1) (-3, 1, 5, -3) (3, -1, -5, 3) 5 *
14 (-5, 3, 3, -1) (-3, 5, -3, 1) (3, -5, 3, -1) 5 *
15 (-5, 3, 3, -1) (-3, 5, 1, -3) (3, -5, -1, 3) 5 *
16 (-5, 3, 3, -1) (-1, -5, 3, 3) (1, 5, -3, -3) 5 *
17 (-5, 3, 3, -1) (-1, 3, -5, 3) (1, -3, 5, -3) 5 *
18 (-5, 3, 3, -1) (-1, 3, 3, -5) (1, -3, -3, 5) 5 *
19 (-3, -1, 3, 1) (-3, 3, 1, -1) (3, 1, -1, -3) 3 *
20 (-3, -1, 3, 1) (1, -1, -3, 3) (3, 1, -1, -3) 3
21 (-3, 1, 1, 1) (-3, 1, 1, 1) (3, -1, -1, -1) 3 *
22 (-3, 1, 1, 1) (-2, -2, 2, 2) (2, 2, -2, -2) 3 *
23 (-3, 1, 1, 1) (-2, 2, -2, 2) (2, -2, 2, -2) 3 *
24 (-3, 1, 1, 1) (-2, 2, 2, -2) (2, -2, -2, 2) 3 *
25 (-3, 1, 1, 1) (-1, -1, -1, 3) (1, 1, 1, -3) 3 *
26 (-3, 1, 1, 1) (-1, -1, 3, -1) (1, 1, -3, 1) 3 *
27 (-3, 1, 1, 1) (-1, 3, -1, -1) (1, -3, 1, 1) 3 *
28 (-3, 3, 1, -1) (-3, 3, 1, -1) (3, -1, -3, 1) 3 *
29 (-3, 3, 1, -1) (-1, -3, 1, 3) (3, 1, -1, -3) 3
30 (-3, 3, 1, -1) (-1, -3, 3, 1) (1, 3, -1, -3) 3 *
31 (-3, 3, 1, -1) (-1, -3, 3, 1) (3, 1, -3, -1) 3
32 (-3, 3, 1, -1) (-1, 3, 1, -3) (1, -1, -3, 3) 3 *
33 (-2, -2, 2, 2) (-2, 2, 2, -2) (1, 1, -3, 1) 3 *
34 (-2, 2, -2, 2) (-2, 2, 2, -2) (1, -3, 1, 1) 3 *
35 (-1, -1, -1, 3) (0, 0, 0, 0) (0, 0, 0, 0) 1 *
36 (-1, 0, 0, 1) (-1, 1, 0, 0) (1, 0, 0, -1) 1 *
37 (-1, 0, 0, 1) (0, 0, -1, 1) (1, 0, 0, -1) 1
38 (-1, 0, 1, 0) (-1, 0, 1, 0) (1, 0, 0, -1) 1 *
39 (-1, 0, 1, 0) (-1, 1, 0, 0) (1, 0, -1, 0) 1 *
40 (-1, 0, 1, 0) (0, -1, 0, 1) (1, 0, 0, -1) 1
41 (-1, 0, 1, 0) (0, -1, 1, 0) (0, 1, 0, -1) 1 *
42 (-1, 0, 1, 0) (0, -1, 1, 0) (1, 0, -1, 0) 1
43 (-1, 0, 1, 0) (0, 0, -1, 1) (0, 1, 0, -1) 1 *
44 (-1, 1, 0, 0) (-1, 1, 0, 0) (1, -1, 0, 0) 1 *
45 (-1, 1, 0, 0) (0, -1, 0, 1) (0, 1, 0, -1) 1 *
46 (-1, 1, 0, 0) (0, -1, 1, 0) (0, 1, -1, 0) 1 *
47 (-1, 1, 0, 0) (0, 0, -1, 1) (0, 0, 1, -1) 1 *
48 (0, 0, 0, 0) (0, 0, 0, 0) (0, 0, 1, -1) 0 o, *
49 (0, 0, 0, 0) (0, 0, 0, 0) (0, 1, -1, 0) 0 o, *
50 (0, 0, 0, 0) (0, 0, 0, 0) (1, -1, 0, 0) 0 o
Facet format is (H_A,lambda_A) + ... + z >= 0. The last column states
whether the facet includes the origin (o) or the highest weight (*).
Vertices
--------
# V_A V_B V_C
--- ------------------------ ------------------------ -------------------------
1 (1/4, 1/4, 1/4, 1/4) (1/4, 1/4, 1/4, 1/4) (1/4, 1/4, 1/4, 1/4)
2 (1/4, 1/4, 1/4, 1/4) (1/4, 1/4, 1/4, 1/4) (1/3, 1/3, 1/3, 0)
3 (1/4, 1/4, 1/4, 1/4) (1/4, 1/4, 1/4, 1/4) (1/2, 1/2, 0, 0)
4 (1/4, 1/4, 1/4, 1/4) (1/4, 1/4, 1/4, 1/4) (1, 0, 0, 0)
5 (1/4, 1/4, 1/4, 1/4) (1/3, 1/3, 1/3, 0) (1/3, 1/3, 1/3, 0)
6 (1/4, 1/4, 1/4, 1/4) (1/3, 1/3, 1/3, 0) (1/2, 1/2, 0, 0)
7 (1/4, 1/4, 1/4, 1/4) (1/3, 1/3, 1/3, 0) (2/3, 1/6, 1/6, 0)
8 (1/4, 1/4, 1/4, 1/4) (1/3, 1/3, 1/3, 0) (2/3, 1/4, 1/12, 0)
9 (1/4, 1/4, 1/4, 1/4) (1/3, 1/3, 1/3, 0) (3/4, 1/12, 1/12, 1/12)
10 (1/4, 1/4, 1/4, 1/4) (3/8, 3/8, 1/4, 0) (5/8, 3/8, 0, 0)
11 (1/4, 1/4, 1/4, 1/4) (3/8, 3/8, 1/4, 0) (3/4, 1/8, 1/8, 0)
12 (1/4, 1/4, 1/4, 1/4) (2/5, 3/10, 3/10, 0) (7/10, 3/20, 3/20, 0)
13 (1/4, 1/4, 1/4, 1/4) (5/12, 5/12, 1/6, 0) (2/3, 1/6, 1/12, 1/12)
14 (1/4, 1/4, 1/4, 1/4) (1/2, 1/6, 1/6, 1/6) (1/2, 1/2, 0, 0)
15 (1/4, 1/4, 1/4, 1/4) (1/2, 1/4, 1/8, 1/8) (5/8, 3/8, 0, 0)
16 (1/4, 1/4, 1/4, 1/4) (1/2, 1/4, 1/4, 0) (1/2, 1/2, 0, 0)
17 (1/4, 1/4, 1/4, 1/4) (1/2, 1/4, 1/4, 0) (2/3, 1/6, 1/6, 0)
18 (1/4, 1/4, 1/4, 1/4) (1/2, 1/4, 1/4, 0) (3/4, 1/4, 0, 0)
19 (1/4, 1/4, 1/4, 1/4) (1/2, 3/8, 1/8, 0) (5/8, 1/8, 1/8, 1/8)
20 (1/4, 1/4, 1/4, 1/4) (1/2, 1/2, 0, 0) (1/2, 1/2, 0, 0)
21 (2/7, 2/7, 2/7, 1/7) (4/7, 1/7, 1/7, 1/7) (4/7, 3/7, 0, 0)
22 (7/24, 7/24, 5/24, 5/24) (1/3, 1/3, 1/3, 0) (3/4, 1/8, 1/8, 0)
23 (3/10, 3/10, 1/5, 1/5) (2/5, 3/10, 3/10, 0) (4/5, 1/10, 1/10, 0)
24 (3/10, 3/10, 3/10, 1/10) (1/2, 1/2, 0, 0) (11/20, 3/20, 3/20, 3/20)
25 (3/10, 3/10, 3/10, 1/10) (1/2, 1/2, 0, 0) (3/5, 1/5, 1/10, 1/10)
26 (1/3, 2/9, 2/9, 2/9) (1/3, 1/3, 1/3, 0) (2/3, 1/3, 0, 0)
27 (1/3, 2/9, 2/9, 2/9) (1/3, 1/3, 1/3, 0) (7/9, 1/9, 1/9, 0)
28 (1/3, 2/9, 2/9, 2/9) (4/9, 4/9, 1/9, 0) (2/3, 1/9, 1/9, 1/9)
29 (1/3, 1/3, 1/6, 1/6) (1/3, 1/3, 1/3, 0) (7/9, 1/9, 1/9, 0)
30 (1/3, 1/3, 1/6, 1/6) (1/3, 1/3, 1/3, 0) (5/6, 1/6, 0, 0)
31 (1/3, 1/3, 1/6, 1/6) (1/2, 1/4, 1/4, 0) (3/4, 1/12, 1/12, 1/12)
32 (1/3, 1/3, 1/6, 1/6) (2/3, 1/6, 1/6, 0) (2/3, 1/6, 1/6, 0)
33 (1/3, 1/3, 1/3, 0) (1/3, 1/3, 1/3, 0) (1/3, 1/3, 1/3, 0)
34 (1/3, 1/3, 1/3, 0) (1/3, 1/3, 1/3, 0) (1/2, 1/2, 0, 0)
35 (1/3, 1/3, 1/3, 0) (1/3, 1/3, 1/3, 0) (1, 0, 0, 0)
36 (1/3, 1/3, 1/3, 0) (2/5, 1/5, 1/5, 1/5) (11/15, 2/15, 1/15, 1/15)
37 (1/3, 1/3, 1/3, 0) (5/12, 1/4, 1/6, 1/6) (3/4, 1/12, 1/12, 1/12)
38 (1/3, 1/3, 1/3, 0) (5/12, 5/12, 1/12, 1/12) (3/4, 1/12, 1/12, 1/12)
39 (1/3, 1/3, 1/3, 0) (4/9, 1/3, 1/9, 1/9) (7/9, 1/9, 1/9, 0)
40 (1/3, 1/3, 1/3, 0) (1/2, 1/6, 1/6, 1/6) (1/2, 1/2, 0, 0)
41 (1/3, 1/3, 1/3, 0) (1/2, 1/6, 1/6, 1/6) (2/3, 1/9, 1/9, 1/9)
42 (1/3, 1/3, 1/3, 0) (1/2, 1/6, 1/6, 1/6) (2/3, 1/3, 0, 0)
43 (1/3, 1/3, 1/3, 0) (1/2, 1/2, 0, 0) (1/2, 1/2, 0, 0)
44 (1/3, 1/3, 1/3, 0) (1/2, 1/2, 0, 0) (7/12, 1/4, 1/12, 1/12)
45 (1/3, 1/3, 1/3, 0) (1/2, 1/2, 0, 0) (2/3, 1/6, 1/6, 0)
46 (1/3, 1/3, 1/3, 0) (5/9, 2/9, 1/9, 1/9) (2/3, 1/9, 1/9, 1/9)
47 (1/3, 1/3, 1/3, 0) (2/3, 1/3, 0, 0) (2/3, 1/3, 0, 0)
48 (5/14, 5/14, 1/7, 1/7) (3/7, 2/7, 2/7, 0) (11/14, 1/14, 1/14, 1/14)
49 (4/11, 4/11, 3/11, 0) (5/11, 2/11, 2/11, 2/11) (8/11, 1/11, 1/11, 1/11)
50 (3/8, 1/4, 1/4, 1/8) (1/2, 1/2, 0, 0) (5/8, 1/8, 1/8, 1/8)
51 (3/8, 3/8, 1/4, 0) (5/8, 1/8, 1/8, 1/8) (5/8, 1/8, 1/8, 1/8)
52 (2/5, 1/5, 1/5, 1/5) (2/5, 2/5, 1/5, 0) (4/5, 1/5, 0, 0)
53 (2/5, 1/5, 1/5, 1/5) (1/2, 1/2, 0, 0) (3/5, 1/5, 1/10, 1/10)
54 (2/5, 3/10, 3/10, 0) (2/5, 2/5, 1/10, 1/10) (4/5, 1/10, 1/10, 0)
55 (2/5, 2/5, 1/10, 1/10) (3/5, 1/5, 1/5, 0) (7/10, 1/10, 1/10, 1/10)
56 (5/12, 5/12, 1/12, 1/12) (1/2, 1/4, 1/4, 0) (3/4, 1/12, 1/12, 1/12)
57 (3/7, 3/7, 1/7, 0) (4/7, 1/7, 1/7, 1/7) (5/7, 1/7, 1/7, 0)
58 (1/2, 1/6, 1/6, 1/6) (1/2, 1/2, 0, 0) (2/3, 1/6, 1/6, 0)
59 (1/2, 1/4, 1/4, 0) (1/2, 1/2, 0, 0) (5/8, 1/8, 1/8, 1/8)
60 (1/2, 1/4, 1/4, 0) (1/2, 1/2, 0, 0) (3/4, 1/4, 0, 0)
61 (1/2, 1/2, 0, 0) (1/2, 1/2, 0, 0) (1/2, 1/2, 0, 0)
62 (1/2, 1/2, 0, 0) (1/2, 1/2, 0, 0) (1, 0, 0, 0)
63 (1/2, 1/2, 0, 0) (5/8, 1/8, 1/8, 1/8) (5/8, 1/8, 1/8, 1/8)
64 (1/2, 1/2, 0, 0) (2/3, 1/6, 1/6, 0) (2/3, 1/6, 1/6, 0)
65 (1, 0, 0, 0) (1, 0, 0, 0) (1, 0, 0, 0)
All data is up to permutations of subsystems.
