Generated by sphericalReport.pl Thu Nov  4 05:35:45 2004
Data from F4/facets2
Data from Dan Barbasch and Dan Cibotaru
List of positive coroots from F4/data

Number of facets of each dimension: 4:2 3:3 2:13 1:17 0:24 
Total number of facets: 59

[number(line number)] dimension (standard){weight}<facet>
[1(62)] 4 (0,0,0,0) {0,0,0,0} <-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,->
[2(64)] 4 (2/3,1/6,1/6,1/6) {1/6,1/3,0,0} <-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,+,-,+,->
[3(61)] 3 (9/16,13/48,3/16,1/48) {1/12,1/24,1/6,1/12} <-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,1,-,+,-,+,->
[4(60)] 3 (9/16,13/48,5/48,1/16) {1/8,1/8,1/24,1/6} <-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,1,-,+,->
[5(55)] 3 (1/2,0,0,0) {1/2,0,0,0} <-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,1,->
[6(46)] 2 (9/8,1/2,1/8,1/16) {7/16,1/8,1/16,3/8} <-,-,-,-,-,-,-,-,-,1,-,-,-,+,1,-,+,+,+,+,+,+,+,+>
[7(47)] 2 (17/16,1/2,3/16,1/16) {5/16,1/8,1/8,5/16} <-,-,-,-,-,-,-,-,-,1,-,-,-,+,-,-,+,1,+,+,+,+,+,+>
[8(48)] 2 (15/16,1/2,1/4,1/16) {1/8,1/8,3/16,1/4} <-,-,-,-,-,-,-,-,-,1,-,-,-,+,-,-,+,-,+,1,+,+,+,+>
[9(50)] 2 (5/6,1/2,1/6,1/12) {1/12,1/6,1/12,1/3} <-,-,-,-,-,-,-,-,-,1,-,-,-,+,-,-,+,-,+,-,+,1,+,+>
[10(49)] 2 (15/16,7/16,5/16,1/16) {1/8,1/8,1/4,1/8} <-,-,-,-,-,-,-,-,-,-,-,-,-,1,-,-,+,-,+,1,+,+,+,+>
[11(51)] 2 (5/6,5/12,1/6,1/12) {1/6,1/6,1/12,1/4} <-,-,-,-,-,-,-,-,-,-,-,-,-,1,-,-,+,-,+,-,+,1,+,+>
[12(44)] 2 (13/16,5/16,3/16,1/16) {1/4,1/8,1/8,1/8} <-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,1,-,+,-,+,1,+,+>
[13(58)] 2 (2/3,1/6,1/6,0) {1/3,0,1/6,0} <-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,1,-,1,-,+,->
[14(56)] 2 (1/2,1/6,1/6,1/6) {0,1/3,0,0} <-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,1,-,1,->
[15(32)] 2 (5/4,3/4,1/4,1/12) {1/6,1/6,1/6,1/2} <-,-,-,-,-,-,-,-,-,+,-,-,-,+,1,1,+,+,+,+,+,+,+,+>
[16(27)] 2 (3/2,1/2,1/4,1/8) {5/8,1/4,1/8,1/4} <-,-,-,-,-,-,-,-,+,1,1,-,+,+,+,-,+,+,+,+,+,+,+,+>
[17(45)] 2 (11/8,1/2,3/8,1/8) {3/8,1/4,1/4,1/8} <-,-,-,-,-,-,-,-,+,1,-,-,+,+,1,-,+,+,+,+,+,+,+,+>
[18(33)] 2 (17/12,7/12,5/12,1/12) {1/3,1/6,1/3,1/6} <-,-,-,-,-,-,-,-,+,+,-,-,+,+,1,1,+,+,+,+,+,+,+,+>
[19(10)] 1 (5/2,3/4,1/2,1/4) {1,1/2,1/4,1/4} <1,-,-,-,+,1,-,-,+,+,+,1,+,+,+,+,+,+,+,+,+,+,+,+>
[20(12)] 1 (5/2,3/2,1/2,0) {1/2,0,1/2,1} <-,-,-,1,-,1,-,+,+,+,1,+,+,+,+,+,+,+,+,+,+,+,+,+>