\(C(2,2,3,12)\)¶
#qmp.pretty((2, 2, 3, 12), algorithm='mathematica', show_vrepr=False)
Further Examples¶
qmp.pretty((2, 2, 2))
C(2,2,2)
========
Facets
------
# H_A H_B H_C z Remarks
--- ------- ------- ------- --- ---------
1 (-1, 1) (-1, 1) (1, -1) 1 *
2 (0, 0) (0, 0) (1, -1) 0 o
Facet format is (H_A,lambda_A) + ... + z >= 0. The last column states
whether the facet includes the origin (o) or the highest weight (*).
Vertices
--------
# V_A V_B V_C
--- ---------- ---------- ----------
1 (1/2, 1/2) (1/2, 1/2) (1/2, 1/2)
2 (1/2, 1/2) (1/2, 1/2) (1, 0)
3 (1, 0) (1, 0) (1, 0)
All data is up to permutations of subsystems.
qmp.pretty((2, 2, 4))
C(2,2,4)
========
Facets
------
# H_A H_B H_C z Remarks
--- ------- ------- --------------- --- ---------
1 (-1, 1) (-1, 1) (2, 0, 0, -2) 0 o, *
2 (-1, 1) (0, 0) (1, 1, -1, -1) 0 o, *
3 (-1, 1) (1, -1) (0, 2, 0, -2) 0 o, *
4 (-1, 1) (1, -1) (2, 0, -2, 0) 0 o
5 (0, 0) (0, 0) (-1, -1, -1, 3) 1 *
6 (0, 0) (0, 0) (0, 0, 1, -1) 0 o, *
7 (0, 0) (0, 0) (0, 1, -1, 0) 0 o, *
8 (0, 0) (0, 0) (1, -1, 0, 0) 0 o
9 (0, 0) (1, -1) (0, 0, 0, 0) 0 o
Facet format is (H_A,lambda_A) + ... + z >= 0. The last column states
whether the facet includes the origin (o) or the highest weight (*).
Vertices
--------
# V_A V_B V_C
--- ---------- ---------- --------------------
1 (1/2, 1/2) (1/2, 1/2) (1/4, 1/4, 1/4, 1/4)
2 (1/2, 1/2) (1/2, 1/2) (1/3, 1/3, 1/3, 0)
3 (1/2, 1/2) (1/2, 1/2) (1/2, 1/2, 0, 0)
4 (1/2, 1/2) (1/2, 1/2) (1, 0, 0, 0)
5 (1/2, 1/2) (3/4, 1/4) (1/2, 1/4, 1/4, 0)
6 (1/2, 1/2) (1, 0) (1/2, 1/2, 0, 0)
7 (2/3, 1/3) (2/3, 1/3) (1/3, 1/3, 1/3, 0)
8 (1, 0) (1, 0) (1, 0, 0, 0)
All data is up to permutations of subsystems.
qmp.pretty((2, 2, 2, 8))
C(2,2,2,8)
==========
Facets
------
# H_A H_B H_C H_D z Remarks
--- ------- ------- ------- ------------------------------- --- ---------
1 (-2, 2) (-1, 1) (-1, 1) (4, 2, 2, 0, 0, -2, -2, -4) 0 o, *
2 (-2, 2) (-1, 1) (1, -1) (2, 4, 2, 0, 0, -2, -2, -4) 0 o, *
3 (-2, 2) (-1, 1) (1, -1) (4, 2, 0, 2, 0, -2, -2, -4) 0 o
4 (-2, 2) (-1, 1) (1, -1) (4, 2, 2, 0, -2, 0, -2, -4) 0 o
5 (-2, 2) (-1, 1) (1, -1) (4, 2, 2, 0, 0, -2, -4, -2) 0 o
6 (-1, 1) (-1, 1) (-1, 1) (3, 1, 1, 1, -1, -1, -1, -3) 0 o, *
7 (-1, 1) (-1, 1) (0, 0) (2, 2, 0, 0, 0, 0, -2, -2) 0 o, *
8 (-1, 1) (-1, 1) (1, -1) (1, 3, 1, 1, -1, -1, -1, -3) 0 o, *
9 (-1, 1) (-1, 1) (1, -1) (3, 1, 1, 1, -1, -1, -3, -1) 0 o
10 (-1, 1) (0, 0) (0, 0) (1, 1, 1, 1, -1, -1, -1, -1) 0 o, *
11 (0, 0) (0, 0) (0, 0) (-1, -1, -1, -1, -1, -1, -1, 7) 1 *
12 (0, 0) (0, 0) (0, 0) (0, 0, 0, 0, 0, 0, 1, -1) 0 o, *
13 (0, 0) (0, 0) (0, 0) (0, 0, 0, 0, 0, 1, -1, 0) 0 o, *
14 (0, 0) (0, 0) (0, 0) (0, 0, 0, 0, 1, -1, 0, 0) 0 o, *
15 (0, 0) (0, 0) (0, 0) (0, 0, 0, 1, -1, 0, 0, 0) 0 o, *
16 (0, 0) (0, 0) (0, 0) (0, 0, 1, -1, 0, 0, 0, 0) 0 o, *
17 (0, 0) (0, 0) (0, 0) (0, 1, -1, 0, 0, 0, 0, 0) 0 o, *
18 (0, 0) (0, 0) (0, 0) (1, -1, 0, 0, 0, 0, 0, 0) 0 o
19 (0, 0) (0, 0) (1, -1) (0, 0, 0, 0, 0, 0, 0, 0) 0 o
Facet format is (H_A,lambda_A) + ... + z >= 0. The last column states
whether the facet includes the origin (o) or the highest weight (*).
Vertices
--------
# V_A V_B V_C V_D
--- ---------- ------------- ------------- ------------------------------------------
1 (1/2, 1/2) (1/2, 1/2) (1/2, 1/2) (1/8, 1/8, 1/8, 1/8, 1/8, 1/8, 1/8, 1/8)
2 (1/2, 1/2) (1/2, 1/2) (1/2, 1/2) (1/7, 1/7, 1/7, 1/7, 1/7, 1/7, 1/7, 0)
3 (1/2, 1/2) (1/2, 1/2) (1/2, 1/2) (1/6, 1/6, 1/6, 1/6, 1/6, 1/6, 0, 0)
4 (1/2, 1/2) (1/2, 1/2) (1/2, 1/2) (1/5, 1/5, 1/5, 1/5, 1/5, 0, 0, 0)
5 (1/2, 1/2) (1/2, 1/2) (1/2, 1/2) (1/4, 1/4, 1/4, 1/4, 0, 0, 0, 0)
6 (1/2, 1/2) (1/2, 1/2) (1/2, 1/2) (1/3, 1/3, 1/3, 0, 0, 0, 0, 0)
7 (1/2, 1/2) (1/2, 1/2) (1/2, 1/2) (1/2, 1/2, 0, 0, 0, 0, 0, 0)
8 (1/2, 1/2) (1/2, 1/2) (1/2, 1/2) (1, 0, 0, 0, 0, 0, 0, 0)
9 (1/2, 1/2) (1/2, 1/2) (4/7, 3/7) (1/7, 1/7, 1/7, 1/7, 1/7, 1/7, 1/7, 0)
10 (1/2, 1/2) (1/2, 1/2) (2/3, 1/3) (1/6, 1/6, 1/6, 1/6, 1/6, 1/6, 0, 0)
11 (1/2, 1/2) (1/2, 1/2) (4/5, 1/5) (1/5, 1/5, 1/5, 1/5, 1/5, 0, 0, 0)
12 (1/2, 1/2) (1/2, 1/2) (1, 0) (1/4, 1/4, 1/4, 1/4, 0, 0, 0, 0)
13 (1/2, 1/2) (1/2, 1/2) (1, 0) (1/3, 1/3, 1/3, 0, 0, 0, 0, 0)
14 (1/2, 1/2) (1/2, 1/2) (1, 0) (1/2, 1/2, 0, 0, 0, 0, 0, 0)
15 (1/2, 1/2) (1/2, 1/2) (1, 0) (1, 0, 0, 0, 0, 0, 0, 0)
16 (1/2, 1/2) (7/12, 5/12) (2/3, 1/3) (1/6, 1/6, 1/6, 1/6, 1/6, 1/12, 1/12, 0)
17 (1/2, 1/2) (3/5, 2/5) (7/10, 3/10) (1/5, 1/5, 1/5, 1/10, 1/10, 1/10, 1/10, 0)
18 (1/2, 1/2) (11/18, 7/18) (11/18, 7/18) (1/6, 1/6, 1/6, 1/6, 1/9, 1/9, 1/9, 0)
19 (1/2, 1/2) (5/8, 3/8) (5/8, 3/8) (1/4, 1/8, 1/8, 1/8, 1/8, 1/8, 1/8, 0)
20 (1/2, 1/2) (5/8, 3/8) (7/8, 1/8) (1/4, 1/4, 1/4, 1/8, 1/8, 0, 0, 0)
21 (1/2, 1/2) (2/3, 1/3) (2/3, 1/3) (1/6, 1/6, 1/6, 1/6, 1/6, 1/6, 0, 0)
22 (1/2, 1/2) (2/3, 1/3) (5/6, 1/6) (1/3, 1/6, 1/6, 1/6, 1/6, 0, 0, 0)
23 (1/2, 1/2) (7/10, 3/10) (7/10, 3/10) (1/5, 1/5, 1/5, 1/5, 1/5, 0, 0, 0)
24 (1/2, 1/2) (3/4, 1/4) (1, 0) (1/2, 1/4, 1/4, 0, 0, 0, 0, 0)
25 (1/2, 1/2) (5/6, 1/6) (5/6, 1/6) (1/3, 1/3, 1/3, 0, 0, 0, 0, 0)
26 (1/2, 1/2) (5/6, 1/6) (5/6, 1/6) (1/2, 1/6, 1/6, 1/6, 0, 0, 0, 0)
27 (1/2, 1/2) (1, 0) (1, 0) (1/2, 1/2, 0, 0, 0, 0, 0, 0)
28 (4/7, 3/7) (4/7, 3/7) (4/7, 3/7) (1/7, 1/7, 1/7, 1/7, 1/7, 1/7, 1/7, 0)
29 (3/5, 2/5) (3/5, 2/5) (4/5, 1/5) (1/5, 1/5, 1/5, 1/5, 1/5, 0, 0, 0)
30 (2/3, 1/3) (2/3, 1/3) (1, 0) (1/3, 1/3, 1/3, 0, 0, 0, 0, 0)
31 (3/4, 1/4) (3/4, 1/4) (3/4, 1/4) (1/4, 1/4, 1/4, 1/4, 0, 0, 0, 0)
32 (1, 0) (1, 0) (1, 0) (1, 0, 0, 0, 0, 0, 0, 0)
All data is up to permutations of subsystems.
#qmp.pretty((2, 2, 2, 2, 16), algorithm='mathematica', show_vrepr=False)
qmp.pretty((3, 3, 9), algorithm='mathematica', show_vrepr=False)
C(3,3,9)
========
Facets
------
# H_A H_B H_C z Remarks
--- ----------- ----------- ----------------------------------- --- ---------
1 (-5, 1, 4) (-3, 0, 3) (8, 5, 2, 2, -1, -1, -4, -4, -7) 0 o, *
2 (-5, 1, 4) (-3, 3, 0) (8, 2, 5, 2, -1, -1, -4, -4, -7) 0 o, *
3 (-5, 1, 4) (-3, 3, 0) (8, 5, 2, 2, -1, -4, -1, -4, -7) 0 o, *
4 (-5, 1, 4) (-3, 3, 0) (8, 5, 2, 2, -1, -1, -4, -7, -4) 0 o, *
5 (-5, 1, 4) (0, -3, 3) (5, 8, 2, 2, -1, -1, -4, -4, -7) 0 o, *
6 (-5, 1, 4) (0, -3, 3) (8, 5, 2, -1, 2, -1, -4, -4, -7) 0 o
7 (-5, 1, 4) (0, -3, 3) (8, 5, 2, 2, -1, -4, -1, -4, -7) 0 o
8 (-5, 1, 4) (0, 3, -3) (5, 2, 8, 2, -1, -1, -4, -4, -7) 0 o, *
9 (-5, 1, 4) (3, -3, 0) (2, 8, 5, 2, -1, -1, -4, -4, -7) 0 o, *
10 (-5, 1, 4) (3, 0, -3) (2, 5, 8, 2, -1, -1, -4, -4, -7) 0 o, *
11 (-5, 1, 4) (3, 0, -3) (2, 8, 5, -1, 2, -1, -4, -4, -7) 0 o, *
12 (-5, 1, 4) (3, 0, -3) (2, 8, 5, 2, -1, -4, -1, -4, -7) 0 o, *
13 (-5, 1, 4) (3, 0, -3) (5, 2, 8, 2, -1, -4, -1, -4, -7) 0 o
14 (-5, 1, 4) (3, 0, -3) (5, 2, 8, 2, -1, -1, -4, -7, -4) 0 o
15 (-5, 1, 4) (3, 0, -3) (8, 5, 2, -4, 2, -1, -1, -4, -7) 0 o
16 (-5, 1, 4) (3, 0, -3) (8, 5, 2, -1, -4, 2, -1, -4, -7) 0 o
17 (-5, 1, 4) (3, 0, -3) (8, 5, 2, 2, -1, -4, -7, -1, -4) 0 o
18 (-5, 1, 4) (3, 0, -3) (8, 5, 2, 2, -1, -4, -4, -7, -1) 0 o
19 (-5, 4, 1) (-3, 0, 3) (8, 5, 2, -1, 2, -1, -4, -4, -7) 0 o, *
20 (-5, 4, 1) (-3, 0, 3) (8, 5, 2, 2, -1, -4, -1, -4, -7) 0 o, *
21 (-5, 4, 1) (-3, 0, 3) (8, 5, 2, 2, -1, -1, -4, -7, -4) 0 o, *
22 (-5, 4, 1) (-3, 3, 0) (8, 2, 5, -1, 2, -1, -4, -4, -7) 0 o, *
23 (-5, 4, 1) (-3, 3, 0) (8, 2, 5, 2, -1, -4, -1, -4, -7) 0 o, *
24 (-5, 4, 1) (-3, 3, 0) (8, 2, 5, 2, -1, -1, -4, -7, -4) 0 o, *
25 (-5, 4, 1) (-3, 3, 0) (8, 5, 2, -1, 2, -4, -1, -4, -7) 0 o, *
26 (-5, 4, 1) (-3, 3, 0) (8, 5, 2, -1, 2, -1, -4, -7, -4) 0 o, *
27 (-5, 4, 1) (0, -3, 3) (5, 8, 2, -1, 2, -1, -4, -4, -7) 0 o, *
28 (-5, 4, 1) (0, -3, 3) (5, 8, 2, 2, -1, -4, -1, -4, -7) 0 o, *
29 (-5, 4, 1) (0, -3, 3) (5, 8, 2, 2, -1, -1, -4, -7, -4) 0 o, *
30 (-5, 4, 1) (0, -3, 3) (8, 5, 2, -1, 2, -1, -4, -7, -4) 0 o
31 (-5, 4, 1) (0, -3, 3) (8, 5, 2, 2, -1, -4, -1, -7, -4) 0 o
32 (-5, 4, 1) (0, 3, -3) (5, 2, 8, -1, 2, -1, -4, -4, -7) 0 o, *
33 (-5, 4, 1) (0, 3, -3) (5, 2, 8, 2, -1, -4, -1, -4, -7) 0 o, *
34 (-5, 4, 1) (0, 3, -3) (5, 2, 8, 2, -1, -1, -4, -7, -4) 0 o, *
35 (-5, 4, 1) (0, 3, -3) (8, 5, 2, -4, 2, -1, -1, -4, -7) 0 o
36 (-5, 4, 1) (3, -3, 0) (2, 8, 5, -1, 2, -1, -4, -4, -7) 0 o, *
37 (-5, 4, 1) (3, -3, 0) (2, 8, 5, 2, -1, -4, -1, -4, -7) 0 o, *
38 (-5, 4, 1) (3, -3, 0) (2, 8, 5, 2, -1, -1, -4, -7, -4) 0 o, *
39 (-5, 4, 1) (3, -3, 0) (8, 5, 2, 2, -1, -4, -4, -7, -1) 0 o
40 (-5, 4, 1) (3, 0, -3) (2, 5, 8, -1, 2, -1, -4, -4, -7) 0 o, *
41 (-5, 4, 1) (3, 0, -3) (2, 5, 8, 2, -1, -4, -1, -4, -7) 0 o, *
42 (-5, 4, 1) (3, 0, -3) (2, 5, 8, 2, -1, -1, -4, -7, -4) 0 o, *
43 (-5, 4, 1) (3, 0, -3) (2, 8, 5, -1, 2, -1, -4, -7, -4) 0 o, *
44 (-5, 4, 1) (3, 0, -3) (2, 8, 5, 2, -1, -4, -1, -7, -4) 0 o, *
45 (-5, 4, 1) (3, 0, -3) (5, 2, 8, -1, 2, -4, -1, -4, -7) 0 o
46 (-5, 4, 1) (3, 0, -3) (5, 2, 8, -1, 2, -1, -4, -7, -4) 0 o
47 (-5, 4, 1) (3, 0, -3) (5, 8, 2, 2, -1, -4, -4, -7, -1) 0 o
48 (-5, 4, 1) (3, 0, -3) (8, 2, 5, -4, 2, -1, -1, -4, -7) 0 o
49 (-5, 4, 1) (3, 0, -3) (8, 5, 2, -4, -1, 2, -1, -4, -7) 0 o
50 (-5, 4, 1) (3, 0, -3) (8, 5, 2, 2, -1, -4, -7, -4, -1) 0 o
51 (-4, -1, 5) (-3, 0, 3) (7, 4, 4, 1, 1, -2, -2, -5, -8) 0 o, *
52 (-4, -1, 5) (-3, 3, 0) (7, 4, 1, 4, 1, -2, -2, -5, -8) 0 o, *
53 (-4, -1, 5) (-3, 3, 0) (7, 4, 4, 1, -2, 1, -2, -5, -8) 0 o, *
54 (-4, -1, 5) (-3, 3, 0) (7, 4, 4, 1, 1, -2, -2, -8, -5) 0 o, *
55 (-4, -1, 5) (0, -3, 3) (4, 7, 4, 1, 1, -2, -2, -5, -8) 0 o, *
56 (-4, -1, 5) (0, -3, 3) (7, 4, 1, 4, 1, -2, -2, -5, -8) 0 o
57 (-4, -1, 5) (0, -3, 3) (7, 4, 4, 1, 1, -2, -5, -2, -8) 0 o
58 (-4, -1, 5) (0, 3, -3) (7, 4, 4, 1, 1, -2, -5, -8, -2) 0 o
59 (-4, -1, 5) (3, -3, 0) (7, 4, 4, 1, 1, -2, -8, -2, -5) 0 o
60 (-4, -1, 5) (3, 0, -3) (1, 7, 4, 4, 1, -2, -2, -5, -8) 0 o, *
61 (-4, -1, 5) (3, 0, -3) (4, 1, 7, 4, 1, -2, -2, -5, -8) 0 o
62 (-4, -1, 5) (3, 0, -3) (4, 7, 4, 1, 1, -2, -8, -2, -5) 0 o
63 (-4, -1, 5) (3, 0, -3) (7, 4, 1, -2, 4, 1, -2, -5, -8) 0 o
64 (-4, -1, 5) (3, 0, -3) (7, 4, 1, 1, -2, 4, -2, -5, -8) 0 o
65 (-4, -1, 5) (3, 0, -3) (7, 4, 1, 4, 1, -2, -8, -2, -5) 0 o
66 (-4, -1, 5) (3, 0, -3) (7, 4, 1, 4, 1, -2, -5, -8, -2) 0 o
67 (-4, -1, 5) (3, 0, -3) (7, 4, 4, 1, -2, 1, -5, -8, -2) 0 o
68 (-4, -1, 5) (3, 0, -3) (7, 4, 4, 1, 1, -2, -8, -5, -2) 0 o
69 (-4, 5, -1) (0, -3, 3) (7, 4, 4, 1, 1, -2, -5, -8, -2) 0 o
70 (-3, 0, 3) (-2, 1, 1) (5, 2, 2, 2, -1, -1, -1, -4, -4) 0 o, *
71 (-3, 0, 3) (-1, -4, 5) (4, 7, 4, 1, 1, -2, -2, -5, -8) 0 o, *
72 (-3, 0, 3) (-1, -4, 5) (7, 4, 1, 4, 1, -2, -2, -5, -8) 0 o
73 (-3, 0, 3) (-1, -4, 5) (7, 4, 4, 1, -2, 1, -2, -5, -8) 0 o
74 (-3, 0, 3) (-1, -1, 2) (4, 4, 1, 1, 1, -2, -2, -2, -5) 0 o, *
75 (-3, 0, 3) (-1, 2, -1) (4, 1, 4, 1, 1, -2, -2, -2, -5) 0 o, *
76 (-3, 0, 3) (-1, 2, -1) (4, 4, 1, 1, -2, 1, -2, -2, -5) 0 o, *
77 (-3, 0, 3) (-1, 2, -1) (4, 4, 1, 1, 1, -2, -2, -5, -2) 0 o, *
78 (-3, 0, 3) (1, -2, 1) (2, 5, 2, 2, -1, -1, -1, -4, -4) 0 o, *
79 (-3, 0, 3) (1, -2, 1) (5, 2, 2, -1, 2, -1, -1, -4, -4) 0 o
80 (-3, 0, 3) (1, -2, 1) (5, 2, 2, 2, -1, -1, -4, -1, -4) 0 o
81 (-3, 0, 3) (1, 1, -2) (2, 2, 5, 2, -1, -1, -1, -4, -4) 0 o, *