[21(9)] 1 (5/2,5/4,1/2,1/4) {1/2,1/2,1/4,3/4} <-,-,-,-,1,1,-,1,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+>
[22(19)] 1 (11/8,1/2,3/8,1/4) {1/4,1/2,1/8,1/8} <-,-,-,-,-,-,-,-,1,1,-,-,+,+,1,-,+,+,+,+,+,+,+,+>
[23(25)] 1 (17/12,7/12,5/12,1/4) {1/6,1/2,1/6,1/6} <-,-,-,-,-,-,-,-,1,+,-,-,+,+,1,1,+,+,+,+,+,+,+,+>
[24(20)] 1 (29/24,1/2,5/24,1/12) {5/12,1/6,1/8,7/24} <-,-,-,-,-,-,-,-,-,1,-,-,1,+,1,-,+,+,+,+,+,+,+,+>
[25(21)] 1 (13/12,1/2,1/3,1/12) {1/6,1/6,1/4,1/6} <-,-,-,-,-,-,-,-,-,1,-,-,1,+,-,-,+,1,+,+,+,+,+,+>
[26(37)] 1 (7/8,1/2,1/4,1/8) {0,1/4,1/8,1/4} <-,-,-,-,-,-,-,-,-,1,-,-,-,1,-,-,+,-,+,1,+,+,+,+>
[27(40)] 1 (13/16,1/2,3/16,1/8) {0,1/4,1/16,5/16} <-,-,-,-,-,-,-,-,-,1,-,-,-,1,-,-,+,-,+,-,+,1,+,+>
[28(34)] 1 (9/8,1/2,1/8,1/8) {3/8,1/4,0,3/8} <-,-,-,-,-,-,-,-,-,1,-,-,-,+,1,-,+,1,+,+,+,+,+,+>
[29(36)] 1 (1,1/2,1/4,0) {1/4,0,1/4,1/4} <-,-,-,-,-,-,-,-,-,1,-,-,-,+,-,-,+,1,+,1,+,+,+,+>
[30(39)] 1 (7/8,1/2,1/8,1/8) {1/8,1/4,0,3/8} <-,-,-,-,-,-,-,-,-,1,-,-,-,+,-,-,+,-,+,1,+,1,+,+>
[31(42)] 1 (7/8,1/4,1/8,0) {1/2,0,1/8,1/8} <-,-,-,-,-,-,-,-,-,-,-,-,-,1,-,-,1,-,+,-,+,1,+,+>
[32(43)] 1 (7/8,3/8,1/8,1/8) {1/4,1/4,0,1/4} <-,-,-,-,-,-,-,-,-,-,-,-,-,1,-,-,+,-,+,1,+,1,+,+>
[33(54)] 1 (11/16,5/16,1/16,1/16) {1/4,1/8,0,1/4} <-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,1,-,1,-,+,-,+,1>
[34(57)] 1 (1/2,1/4,1/4,0) {0,0,1/4,0} <-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,1,-,1,-,1,->
[35(24)] 1 (31/24,17/24,7/24,1/8) {1/6,1/4,1/6,5/12} <-,-,-,-,-,-,-,-,-,+,-,-,1,+,1,1,+,+,+,+,+,+,+,+>
[36(4)] 0 (11/2,5/2,3/2,1/2) {1,1,1,1} <1,1,1,1,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+>
[37(5)] 0 (7/2,3/2,1/2,1/2) {1,1,0,1} <1,1,-,1,+,1,1,1,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+>
[38(8)] 0 (5/2,1/2,1/2,1/2) {1,1,0,0} <1,1,-,-,+,1,1,-,+,1,+,1,+,+,+,1,+,+,+,+,+,+,+,+>
[39(11)] 0 (5/2,1,1/2,0) {1,0,1/2,1/2} <1,-,-,-,1,1,-,1,+,+,+,1,+,+,+,+,+,+,+,+,+,+,+,+>
[40(26)] 0 (3/2,1/2,0,0) {1,0,0,1/2} <1,-,-,-,1,-,-,-,1,1,1,-,1,+,+,-,+,+,+,+,+,+,+,+>
[41(29)] 0 (1,0,0,0) {1,0,0,0} <1,-,-,-,1,-,-,-,1,-,1,-,1,1,1,-,1,1,1,1,1,1,+,1>
[42(6)] 0 (5/2,3/2,1/2,1/2) {0,1,0,1} <-,1,-,1,1,1,1,1,1,+,1,+,+,+,+,+,+,+,+,+,+,+,+,+>
[43(7)] 0 (3/2,1/2,1/2,1/2) {0,1,0,0} <-,1,-,-,1,1,1,-,1,1,1,1,+,1,1,1,+,1,+,+,+,+,+,+>
[44(31)] 0 (1,1,0,0) {0,0,0,1} <-,-,-,1,-,-,-,1,-,+,-,1,-,+,1,1,+,1,+,1,+,1,+,+>
[45(28)] 0 (3/2,1/2,1/4,1/4) {1/2,1/2,0,1/4} <-,-,-,-,1,-,-,-,1,1,1,-,+,+,+,-,+,+,+,+,+,+,+,+>