82 (-3, 0, 3) (1, 1, -2) (2, 5, 2, -1, 2, -1, -1, -4, -4) 0 o, *
83 (-3, 0, 3) (1, 1, -2) (2, 5, 2, 2, -1, -1, -4, -1, -4) 0 o, *
84 (-3, 0, 3) (1, 1, -2) (5, 2, 2, -1, -1, 2, -1, -4, -4) 0 o
85 (-3, 0, 3) (1, 1, -2) (5, 2, 2, -1, 2, -1, -4, -1, -4) 0 o
86 (-3, 0, 3) (1, 1, -2) (5, 2, 2, 2, -1, -1, -4, -4, -1) 0 o
87 (-3, 0, 3) (2, -1, -1) (1, 4, 4, 1, 1, -2, -2, -2, -5) 0 o, *
88 (-3, 0, 3) (2, -1, -1) (4, 1, 4, 1, -2, 1, -2, -2, -5) 0 o
89 (-3, 0, 3) (2, -1, -1) (4, 1, 4, 1, 1, -2, -2, -5, -2) 0 o
90 (-3, 0, 3) (2, -1, -1) (4, 4, 1, -2, 1, 1, -2, -2, -5) 0 o
91 (-3, 0, 3) (2, -1, -1) (4, 4, 1, 1, -2, 1, -2, -5, -2) 0 o
92 (-3, 0, 3) (2, -1, -1) (4, 4, 1, 1, 1, -2, -5, -2, -2) 0 o
93 (-3, 3, 0) (-2, 1, 1) (5, 2, 2, -1, 2, -1, -1, -4, -4) 0 o, *
94 (-3, 3, 0) (-1, -4, 5) (4, 7, 1, 4, 1, -2, -2, -5, -8) 0 o, *
95 (-3, 3, 0) (-1, -4, 5) (4, 7, 4, 1, -2, 1, -2, -5, -8) 0 o, *
96 (-3, 3, 0) (-1, -4, 5) (4, 7, 4, 1, 1, -2, -2, -8, -5) 0 o, *
97 (-3, 3, 0) (-1, -4, 5) (7, 4, 1, 4, 1, -2, -2, -8, -5) 0 o
98 (-3, 3, 0) (-1, -4, 5) (7, 4, 4, 1, -2, 1, -2, -8, -5) 0 o
99 (-3, 3, 0) (-1, -1, 2) (4, 4, 1, 1, 1, -2, -2, -5, -2) 0 o, *
100 (-3, 3, 0) (-1, 2, -1) (4, 1, 4, 1, 1, -2, -2, -5, -2) 0 o, *
101 (-3, 3, 0) (-1, 2, -1) (4, 4, 1, -2, 1, 1, -2, -2, -5) 0 o, *
102 (-3, 3, 0) (1, -5, 4) (2, 8, 5, 2, -1, -1, -4, -4, -7) 0 o, *
103 (-3, 3, 0) (1, -2, 1) (2, 5, 2, -1, 2, -1, -1, -4, -4) 0 o, *
104 (-3, 3, 0) (1, -2, 1) (5, 2, 2, 2, -1, -1, -4, -4, -1) 0 o
105 (-3, 3, 0) (1, 1, -2) (2, 2, 5, -1, 2, -1, -1, -4, -4) 0 o, *
106 (-3, 3, 0) (1, 1, -2) (2, 5, 2, 2, -1, -1, -4, -4, -1) 0 o, *
107 (-3, 3, 0) (2, -1, -1) (1, 4, 4, 1, 1, -2, -2, -5, -2) 0 o, *
108 (-3, 3, 0) (2, -1, -1) (4, 1, 4, -2, 1, 1, -2, -2, -5) 0 o
109 (-2, 1, 1) (-2, 1, 1) (4, 1, 1, 1, 1, -2, -2, -2, -2) 0 o, *
110 (-2, 1, 1) (-1, -1, 2) (3, 3, 0, 0, 0, 0, 0, -3, -3) 0 o, *
111 (-2, 1, 1) (-1, 2, -1) (3, 0, 3, 0, 0, 0, 0, -3, -3) 0 o, *
112 (-2, 1, 1) (0, -3, 3) (2, 5, 2, 2, -1, -1, -1, -4, -4) 0 o, *
113 (-2, 1, 1) (0, 0, 0) (2, 2, 2, -1, -1, -1, -1, -1, -1) 0 o, *
114 (-2, 1, 1) (1, -2, 1) (1, 4, 1, 1, 1, -2, -2, -2, -2) 0 o, *
115 (-2, 1, 1) (1, 1, -2) (1, 1, 4, 1, 1, -2, -2, -2, -2) 0 o, *
116 (-2, 1, 1) (1, 1, -2) (4, 1, 1, -2, 1, 1, -2, -2, -2) 0 o
117 (-2, 1, 1) (2, -1, -1) (0, 3, 3, 0, 0, 0, 0, -3, -3) 0 o, *
118 (-2, 1, 1) (2, -1, -1) (3, 3, 0, 0, 0, 0, -3, -3, 0) 0 o
119 (-1, -4, 5) (0, -3, 3) (4, 7, 4, 1, -2, 1, -2, -5, -8) 0 o
120 (-1, -4, 5) (0, -3, 3) (4, 7, 4, 1, 1, -2, -5, -2, -8) 0 o
121 (-1, -4, 5) (0, -3, 3) (7, 4, 1, 4, -2, 1, -2, -5, -8) 0 o
122 (-1, -4, 5) (0, -3, 3) (7, 4, 1, 4, 1, -2, -5, -2, -8) 0 o
123 (-1, -4, 5) (0, -3, 3) (7, 4, 4, 1, -2, 1, -5, -2, -8) 0 o
124 (-1, -4, 5) (0, 3, -3) (1, 7, 4, 4, 1, -2, -2, -5, -8) 0 o, *
125 (-1, -4, 5) (0, 3, -3) (4, 7, 4, 1, 1, -2, -5, -8, -2) 0 o
126 (-1, -4, 5) (0, 3, -3) (7, 4, 1, 4, 1, -2, -5, -8, -2) 0 o
127 (-1, -4, 5) (0, 3, -3) (7, 4, 4, 1, -2, 1, -5, -8, -2) 0 o
128 (-1, -4, 5) (3, -3, 0) (4, 7, 4, 1, 1, -2, -8, -2, -5) 0 o
129 (-1, -4, 5) (3, -3, 0) (7, 4, 1, 1, -2, 4, -2, -5, -8) 0 o
130 (-1, -4, 5) (3, -3, 0) (7, 4, 1, 4, 1, -2, -8, -2, -5) 0 o
131 (-1, -4, 5) (3, -3, 0) (7, 4, 4, 1, -2, 1, -8, -2, -5) 0 o
132 (-1, -4, 5) (3, 0, -3) (1, 4, 7, 4, 1, -2, -2, -5, -8) 0 o
133 (-1, -4, 5) (3, 0, -3) (1, 7, 4, 4, 1, -2, -2, -8, -5) 0 o
134 (-1, -4, 5) (3, 0, -3) (4, 7, 1, 4, 1, -2, -5, -8, -2) 0 o
135 (-1, -4, 5) (3, 0, -3) (4, 7, 4, 1, -2, 1, -8, -2, -5) 0 o
136 (-1, -4, 5) (3, 0, -3) (4, 7, 4, 1, -2, 1, -5, -8, -2) 0 o
137 (-1, -4, 5) (3, 0, -3) (4, 7, 4, 1, 1, -2, -8, -5, -2) 0 o
138 (-1, -4, 5) (3, 0, -3) (7, 4, 1, -2, 1, 4, -2, -5, -8) 0 o
139 (-1, -4, 5) (3, 0, -3) (7, 4, 1, 1, -2, 4, -5, -2, -8) 0 o
140 (-1, -4, 5) (3, 0, -3) (7, 4, 1, 4, -2, 1, -8, -2, -5) 0 o
141 (-1, -4, 5) (3, 0, -3) (7, 4, 1, 4, 1, -2, -8, -5, -2) 0 o
142 (-1, -4, 5) (3, 0, -3) (7, 4, 4, 1, -2, 1, -8, -5, -2) 0 o
143 (-1, -1, 2) (-1, -1, 2) (2, 2, 2, 2, -1, -1, -1, -1, -4) 0 o, *
144 (-1, -1, 2) (-1, 2, -1) (2, 2, 2, 2, -1, -1, -1, -4, -1) 0 o, *
145 (-1, -1, 2) (0, -3, 3) (4, 4, 1, 1, -2, 1, -2, -2, -5) 0 o
146 (-1, -1, 2) (0, 0, 0) (1, 1, 1, 1, 1, 1, -2, -2, -2) 0 o, *
147 (-1, -1, 2) (1, -2, 1) (3, 3, 0, 0, 0, 0, -3, 0, -3) 0 o
148 (-1, -1, 2) (1, 1, -2) (0, 3, 3, 0, 0, 0, 0, -3, -3) 0 o, *
149 (-1, -1, 2) (1, 1, -2) (3, 3, 0, 0, 0, 0, -3, -3, 0) 0 o
150 (-1, -1, 2) (2, -1, -1) (2, 2, 2, -1, -1, 2, -1, -1, -4) 0 o
151 (-1, -1, 2) (2, -1, -1) (2, 2, 2, 2, -1, -1, -4, -1, -1) 0 o
152 (-1, 0, 1) (-1, 0, 1) (2, 1, 1, 0, 0, 0, -1, -1, -2) 0 o, *
153 (-1, 0, 1) (-1, 1, 0) (2, 1, 0, 1, 0, 0, -1, -1, -2) 0 o, *
154 (-1, 0, 1) (-1, 1, 0) (2, 1, 1, 0, 0, -1, 0, -1, -2) 0 o, *
155 (-1, 0, 1) (-1, 1, 0) (2, 1, 1, 0, 0, 0, -1, -2, -1) 0 o, *
156 (-1, 0, 1) (0, -1, 1) (1, 2, 1, 0, 0, 0, -1, -1, -2) 0 o, *
157 (-1, 0, 1) (0, -1, 1) (2, 1, 0, 1, 0, 0, -1, -1, -2) 0 o
158 (-1, 0, 1) (0, -1, 1) (2, 1, 1, 0, 0, -1, 0, -1, -2) 0 o
159 (-1, 0, 1) (1, 0, -1) (0, 2, 1, 1, 0, 0, -1, -1, -2) 0 o, *
160 (-1, 0, 1) (1, 0, -1) (1, 0, 2, 1, 0, 0, -1, -1, -2) 0 o
161 (-1, 0, 1) (1, 0, -1) (2, 1, 1, 0, 0, -1, -2, 0, -1) 0 o
162 (-1, 0, 1) (1, 0, -1) (2, 1, 1, 0, 0, -1, -1, -2, 0) 0 o
163 (-1, 1, 0) (-1, 1, 0) (2, 0, 1, 1, 0, 0, -1, -1, -2) 0 o, *
164 (-1, 1, 0) (-1, 1, 0) (2, 1, 0, 0, 1, 0, -1, -1, -2) 0 o, *
165 (-1, 1, 0) (0, -1, 1) (1, 2, 0, 1, 0, 0, -1, -1, -2) 0 o, *
166 (-1, 1, 0) (0, -1, 1) (1, 2, 1, 0, 0, -1, 0, -1, -2) 0 o, *
167 (-1, 1, 0) (0, -1, 1) (1, 2, 1, 0, 0, 0, -1, -2, -1) 0 o, *