[46(16)] 0 (1,1/2,1/2,0) {0,0,1/2,0} <-,-,-,-,-,1,-,-,1,1,-,-,1,1,-,1,1,1,+,1,+,+,+,+>
[47(14)] 0 (3/2,1/2,1/2,0) {1/2,0,1/2,0} <-,-,-,-,-,1,-,-,+,1,1,-,+,+,1,1,+,+,+,+,+,+,+,+>
[48(18)] 0 (5/4,1/2,1/4,0) {1/2,0,1/4,1/4} <-,-,-,-,-,-,-,-,1,1,-,-,1,+,1,-,+,+,+,+,+,+,+,+>
[49(30)] 0 (1,1/4,1/4,0) {1/2,0,1/4,0} <-,-,-,-,-,-,-,-,1,-,-,-,1,1,-,-,1,1,+,1,+,+,+,+>
[50(23)] 0 (4/3,2/3,1/3,0) {1/3,0,1/3,1/3} <-,-,-,-,-,-,-,-,1,+,-,-,1,+,1,1,+,+,+,+,+,+,+,+>
[51(17)] 0 (7/6,1/2,1/6,1/6) {1/3,1/3,0,1/3} <-,-,-,-,-,-,-,-,-,1,-,-,1,+,1,-,+,1,+,+,+,+,+,+>
[52(53)] 0 (1/2,1/2,0,0) {0,0,0,1/2} <-,-,-,-,-,-,-,-,-,1,-,-,-,1,-,-,1,-,1,-,1,-,1,1>
[53(41)] 0 (3/4,1/2,1/4,0) {0,0,1/4,1/4} <-,-,-,-,-,-,-,-,-,1,-,-,-,1,-,-,1,-,+,-,+,1,+,+>
[54(38)] 0 (5/6,1/2,1/6,1/6) {0,1/3,0,1/3} <-,-,-,-,-,-,-,-,-,1,-,-,-,1,-,-,+,-,+,1,+,1,+,+>
[55(35)] 0 (1,1/2,0,0) {1/2,0,0,1/2} <-,-,-,-,-,-,-,-,-,1,-,-,-,+,1,-,+,1,+,1,+,1,+,+>
[56(52)] 0 (3/4,1/4,1/4,1/4) {0,1/2,0,0} <-,-,-,-,-,-,-,-,-,-,-,-,1,-,-,-,1,-,1,1,+,1,+,1>
[57(65)] 0 (5/8,3/8,0,0) {1/4,0,0,3/8} <-,-,-,-,-,-,-,-,-,-,-,-,-,1,-,-,1,-,1,-,1,-,+,1>
[58(22)] 0 (5/4,3/4,1/4,1/4) {0,1/2,0,1/2} <-,-,-,-,-,-,-,-,-,+,-,1,1,+,1,1,+,1,+,+,+,+,+,+>
[59(66)] 0 (9/8,7/8,1/8,1/8) {0,1/4,0,3/4} <-,-,-,-,-,-,-,-,-,+,-,1,-,+,1,1,+,1,+,+,+,+,+,+>

Facet Closures [Facet number/dimension]
 Maximal Facets:
 [1/4]:[1/4][5/3][14/2][34/1][52/0]
 [2/4]:[2/4][3/3][4/3][13/2][14/2][33/1][34/1][41/0][52/0][56/0][57/0]
 [6/2]:[6/2][24/1][28/1][48/0][51/0][55/0]
 [7/2]:[7/2][25/1][28/1][29/1][46/0][51/0][55/0]
 [8/2]:[8/2][26/1][29/1][30/1][46/0][54/0][55/0]
 [9/2]:[9/2][27/1][30/1][53/0][54/0][55/0]
 [10/2]:[10/2][26/1][32/1][41/0][46/0][49/0][54/0]
 [11/2]:[11/2][27/1][31/1][32/1][41/0][53/0][54/0]
 [12/2]:[12/2][31/1][41/0][53/0][56/0]
 [15/2]:[15/2][35/1][44/0][50/0][58/0][59/0]
 [16/2]:[16/2][40/0][43/0][45/0][47/0]
 [17/2]:[17/2][22/1][43/0][47/0][48/0]
 [18/2]:[18/2][23/1][43/0][47/0][50/0]
 [19/1]:[19/1][38/0][39/0]
 [20/1]:[20/1][42/0]
 [21/1]:[21/1][39/0][42/0]
 [36/0]:[36/0]
 [37/0]:[37/0]
 
 Other Facets:
 [3/3]:[3/3][13/2][33/1][34/1][41/0][52/0][56/0][57/0]
 [4/3]:[4/3][13/2][14/2][34/1][41/0][52/0][57/0]
 [5/3]:[5/3][14/2][34/1][52/0]
 [13/2]:[13/2][34/1][41/0][52/0][57/0]
 [14/2]:[14/2][34/1][52/0]
 [22/1]:[22/1][43/0][48/0]
 [23/1]:[23/1][43/0][50/0]
 [24/1]:[24/1][48/0][51/0]
 [25/1]:[25/1][46/0][51/0]
 [26/1]:[26/1][46/0][54/0]