168 (-1, 1, 0) (0, -1, 1) (2, 1, 0, 1, 0, 0, -1, -2, -1) 0 o
169 (-1, 1, 0) (0, -1, 1) (2, 1, 1, 0, 0, -1, 0, -2, -1) 0 o
170 (-1, 1, 0) (0, 1, -1) (1, 0, 2, 1, 0, 0, -1, -1, -2) 0 o, *
171 (-1, 1, 0) (1, -1, 0) (0, 2, 1, 1, 0, 0, -1, -1, -2) 0 o, *
172 (-1, 1, 0) (1, -1, 0) (2, 1, 1, 0, 0, -1, -1, -2, 0) 0 o
173 (-1, 1, 0) (1, 0, -1) (0, 1, 2, 1, 0, 0, -1, -1, -2) 0 o, *
174 (-1, 1, 0) (1, 0, -1) (0, 2, 1, 1, 0, 0, -1, -2, -1) 0 o, *
175 (-1, 1, 0) (1, 0, -1) (1, 0, 2, 0, 1, 0, -1, -1, -2) 0 o
176 (-1, 1, 0) (1, 0, -1) (1, 2, 1, 0, 0, -1, -1, -2, 0) 0 o
177 (-1, 1, 0) (1, 0, -1) (2, 1, 1, 0, 0, -1, -2, -1, 0) 0 o
178 (-1, 2, -1) (0, -3, 3) (1, 4, 4, 1, 1, -2, -2, -2, -5) 0 o, *
179 (-1, 2, -1) (0, -3, 3) (4, 4, 1, 1, -2, 1, -2, -5, -2) 0 o
180 (-1, 2, -1) (1, -2, 1) (0, 3, 3, 0, 0, 0, 0, -3, -3) 0 o, *
181 (-1, 2, -1) (1, -2, 1) (3, 3, 0, 0, 0, 0, -3, -3, 0) 0 o
182 (0, -3, 3) (1, -2, 1) (2, 5, 2, 2, -1, -1, -4, -1, -4) 0 o
183 (0, -3, 3) (1, -2, 1) (5, 2, 2, -1, -1, 2, -1, -4, -4) 0 o
184 (0, -3, 3) (1, 1, -2) (2, 5, 2, 2, -1, -1, -4, -4, -1) 0 o
185 (0, -3, 3) (1, 1, -2) (5, 2, 2, -1, -1, 2, -4, -1, -4) 0 o
186 (0, -3, 3) (2, -1, -1) (1, 4, 4, 1, 1, -2, -2, -5, -2) 0 o
187 (0, -3, 3) (2, -1, -1) (4, 4, 1, 1, -2, 1, -5, -2, -2) 0 o
188 (0, -1, 1) (0, -1, 1) (2, 1, 1, 0, -1, 0, 0, -1, -2) 0 o
189 (0, -1, 1) (0, -1, 1) (2, 1, 1, 0, 0, -1, -1, 0, -2) 0 o
190 (0, -1, 1) (0, 1, -1) (0, 2, 1, 1, 0, 0, -1, -1, -2) 0 o, *
191 (0, -1, 1) (0, 1, -1) (2, 1, 1, 0, 0, -1, -1, -2, 0) 0 o
192 (0, -1, 1) (1, -1, 0) (2, 1, 1, 0, 0, -1, -2, 0, -1) 0 o
193 (0, -1, 1) (1, 0, -1) (0, 1, 2, 1, 0, 0, -1, -1, -2) 0 o
194 (0, -1, 1) (1, 0, -1) (0, 2, 1, 1, 0, 0, -1, -2, -1) 0 o
195 (0, -1, 1) (1, 0, -1) (1, 2, 1, 0, 0, -1, -1, -2, 0) 0 o
196 (0, -1, 1) (1, 0, -1) (2, 1, 1, 0, -1, 0, -2, 0, -1) 0 o
197 (0, -1, 1) (1, 0, -1) (2, 1, 1, 0, 0, -1, -2, -1, 0) 0 o
198 (0, 0, 0) (0, 0, 0) (-1, -1, -1, -1, -1, -1, -1, -1, 8) 1 *
199 (0, 0, 0) (0, 0, 0) (0, 0, 0, 0, 0, 0, 0, 1, -1) 0 o, *
200 (0, 0, 0) (0, 0, 0) (0, 0, 0, 0, 0, 0, 1, -1, 0) 0 o, *
201 (0, 0, 0) (0, 0, 0) (0, 0, 0, 0, 0, 1, -1, 0, 0) 0 o, *
202 (0, 0, 0) (0, 0, 0) (0, 0, 0, 0, 1, -1, 0, 0, 0) 0 o, *
203 (0, 0, 0) (0, 0, 0) (0, 0, 0, 1, -1, 0, 0, 0, 0) 0 o, *
204 (0, 0, 0) (0, 0, 0) (0, 0, 1, -1, 0, 0, 0, 0, 0) 0 o, *
205 (0, 0, 0) (0, 0, 0) (0, 1, -1, 0, 0, 0, 0, 0, 0) 0 o, *
206 (0, 0, 0) (0, 0, 0) (1, -1, 0, 0, 0, 0, 0, 0, 0) 0 o
207 (0, 0, 0) (0, 1, -1) (0, 0, 0, 0, 0, 0, 0, 0, 0) 0 o, *
208 (0, 0, 0) (1, -1, 0) (0, 0, 0, 0, 0, 0, 0, 0, 0) 0 o
Facet format is (H_A,lambda_A) + ... + z >= 0. The last column states
whether the facet includes the origin (o) or the highest weight (*).
All data is up to permutations of subsystems.
qmp.pretty((2, 3, 6))
C(2,3,6)
========
Facets
------
# H_A H_B H_C z Remarks
--- ------- ----------- ----------------------- --- ---------
1 (-3, 3) (-4, 2, 2) (7, 1, 1, 1, -5, -5) 0 o, *
2 (-3, 3) (-2, -2, 4) (5, 5, -1, -1, -1, -7) 0 o, *
3 (-3, 3) (-2, 4, -2) (5, -1, 5, -1, -1, -7) 0 o, *
4 (-3, 3) (-2, 4, -2) (5, 5, -1, -1, -7, -1) 0 o, *
5 (-3, 3) (2, -4, 2) (1, 7, 1, 1, -5, -5) 0 o, *
6 (-3, 3) (2, -4, 2) (7, 1, 1, -5, 1, -5) 0 o
7 (-3, 3) (2, 2, -4) (1, 1, 7, 1, -5, -5) 0 o, *
8 (-3, 3) (2, 2, -4) (1, 7, 1, -5, 1, -5) 0 o, *
9 (-3, 3) (2, 2, -4) (7, 1, 1, -5, -5, 1) 0 o
10 (-3, 3) (4, -2, -2) (-1, 5, 5, -1, -1, -7) 0 o, *
11 (-3, 3) (4, -2, -2) (5, -1, 5, -1, -7, -1) 0 o
12 (-3, 3) (4, -2, -2) (5, 5, -1, -7, -1, -1) 0 o
13 (-1, 1) (-2, 0, 2) (3, 1, 1, -1, -1, -3) 0 o, *
14 (-1, 1) (-2, 2, 0) (3, 1, -1, 1, -1, -3) 0 o, *
15 (-1, 1) (-2, 2, 0) (3, 1, 1, -1, -3, -1) 0 o, *
16 (-1, 1) (0, -2, 2) (1, 3, 1, -1, -1, -3) 0 o, *
17 (-1, 1) (0, -2, 2) (3, 1, -1, 1, -1, -3) 0 o
18 (-1, 1) (0, 0, 0) (1, 1, 1, -1, -1, -1) 0 o, *
19 (-1, 1) (2, 0, -2) (-1, 3, 1, 1, -1, -3) 0 o, *
20 (-1, 1) (2, 0, -2) (1, -1, 3, 1, -1, -3) 0 o
21 (-1, 1) (2, 0, -2) (3, 1, -1, -3, 1, -1) 0 o
22 (-1, 1) (2, 0, -2) (3, 1, -1, -1, -3, 1) 0 o
23 (0, 0) (-2, 1, 1) (2, 2, -1, -1, -1, -1) 0 o, *
24 (0, 0) (-1, -1, 2) (1, 1, 1, 1, -2, -2) 0 o, *
25 (0, 0) (0, 0, 0) (-1, -1, -1, -1, -1, 5) 1 *
26 (0, 0) (0, 0, 0) (0, 0, 0, 0, 1, -1) 0 o, *
27 (0, 0) (0, 0, 0) (0, 0, 0, 1, -1, 0) 0 o, *
28 (0, 0) (0, 0, 0) (0, 0, 1, -1, 0, 0) 0 o, *
29 (0, 0) (0, 0, 0) (0, 1, -1, 0, 0, 0) 0 o, *
30 (0, 0) (0, 0, 0) (1, -1, 0, 0, 0, 0) 0 o
31 (0, 0) (0, 1, -1) (0, 0, 0, 0, 0, 0) 0 o, *
32 (0, 0) (1, -1, 0) (0, 0, 0, 0, 0, 0) 0 o
33 (0, 0) (1, 1, -2) (-1, 2, 2, -1, -1, -1) 0 o, *
34 (0, 0) (2, -1, -1) (1, 1, 1, -2, -2, 1) 0 o
35 (1, -1) (-2, 0, 2) (1, 3, 1, -1, -1, -3) 0 o, *
36 (1, -1) (-2, 0, 2) (3, 1, -1, 1, -1, -3) 0 o
37 (1, -1) (-2, 0, 2) (3, 1, 1, -1, -3, -1) 0 o
38 (1, -1) (-2, 2, 0) (1, 3, -1, 1, -1, -3) 0 o, *
39 (1, -1) (-2, 2, 0) (1, 3, 1, -1, -3, -1) 0 o, *
40 (1, -1) (0, -2, 2) (1, 3, 1, -1, -3, -1) 0 o
41 (1, -1) (0, -2, 2) (3, 1, -1, 1, -3, -1) 0 o
42 (1, -1) (0, 0, 0) (0, 0, 0, 0, 0, 0) 0 o
43 (1, -1) (0, 2, -2) (-1, 3, 1, 1, -1, -3) 0 o, *
44 (1, -1) (2, -2, 0) (3, 1, -1, -1, -3, 1) 0 o
45 (1, -1) (2, 0, -2) (-1, 1, 3, 1, -1, -3) 0 o
46 (1, -1) (2, 0, -2) (3, 1, -1, -3, -1, 1) 0 o
47 (3, -3) (-4, 2, 2) (1, 7, 1, 1, -5, -5) 0 o, *
48 (3, -3) (-2, -2, 4) (5, 5, -1, -1, -7, -1) 0 o
49 (3, -3) (-2, 4, -2) (-1, 5, 5, -1, -1, -7) 0 o, *
50 (3, -3) (2, -4, 2) (7, 1, 1, -5, -5, 1) 0 o
Facet format is (H_A,lambda_A) + ... + z >= 0. The last column states
whether the facet includes the origin (o) or the highest weight (*).
Vertices
--------
# V_A V_B V_C
--- ------------ ------------------ ---------------------------------
1 (1/2, 1/2) (1/3, 1/3, 1/3) (1/6, 1/6, 1/6, 1/6, 1/6, 1/6)
2 (1/2, 1/2) (1/3, 1/3, 1/3) (2/9, 2/9, 2/9, 1/6, 1/6, 0)
3 (1/2, 1/2) (1/3, 1/3, 1/3) (7/30, 7/30, 1/5, 1/5, 2/15, 0)
4 (1/2, 1/2) (1/3, 1/3, 1/3) (1/4, 5/24, 5/24, 5/24, 1/8, 0)
5 (1/2, 1/2) (1/3, 1/3, 1/3) (1/4, 1/4, 1/6, 1/6, 1/6, 0)
6 (1/2, 1/2) (1/3, 1/3, 1/3) (1/4, 1/4, 1/4, 1/4, 0, 0)
7 (1/2, 1/2) (1/3, 1/3, 1/3) (1/3, 1/6, 1/6, 1/6, 1/6, 0)
8 (1/2, 1/2) (1/3, 1/3, 1/3) (1/3, 1/3, 1/3, 0, 0, 0)
9 (1/2, 1/2) (1/3, 1/3, 1/3) (1/2, 1/6, 1/6, 1/6, 0, 0)
10 (1/2, 1/2) (1/3, 1/3, 1/3) (1/2, 1/4, 1/12, 1/12, 1/12, 0)
11 (1/2, 1/2) (1/3, 1/3, 1/3) (1/2, 1/2, 0, 0, 0, 0)
12 (1/2, 1/2) (1/3, 1/3, 1/3) (7/12, 1/4, 1/12, 1/12, 0, 0)
13 (1/2, 1/2) (1/3, 1/3, 1/3) (2/3, 1/6, 1/6, 0, 0, 0)
14 (1/2, 1/2) (5/14, 5/14, 2/7) (3/14, 3/14, 3/14, 3/14, 1/7, 0)
15 (1/2, 1/2) (4/11, 4/11, 3/11) (5/22, 5/22, 2/11, 2/11, 2/11, 0)
16 (1/2, 1/2) (3/8, 3/8, 1/4) (1/4, 3/16, 3/16, 3/16, 3/16, 0)
17 (1/2, 1/2) (7/18, 7/18, 2/9) (2/9, 2/9, 2/9, 1/6, 1/6, 0)
18 (1/2, 1/2) (2/5, 3/10, 3/10) (1/5, 1/5, 1/5, 1/5, 1/5, 0)
19 (1/2, 1/2) (5/12, 5/12, 1/6) (1/4, 1/4, 1/6, 1/6, 1/6, 0)
20 (1/2, 1/2) (3/7, 3/7, 1/7) (2/7, 3/14, 3/14, 1/7, 1/7, 0)
21 (1/2, 1/2) (1/2, 1/4, 1/4) (1/4, 1/4, 1/4, 1/4, 0, 0)
22 (1/2, 1/2) (1/2, 1/4, 1/4) (1/2, 1/8, 1/8, 1/8, 1/8, 0)
23 (1/2, 1/2) (1/2, 1/4, 1/4) (5/8, 1/8, 1/8, 1/8, 0, 0)
24 (1/2, 1/2) (1/2, 1/4, 1/4) (3/4, 1/4, 0, 0, 0, 0)
25 (1/2, 1/2) (1/2, 1/3, 1/6) (1/3, 1/6, 1/6, 1/6, 1/6, 0)
26 (1/2, 1/2) (1/2, 3/8, 1/8) (1/4, 1/4, 1/4, 1/8, 1/8, 0)
27 (1/2, 1/2) (1/2, 1/2, 0) (1/4, 1/4, 1/4, 1/4, 0, 0)
28 (1/2, 1/2) (1/2, 1/2, 0) (1/3, 1/3, 1/3, 0, 0, 0)
29 (1/2, 1/2) (1/2, 1/2, 0) (1/2, 1/2, 0, 0, 0, 0)
30 (1/2, 1/2) (1/2, 1/2, 0) (1, 0, 0, 0, 0, 0)
31 (1/2, 1/2) (3/5, 1/5, 1/5) (2/5, 1/5, 1/5, 1/10, 1/10, 0)
32 (1/2, 1/2) (2/3, 1/6, 1/6) (1/3, 1/3, 1/3, 0, 0, 0)
33 (1/2, 1/2) (2/3, 1/6, 1/6) (1/2, 1/6, 1/6, 1/6, 0, 0)
34 (1/2, 1/2) (2/3, 1/6, 1/6) (2/3, 1/6, 1/6, 0, 0, 0)
35 (1/2, 1/2) (3/4, 1/4, 0) (1/2, 1/4, 1/4, 0, 0, 0)
36 (1/2, 1/2) (1, 0, 0) (1/2, 1/2, 0, 0, 0, 0)
37 (5/9, 4/9) (1/3, 1/3, 1/3) (2/9, 2/9, 2/9, 2/9, 1/9, 0)
38 (7/12, 5/12) (1/3, 1/3, 1/3) (1/4, 1/4, 1/6, 1/6, 1/6, 0)
39 (3/5, 2/5) (2/5, 2/5, 1/5) (1/5, 1/5, 1/5, 1/5, 1/5, 0)
40 (5/8, 3/8) (3/8, 3/8, 1/4) (1/4, 1/4, 1/4, 1/4, 0, 0)
41 (5/8, 3/8) (1/2, 1/4, 1/4) (1/4, 1/4, 1/4, 1/8, 1/8, 0)
42 (2/3, 1/3) (1/3, 1/3, 1/3) (1/3, 1/6, 1/6, 1/6, 1/6, 0)
43 (2/3, 1/3) (1/3, 1/3, 1/3) (1/3, 2/9, 2/9, 2/9, 0, 0)
44 (2/3, 1/3) (1/3, 1/3, 1/3) (1/3, 1/3, 1/9, 1/9, 1/9, 0)
45 (2/3, 1/3) (1/3, 1/3, 1/3) (1/2, 1/6, 1/6, 1/6, 0, 0)
46 (2/3, 1/3) (1/3, 1/3, 1/3) (2/3, 1/3, 0, 0, 0, 0)
47 (2/3, 1/3) (2/3, 1/3, 0) (1/3, 1/3, 1/3, 0, 0, 0)
48 (5/7, 2/7) (3/7, 2/7, 2/7) (2/7, 2/7, 1/7, 1/7, 1/7, 0)
49 (3/4, 1/4) (1/2, 1/4, 1/4) (1/4, 1/4, 1/4, 1/4, 0, 0)
50 (3/4, 1/4) (1/2, 1/4, 1/4) (1/2, 1/2, 0, 0, 0, 0)
51 (3/4, 1/4) (1/2, 1/2, 0) (1/2, 1/4, 1/4, 0, 0, 0)
52 (4/5, 1/5) (2/5, 2/5, 1/5) (2/5, 1/5, 1/5, 1/5, 0, 0)
53 (5/6, 1/6) (1/3, 1/3, 1/3) (1/3, 1/3, 1/6, 1/6, 0, 0)
54 (1, 0) (1/3, 1/3, 1/3) (1/3, 1/3, 1/3, 0, 0, 0)
55 (1, 0) (1/2, 1/2, 0) (1/2, 1/2, 0, 0, 0, 0)
56 (1, 0) (1, 0, 0) (1, 0, 0, 0, 0, 0)
All data is up to permutations of subsystems.
qmp.pretty((2, 4, 8), algorithm='mathematica', show_vrepr=False)
C(2,4,8)
========
Facets
------
# H_A H_B H_C z Remarks
--- ------- --------------- ------------------------------- --- ---------
1 (-2, 2) (-5, -1, 3, 3) (7, 3, 3, -1, -1, -1, -5, -5) 0 o, *
2 (-2, 2) (-5, 3, -1, 3) (7, 3, -1, 3, -1, -1, -5, -5) 0 o, *
3 (-2, 2) (-5, 3, -1, 3) (7, 3, 3, -1, -1, -5, -1, -5) 0 o, *
4 (-2, 2) (-5, 3, 3, -1) (7, 3, -1, -1, 3, -1, -5, -5) 0 o, *
5 (-2, 2) (-5, 3, 3, -1) (7, 3, -1, 3, -1, -5, -1, -5) 0 o, *
6 (-2, 2) (-5, 3, 3, -1) (7, 3, 3, -1, -1, -5, -5, -1) 0 o, *
7 (-2, 2) (-3, -3, 1, 5) (5, 5, 1, 1, 1, -3, -3, -7) 0 o, *
8 (-2, 2) (-3, -3, 5, 1) (5, 5, 1, 1, -3, 1, -3, -7) 0 o, *
9 (-2, 2) (-3, -3, 5, 1) (5, 5, 1, 1, 1, -3, -7, -3) 0 o, *
10 (-2, 2) (-3, 1, -3, 5) (5, 1, 5, 1, 1, -3, -3, -7) 0 o, *
11 (-2, 2) (-3, 1, -3, 5) (5, 5, 1, 1, -3, 1, -3, -7) 0 o, *
12 (-2, 2) (-3, 1, 1, 1) (5, 1, 1, 1, 1, -3, -3, -3) 0 o, *
13 (-2, 2) (-3, 5, 1, -3) (5, 5, 1, 1, -3, -7, 1, -3) 0 o, *
14 (-2, 2) (-3, 5, 1, -3) (5, 5, 1, 1, -3, -3, -7, 1) 0 o, *
15 (-2, 2) (-1, -5, 3, 3) (3, 7, 3, -1, -1, -1, -5, -5) 0 o, *
16 (-2, 2) (-1, -5, 3, 3) (7, 3, -1, 3, -1, -1, -5, -5) 0 o
17 (-2, 2) (-1, -1, -1, 3) (3, 3, 3, -1, -1, -1, -1, -5) 0 o, *
18 (-2, 2) (-1, -1, 3, -1) (3, 3, -1, 3, -1, -1, -1, -5) 0 o, *
19 (-2, 2) (-1, -1, 3, -1) (3, 3, 3, -1, -1, -1, -5, -1) 0 o, *
20 (-2, 2) (-1, 3, -1, -1) (3, -1, 3, 3, -1, -1, -1, -5) 0 o, *
21 (-2, 2) (-1, 3, -1, -1) (3, 3, -1, 3, -1, -1, -5, -1) 0 o, *
22 (-2, 2) (-1, 3, -1, -1) (3, 3, 3, -1, -1, -5, -1, -1) 0 o, *
23 (-2, 2) (1, -3, -3, 5) (1, 5, 5, 1, 1, -3, -3, -7) 0 o, *
24 (-2, 2) (1, -3, -3, 5) (5, 1, 5, 1, -3, 1, -3, -7) 0 o
25 (-2, 2) (1, -3, -3, 5) (5, 5, 1, -3, 1, 1, -3, -7) 0 o
26 (-2, 2) (1, -3, 1, 1) (1, 5, 1, 1, 1, -3, -3, -3) 0 o, *
27 (-2, 2) (1, -3, 1, 1) (5, 1, 1, 1, -3, 1, -3, -3) 0 o
28 (-2, 2) (1, 1, -3, 1) (1, 1, 5, 1, 1, -3, -3, -3) 0 o, *
29 (-2, 2) (1, 1, -3, 1) (1, 5, 1, 1, -3, 1, -3, -3) 0 o, *
30 (-2, 2) (1, 1, -3, 1) (5, 1, 1, 1, -3, -3, 1, -3) 0 o
31 (-2, 2) (1, 1, 1, -3) (1, 1, 1, 5, 1, -3, -3, -3) 0 o, *
32 (-2, 2) (1, 1, 1, -3) (1, 1, 5, 1, -3, 1, -3, -3) 0 o, *
33 (-2, 2) (1, 1, 1, -3) (1, 5, 1, 1, -3, -3, 1, -3) 0 o, *
34 (-2, 2) (1, 1, 1, -3) (5, 1, 1, 1, -3, -3, -3, 1) 0 o
35 (-2, 2) (3, -1, -5, 3) (-1, 7, 3, 3, -1, -1, -5, -5) 0 o, *
36 (-2, 2) (3, -1, -5, 3) (3, -1, 7, 3, -1, -1, -5, -5) 0 o
37 (-2, 2) (3, -1, -1, -1) (-1, 3, 3, 3, -1, -1, -1, -5) 0 o, *
38 (-2, 2) (3, -1, -1, -1) (3, -1, 3, 3, -1, -1, -5, -1) 0 o
39 (-2, 2) (3, -1, -1, -1) (3, 3, -1, 3, -1, -5, -1, -1) 0 o
40 (-2, 2) (3, -1, -1, -1) (3, 3, 3, -1, -5, -1, -1, -1) 0 o
41 (-2, 2) (3, 3, -1, -5) (3, -1, -1, 7, 3, -1, -5, -5) 0 o
42 (-2, 2) (3, 3, -1, -5) (7, 3, -1, -1, -1, -5, -5, 3) 0 o
43 (-2, 2) (5, 1, -3, -3) (-3, 5, 5, 1, 1, 1, -3, -7) 0 o, *