 [27/1]:[27/1][53/0][54/0]
 [28/1]:[28/1][51/0][55/0]
 [29/1]:[29/1][46/0][55/0]
 [30/1]:[30/1][54/0][55/0]
 [31/1]:[31/1][41/0][53/0]
 [32/1]:[32/1][41/0][54/0]
 [33/1]:[33/1][41/0][52/0][56/0][57/0]
 [34/1]:[34/1][52/0]
 [35/1]:[35/1][50/0][58/0]
 [38/0]:[38/0]
 [39/0]:[39/0]
 [40/0]:[40/0]
 [41/0]:[41/0]
 [42/0]:[42/0]
 [43/0]:[43/0]
 [44/0]:[44/0]
 [45/0]:[40/0][43/0][45/0]
 [46/0]:[46/0]
 [47/0]:[43/0][47/0]
 [48/0]:[48/0]
 [49/0]:[41/0][46/0][49/0]
 [50/0]:[50/0]
 [51/0]:[51/0]
 [52/0]:[52/0]
 [53/0]:[53/0]
 [54/0]:[54/0]
 [55/0]:[55/0]
 [56/0]:[41/0][56/0]
 [57/0]:[41/0][52/0][57/0]
 [58/0]:[58/0]
 [59/0]:[44/0][58/0][59/0]
 

Closure Matrix:
+,0,0,0,+,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0
0,+,+,+,0,0,0,0,0,0,0,0,+,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,+,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,+,0,0,0,+,+,0,0
0,-,+,0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,+,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,+,0,0,0,+,+,0,0
0,-,0,+,0,0,0,0,0,0,0,0,+,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,+,0,0
-,0,0,0,+,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0
0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,+,0,0,0,+,0,0,0,0
0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,+,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,+,0,0,0,+,0,0,0,0
0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,+,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,+,+,0,0,0,0
0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,+,+,0,0,0,0
0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,+,0,0,0,0,0,0,0,0,+,0,0,0,0,+,0,0,+,0,0,0,0,+,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,+,+,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,+,+,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,+,0,0,+,0,0,0
0,-,-,-,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,+,0,0
-,-,0,-,-,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,+,0,0,0,0,0,+,0,0,0,0,0,0,0,+,+
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,+,0,+,0,+,0,0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,+,+,0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,+,0,0,+,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-,0,0,0,0,+,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,+,0,0,0,0,0,0,+,0,0,0,0,0,0,0,0,0
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