44 (-2, 2) (5, 1, -3, -3) (5, 5, 1, -3, -7, 1, 1, -3) 0 o
45 (-1, 1) (-3, -1, 1, 3) (4, 2, 2, 0, 0, -2, -2, -4) 0 o, *
46 (-1, 1) (-3, -1, 3, 1) (4, 2, 2, 0, -2, 0, -2, -4) 0 o, *
47 (-1, 1) (-3, -1, 3, 1) (4, 2, 2, 0, 0, -2, -4, -2) 0 o, *
48 (-1, 1) (-3, 1, -1, 3) (4, 2, 0, 2, 0, -2, -2, -4) 0 o, *
49 (-1, 1) (-3, 1, -1, 3) (4, 2, 2, 0, -2, 0, -2, -4) 0 o, *
50 (-1, 1) (-3, 3, 1, -1) (4, 2, -2, 2, 0, 0, -2, -4) 0 o, *
51 (-1, 1) (-3, 3, 1, -1) (4, 2, 0, -2, 2, 0, -2, -4) 0 o, *
52 (-1, 1) (-3, 3, 1, -1) (4, 2, 2, 0, -2, -4, 0, -2) 0 o, *
53 (-1, 1) (-3, 3, 1, -1) (4, 2, 2, 0, -2, -2, -4, 0) 0 o, *
54 (-1, 1) (-2, 0, 0, 2) (3, 1, 1, 1, -1, -1, -1, -3) 0 o, *
55 (-1, 1) (-2, 0, 2, 0) (3, 1, 1, -1, 1, -1, -1, -3) 0 o, *
56 (-1, 1) (-2, 0, 2, 0) (3, 1, 1, 1, -1, -1, -3, -1) 0 o, *
57 (-1, 1) (-2, 2, 0, 0) (3, 1, -1, 1, 1, -1, -1, -3) 0 o, *
58 (-1, 1) (-2, 2, 0, 0) (3, 1, 1, -1, 1, -1, -3, -1) 0 o, *
59 (-1, 1) (-2, 2, 0, 0) (3, 1, 1, 1, -1, -3, -1, -1) 0 o, *
60 (-1, 1) (-1, -3, 1, 3) (2, 4, 2, 0, 0, -2, -2, -4) 0 o, *
61 (-1, 1) (-1, -3, 1, 3) (4, 2, 0, 2, 0, -2, -2, -4) 0 o
62 (-1, 1) (-1, -3, 3, 1) (2, 4, 2, 0, -2, 0, -2, -4) 0 o, *
63 (-1, 1) (-1, -3, 3, 1) (2, 4, 2, 0, 0, -2, -4, -2) 0 o, *
64 (-1, 1) (-1, -3, 3, 1) (4, 2, 0, 2, -2, 0, -2, -4) 0 o
65 (-1, 1) (-1, -3, 3, 1) (4, 2, 0, 2, 0, -2, -4, -2) 0 o
66 (-1, 1) (-1, -1, 1, 1) (2, 2, 0, 0, 0, 0, -2, -2) 0 o, *
67 (-1, 1) (-1, 1, -1, 1) (2, 0, 2, 0, 0, 0, -2, -2) 0 o, *
68 (-1, 1) (-1, 1, -1, 1) (2, 2, 0, 0, 0, -2, 0, -2) 0 o, *
69 (-1, 1) (-1, 1, 1, -1) (2, 0, 0, 2, 0, 0, -2, -2) 0 o, *
70 (-1, 1) (-1, 1, 1, -1) (2, 0, 2, 0, 0, -2, 0, -2) 0 o, *
71 (-1, 1) (-1, 1, 1, -1) (2, 2, 0, 0, 0, -2, -2, 0) 0 o, *
72 (-1, 1) (0, -2, 0, 2) (1, 3, 1, 1, -1, -1, -1, -3) 0 o, *
73 (-1, 1) (0, -2, 0, 2) (3, 1, 1, -1, 1, -1, -1, -3) 0 o
74 (-1, 1) (0, -2, 2, 0) (1, 3, 1, -1, 1, -1, -1, -3) 0 o, *
75 (-1, 1) (0, -2, 2, 0) (1, 3, 1, 1, -1, -1, -3, -1) 0 o, *
76 (-1, 1) (0, -2, 2, 0) (3, 1, -1, 1, 1, -1, -1, -3) 0 o
77 (-1, 1) (0, -2, 2, 0) (3, 1, 1, -1, -1, 1, -1, -3) 0 o
78 (-1, 1) (0, -2, 2, 0) (3, 1, 1, -1, 1, -1, -3, -1) 0 o
79 (-1, 1) (0, 0, -2, 2) (1, 1, 3, 1, -1, -1, -1, -3) 0 o, *
80 (-1, 1) (0, 0, -2, 2) (1, 3, 1, -1, 1, -1, -1, -3) 0 o, *
81 (-1, 1) (0, 0, -2, 2) (3, 1, 1, -1, -1, 1, -1, -3) 0 o
82 (-1, 1) (0, 0, 0, 0) (1, 1, 1, 1, -1, -1, -1, -1) 0 o, *
83 (-1, 1) (0, 2, 0, -2) (1, -1, 3, 1, 1, -1, -1, -3) 0 o, *
84 (-1, 1) (0, 2, 0, -2) (1, 1, -1, 3, 1, -1, -1, -3) 0 o, *
85 (-1, 1) (0, 2, 0, -2) (3, 1, 1, -1, -1, -3, 1, -1) 0 o
86 (-1, 1) (0, 2, 0, -2) (3, 1, 1, -1, -1, -1, -3, 1) 0 o
87 (-1, 1) (1, -1, -3, 3) (0, 4, 2, 2, 0, -2, -2, -4) 0 o, *
88 (-1, 1) (1, -1, -3, 3) (2, 0, 4, 2, 0, -2, -2, -4) 0 o
89 (-1, 1) (1, -1, -3, 3) (4, 2, 0, -2, 2, 0, -2, -4) 0 o
90 (-1, 1) (1, -1, -3, 3) (4, 2, 0, 0, -2, 2, -2, -4) 0 o
91 (-1, 1) (1, -1, -1, 1) (0, 2, 2, 0, 0, 0, -2, -2) 0 o, *
92 (-1, 1) (1, -1, -1, 1) (2, 0, 2, 0, 0, -2, 0, -2) 0 o
93 (-1, 1) (1, -1, -1, 1) (2, 2, 0, 0, -2, 0, 0, -2) 0 o
94 (-1, 1) (1, -1, 1, -1) (0, 2, 0, 2, 0, 0, -2, -2) 0 o, *
95 (-1, 1) (1, -1, 1, -1) (0, 2, 2, 0, 0, -2, 0, -2) 0 o, *
96 (-1, 1) (1, -1, 1, -1) (2, 0, 0, 2, 0, -2, 0, -2) 0 o
97 (-1, 1) (1, -1, 1, -1) (2, 0, 2, 0, -2, 0, 0, -2) 0 o
98 (-1, 1) (1, -1, 1, -1) (2, 0, 2, 0, 0, -2, -2, 0) 0 o
99 (-1, 1) (1, -1, 1, -1) (2, 2, 0, 0, -2, 0, -2, 0) 0 o
100 (-1, 1) (1, 1, -1, -1) (0, 0, 2, 2, 0, 0, -2, -2) 0 o, *
101 (-1, 1) (1, 1, -1, -1) (0, 2, 0, 2, 0, -2, 0, -2) 0 o, *
102 (-1, 1) (1, 1, -1, -1) (0, 2, 2, 0, -2, 0, 0, -2) 0 o, *
103 (-1, 1) (1, 1, -1, -1) (2, 0, 0, 2, 0, -2, -2, 0) 0 o
104 (-1, 1) (1, 1, -1, -1) (2, 0, 2, 0, -2, 0, -2, 0) 0 o
105 (-1, 1) (1, 1, -1, -1) (2, 2, 0, 0, -2, -2, 0, 0) 0 o
106 (-1, 1) (1, 3, -1, -3) (4, 2, 0, 0, -2, -2, -4, 2) 0 o
107 (-1, 1) (2, 0, -2, 0) (-1, 3, 1, 1, 1, -1, -1, -3) 0 o, *
108 (-1, 1) (2, 0, -2, 0) (1, -1, 3, 1, 1, -1, -1, -3) 0 o
109 (-1, 1) (2, 0, -2, 0) (3, 1, 1, -1, -3, 1, -1, -1) 0 o
110 (-1, 1) (2, 0, -2, 0) (3, 1, 1, -1, -1, -3, 1, -1) 0 o
111 (-1, 1) (2, 0, 0, -2) (-1, 1, 3, 1, 1, -1, -1, -3) 0 o, *
112 (-1, 1) (2, 0, 0, -2) (-1, 3, 1, 1, -1, 1, -1, -3) 0 o, *
113 (-1, 1) (2, 0, 0, -2) (1, -1, 1, 3, 1, -1, -1, -3) 0 o
114 (-1, 1) (2, 0, 0, -2) (1, -1, 3, 1, -1, 1, -1, -3) 0 o
115 (-1, 1) (2, 0, 0, -2) (1, -1, 3, 1, 1, -1, -3, -1) 0 o
116 (-1, 1) (2, 0, 0, -2) (1, 1, -1, 3, 1, -1, -3, -1) 0 o
117 (-1, 1) (2, 0, 0, -2) (1, 3, 1, -1, -3, 1, -1, -1) 0 o
118 (-1, 1) (2, 0, 0, -2) (1, 3, 1, -1, -1, -3, 1, -1) 0 o
119 (-1, 1) (2, 0, 0, -2) (3, 1, -1, 1, -1, -3, 1, -1) 0 o
120 (-1, 1) (2, 0, 0, -2) (3, 1, -1, 1, -1, -1, -3, 1) 0 o
121 (-1, 1) (2, 0, 0, -2) (3, 1, 1, -1, -3, -1, 1, -1) 0 o
122 (-1, 1) (2, 0, 0, -2) (3, 1, 1, -1, -1, -3, -1, 1) 0 o
123 (-1, 1) (3, 1, -3, -1) (-2, 4, 2, 2, 0, 0, -2, -4) 0 o, *
124 (-1, 1) (3, 1, -1, -3) (-2, 2, 4, 2, 0, 0, -2, -4) 0 o, *
125 (-1, 1) (3, 1, -1, -3) (-2, 4, 2, 0, 2, 0, -2, -4) 0 o, *
126 (-1, 1) (3, 1, -1, -3) (2, 0, -2, 4, 2, 0, -2, -4) 0 o
127 (-1, 1) (3, 1, -1, -3) (4, 2, 0, -2, -4, 2, 0, -2) 0 o
128 (-1, 1) (3, 1, -1, -3) (4, 2, 0, -2, 0, -2, -4, 2) 0 o
129 (-1, 1) (3, 1, -1, -3) (4, 2, 0, 0, -2, -4, -2, 2) 0 o
130 (0, 0) (-3, 1, 1, 1) (3, 3, -1, -1, -1, -1, -1, -1) 0 o, *
131 (0, 0) (-1, -1, -1, 3) (1, 1, 1, 1, 1, 1, -3, -3) 0 o, *
132 (0, 0) (-1, -1, 1, 1) (1, 1, 1, 1, -1, -1, -1, -1) 0 o, *
133 (0, 0) (-1, 1, 1, -1) (1, 1, -1, 1, 1, -1, -1, -1) 0 o, *
134 (0, 0) (-1, 3, -1, -1) (1, 1, 1, 1, 1, -3, -3, 1) 0 o, *
135 (0, 0) (0, 0, 0, 0) (-1, -1, -1, -1, -1, -1, -1, 7) 1 *
136 (0, 0) (0, 0, 0, 0) (0, 0, 0, 0, 0, 0, 1, -1) 0 o, *
137 (0, 0) (0, 0, 0, 0) (0, 0, 0, 0, 0, 1, -1, 0) 0 o, *
138 (0, 0) (0, 0, 0, 0) (0, 0, 0, 0, 1, -1, 0, 0) 0 o, *
139 (0, 0) (0, 0, 0, 0) (0, 0, 0, 1, -1, 0, 0, 0) 0 o, *
140 (0, 0) (0, 0, 0, 0) (0, 0, 1, -1, 0, 0, 0, 0) 0 o, *
141 (0, 0) (0, 0, 0, 0) (0, 1, -1, 0, 0, 0, 0, 0) 0 o, *
142 (0, 0) (0, 0, 0, 0) (1, -1, 0, 0, 0, 0, 0, 0) 0 o
143 (0, 0) (0, 0, 1, -1) (0, 0, 0, 0, 0, 0, 0, 0) 0 o, *
144 (0, 0) (0, 1, -1, 0) (0, 0, 0, 0, 0, 0, 0, 0) 0 o, *
145 (0, 0) (1, -1, -1, 1) (1, 1, 1, -1, -1, 1, -1, -1) 0 o
146 (0, 0) (1, -1, 0, 0) (0, 0, 0, 0, 0, 0, 0, 0) 0 o
147 (0, 0) (1, 1, -3, 1) (-1, 3, 3, -1, -1, -1, -1, -1) 0 o, *
148 (0, 0) (1, 1, -1, -1) (-1, 1, 1, 1, 1, -1, -1, -1) 0 o, *
149 (0, 0) (1, 1, -1, -1) (1, 1, 1, -1, -1, -1, -1, 1) 0 o
150 (1, -1) (-3, -1, 1, 3) (2, 4, 2, 0, 0, -2, -2, -4) 0 o, *
151 (1, -1) (-3, -1, 1, 3) (4, 2, 0, 2, 0, -2, -2, -4) 0 o
152 (1, -1) (-3, -1, 1, 3) (4, 2, 2, 0, -2, 0, -2, -4) 0 o
153 (1, -1) (-3, -1, 1, 3) (4, 2, 2, 0, 0, -2, -4, -2) 0 o
154 (1, -1) (-3, -1, 3, 1) (2, 4, 2, 0, -2, 0, -2, -4) 0 o, *
155 (1, -1) (-3, -1, 3, 1) (2, 4, 2, 0, 0, -2, -4, -2) 0 o, *
156 (1, -1) (-3, -1, 3, 1) (4, 2, 0, 2, -2, 0, -2, -4) 0 o
157 (1, -1) (-3, -1, 3, 1) (4, 2, 0, 2, 0, -2, -4, -2) 0 o
158 (1, -1) (-3, 1, -1, 3) (2, 4, 0, 2, 0, -2, -2, -4) 0 o, *
159 (1, -1) (-3, 1, -1, 3) (2, 4, 2, 0, -2, 0, -2, -4) 0 o, *
160 (1, -1) (-3, 1, -1, 3) (4, 2, 0, 2, 0, -2, -4, -2) 0 o
161 (1, -1) (-3, 1, -1, 3) (4, 2, 2, 0, -2, 0, -4, -2) 0 o
162 (1, -1) (-3, 1, 3, -1) (4, 2, -2, 2, 0, 0, -2, -4) 0 o
163 (1, -1) (-3, 3, -1, 1) (4, 2, 2, 0, -2, -2, -4, 0) 0 o
164 (1, -1) (-3, 3, 1, -1) (2, 4, -2, 2, 0, 0, -2, -4) 0 o, *
165 (1, -1) (-3, 3, 1, -1) (2, 4, 0, -2, 2, 0, -2, -4) 0 o, *
166 (1, -1) (-3, 3, 1, -1) (2, 4, 2, 0, -2, -4, 0, -2) 0 o, *
167 (1, -1) (-3, 3, 1, -1) (2, 4, 2, 0, -2, -2, -4, 0) 0 o, *
168 (1, -1) (-3, 3, 1, -1) (4, 2, -2, 0, 2, 0, -2, -4) 0 o
169 (1, -1) (-3, 3, 1, -1) (4, 2, 2, 0, -2, -4, -2, 0) 0 o
170 (1, -1) (-2, 0, 0, 2) (1, 3, 1, 1, -1, -1, -1, -3) 0 o, *
171 (1, -1) (-2, 0, 0, 2) (3, 1, 1, 1, -1, -1, -3, -1) 0 o
172 (1, -1) (-2, 0, 2, 0) (1, 3, 1, -1, 1, -1, -1, -3) 0 o, *
173 (1, -1) (-2, 0, 2, 0) (1, 3, 1, 1, -1, -1, -3, -1) 0 o, *
174 (1, -1) (-2, 0, 2, 0) (3, 1, -1, 1, 1, -1, -1, -3) 0 o
175 (1, -1) (-2, 2, 0, 0) (1, 3, -1, 1, 1, -1, -1, -3) 0 o, *
176 (1, -1) (-2, 2, 0, 0) (1, 3, 1, -1, 1, -1, -3, -1) 0 o, *
177 (1, -1) (-2, 2, 0, 0) (1, 3, 1, 1, -1, -3, -1, -1) 0 o, *
178 (1, -1) (-1, -3, 1, 3) (2, 4, 2, 0, -2, 0, -2, -4) 0 o
179 (1, -1) (-1, -3, 1, 3) (2, 4, 2, 0, 0, -2, -4, -2) 0 o
180 (1, -1) (-1, -3, 1, 3) (4, 2, 0, 2, -2, 0, -2, -4) 0 o
181 (1, -1) (-1, -3, 1, 3) (4, 2, 0, 2, 0, -2, -4, -2) 0 o
182 (1, -1) (-1, 1, -3, 3) (0, 4, 2, 2, 0, -2, -2, -4) 0 o, *
183 (1, -1) (-1, 1, -1, 1) (0, 2, 2, 0, 0, 0, -2, -2) 0 o, *
184 (1, -1) (-1, 1, -1, 1) (2, 2, 0, 0, 0, -2, -2, 0) 0 o
185 (1, -1) (-1, 1, 1, -1) (0, 2, 0, 2, 0, 0, -2, -2) 0 o, *
186 (1, -1) (-1, 1, 1, -1) (0, 2, 2, 0, 0, -2, 0, -2) 0 o, *
187 (1, -1) (0, -2, 0, 2) (1, 3, 1, 1, -1, -1, -3, -1) 0 o
188 (1, -1) (0, -2, 0, 2) (3, 1, 1, -1, -1, 1, -1, -3) 0 o
189 (1, -1) (0, -2, 0, 2) (3, 1, 1, -1, 1, -1, -3, -1) 0 o
190 (1, -1) (0, 0, -2, 2) (1, 1, 3, 1, -1, -1, -3, -1) 0 o
191 (1, -1) (0, 0, -2, 2) (1, 3, 1, -1, 1, -1, -3, -1) 0 o
192 (1, -1) (0, 0, -2, 2) (3, 1, 1, -1, -1, 1, -3, -1) 0 o
193 (1, -1) (0, 0, 0, 0) (0, 0, 0, 0, 0, 0, 0, 0) 0 o
194 (1, -1) (0, 2, -2, 0) (-1, 3, 1, 1, 1, -1, -1, -3) 0 o, *
195 (1, -1) (0, 2, -2, 0) (3, 1, 1, -1, -1, -1, -3, 1) 0 o
196 (1, -1) (0, 2, 0, -2) (-1, 1, 3, 1, 1, -1, -1, -3) 0 o, *
197 (1, -1) (0, 2, 0, -2) (-1, 3, 1, 1, -1, 1, -1, -3) 0 o, *
198 (1, -1) (0, 2, 0, -2) (3, 1, 1, -1, -1, -3, -1, 1) 0 o
199 (1, -1) (1, -3, -1, 3) (4, 2, 0, 0, -2, 2, -2, -4) 0 o
200 (1, -1) (1, -1, -3, 3) (0, 2, 4, 2, 0, -2, -2, -4) 0 o
201 (1, -1) (1, -1, -3, 3) (0, 4, 2, 2, 0, -2, -4, -2) 0 o
202 (1, -1) (1, -1, -3, 3) (2, 0, 4, 2, 0, -2, -4, -2) 0 o
203 (1, -1) (1, -1, -3, 3) (4, 2, 0, -2, 0, 2, -2, -4) 0 o
204 (1, -1) (1, -1, -3, 3) (4, 2, 0, -2, 2, 0, -4, -2) 0 o
205 (1, -1) (1, -1, -3, 3) (4, 2, 0, 0, -2, 2, -4, -2) 0 o
206 (1, -1) (1, -1, -1, 1) (2, 0, 2, 0, 0, -2, -2, 0) 0 o
207 (1, -1) (1, -1, -1, 1) (2, 2, 0, 0, -2, 0, -2, 0) 0 o
208 (1, -1) (1, 3, -3, -1) (-2, 4, 2, 2, 0, 0, -2, -4) 0 o, *
209 (1, -1) (1, 3, -3, -1) (4, 2, 0, 0, -2, -2, -4, 2) 0 o
210 (1, -1) (1, 3, -1, -3) (-2, 2, 4, 2, 0, 0, -2, -4) 0 o, *
211 (1, -1) (1, 3, -1, -3) (-2, 4, 2, 0, 2, 0, -2, -4) 0 o, *
212 (1, -1) (1, 3, -1, -3) (4, 2, 0, -2, 0, -2, -4, 2) 0 o
213 (1, -1) (1, 3, -1, -3) (4, 2, 0, 0, -2, -4, -2, 2) 0 o
214 (1, -1) (2, 0, -2, 0) (-1, 1, 3, 1, 1, -1, -1, -3) 0 o
215 (1, -1) (2, 0, -2, 0) (3, 1, -1, 1, -1, -1, -3, 1) 0 o
216 (1, -1) (2, 0, -2, 0) (3, 1, 1, -1, -1, -3, -1, 1) 0 o
217 (1, -1) (3, 1, -3, -1) (-2, 2, 4, 2, 0, 0, -2, -4) 0 o
218 (1, -1) (3, 1, -3, -1) (-2, 4, 2, 0, 2, 0, -2, -4) 0 o
219 (1, -1) (3, 1, -3, -1) (4, 2, 0, -2, 0, -2, -4, 2) 0 o
220 (1, -1) (3, 1, -3, -1) (4, 2, 0, 0, -2, -4, -2, 2) 0 o
221 (2, -2) (-5, -1, 3, 3) (3, 7, 3, -1, -1, -1, -5, -5) 0 o, *
222 (2, -2) (-5, -1, 3, 3) (7, 3, -1, 3, -1, -1, -5, -5) 0 o
223 (2, -2) (-5, 3, -1, 3) (3, 7, -1, 3, -1, -1, -5, -5) 0 o, *
224 (2, -2) (-5, 3, -1, 3) (3, 7, 3, -1, -1, -5, -1, -5) 0 o, *
225 (2, -2) (-5, 3, -1, 3) (7, 3, 3, -1, -1, -5, -5, -1) 0 o
226 (2, -2) (-5, 3, 3, -1) (3, 7, -1, -1, 3, -1, -5, -5) 0 o, *
227 (2, -2) (-5, 3, 3, -1) (3, 7, -1, 3, -1, -5, -1, -5) 0 o, *
228 (2, -2) (-5, 3, 3, -1) (3, 7, 3, -1, -1, -5, -5, -1) 0 o, *
229 (2, -2) (-3, -3, 1, 5) (5, 5, 1, 1, -3, 1, -3, -7) 0 o
230 (2, -2) (-3, -3, 1, 5) (5, 5, 1, 1, 1, -3, -7, -3) 0 o
231 (2, -2) (-3, 1, -3, 5) (1, 5, 5, 1, 1, -3, -3, -7) 0 o, *
232 (2, -2) (-3, 1, -3, 5) (5, 1, 5, 1, 1, -3, -7, -3) 0 o
233 (2, -2) (-3, 1, -3, 5) (5, 5, 1, 1, -3, 1, -7, -3) 0 o
234 (2, -2) (-3, 1, 1, 1) (1, 5, 1, 1, 1, -3, -3, -3) 0 o, *
235 (2, -2) (-3, 5, -3, 1) (5, 5, 1, 1, -3, -3, -7, 1) 0 o
236 (2, -2) (-3, 5, 1, -3) (5, 5, 1, 1, -3, -7, -3, 1) 0 o
237 (2, -2) (-1, -1, -1, 3) (3, 3, 3, -1, -1, -1, -5, -1) 0 o
238 (2, -2) (-1, 3, -5, 3) (-1, 7, 3, 3, -1, -1, -5, -5) 0 o, *
239 (2, -2) (-1, 3, -1, -1) (-1, 3, 3, 3, -1, -1, -1, -5) 0 o, *
240 (2, -2) (1, -3, -3, 5) (1, 5, 5, 1, 1, -3, -7, -3) 0 o
241 (2, -2) (1, -3, -3, 5) (5, 1, 5, 1, -3, 1, -7, -3) 0 o
242 (2, -2) (1, -3, -3, 5) (5, 5, 1, -3, 1, 1, -7, -3) 0 o
243 (2, -2) (1, 1, -3, 1) (5, 1, 1, 1, -3, -3, -3, 1) 0 o
244 (2, -2) (1, 5, -3, -3) (-3, 5, 5, 1, 1, 1, -3, -7) 0 o, *
245 (2, -2) (3, -1, -5, 3) (-1, 3, 7, 3, -1, -1, -5, -5) 0 o
246 (2, -2) (3, 3, -5, -1) (7, 3, -1, -1, -1, -5, -5, 3) 0 o
Facet format is (H_A,lambda_A) + ... + z >= 0. The last column states
whether the facet includes the origin (o) or the highest weight (*).
All data is up to permutations of subsystems.
