Generated by sphericalReport.pl Tue Feb 1 09:30:33 2005 Data from D4/psd_all psd_all (Stembridge) List of positive coroots from D4/data Dynkin Diagram: 2 | | 4---3---1 Number of facets of each dimension: 4:2 3:5 2:7 1:7 0:12 Total number of facets: 33 [number(line number)] dimension (standard){weight} [1(99)] 4 (0,0,0,0) {0,0,0,0} <-,-,-,-,-,-,-,-,-,-,-,-> [2(96)] 4 (7/8,1/4,1/4,0) {1/4,1/4,0,5/8} <-,-,-,-,-,-,-,-,-,-,+,+> [3(95)] 3 (3/4,1/2,1/2,0) {1/2,1/2,0,1/4} <-,-,-,-,-,-,-,1,-,-,+,+> [4(94)] 3 (7/8,3/8,3/8,1/8) {1/2,1/4,0,1/2} <-,-,-,-,-,-,-,-,1,-,+,+> [5(92)] 3 (7/8,3/8,3/8,-1/8) {1/4,1/2,0,1/2} <-,-,-,-,-,-,-,-,-,1,+,+> [6(97)] 3 (3/4,1/2,1/4,0) {1/4,1/4,1/4,1/4} <-,-,-,-,-,-,-,-,-,-,1,+> [7(98)] 3 (1/2,1/2,0,0) {0,0,1/2,0} <-,-,-,-,-,-,-,-,-,-,-,1> [8(93)] 2 (7/8,5/8,3/8,1/8) {1/2,1/4,1/4,1/4} <-,-,-,-,-,-,-,1,1,-,+,+> [9(91)] 2 (3/4,1/2,1/2,-1/4) {1/4,3/4,0,1/4} <-,-,-,-,-,-,-,1,-,1,+,+> [10(43)] 2 (3/4,3/4,1/4,0) {1/4,1/4,1/2,0} <-,-,-,-,-,-,-,1,-,-,1,+> [11(90)] 2 (1,1/4,1/4,0) {1/4,1/4,0,3/4} <-,-,-,-,-,-,-,-,1,1,+,+> [12(75)] 2 (7/8,3/8,1/8,1/8) {1/4,0,1/4,1/2} <-,-,-,-,-,-,-,-,1,-,1,+> [13(80)] 2 (3/4,1/2,1/4,-1/4) {0,1/2,1/4,1/4} <-,-,-,-,-,-,-,-,-,1,1,+> [14(64)] 2 (3/4,1/4,1/4,0) {1/4,1/4,0,1/2} <-,-,-,-,-,-,-,-,-,-,1,1> [15(88)] 1 (15/8,9/8,7/8,1/8) {1,3/4,1/4,3/4} <1,-,-,-,+,1,1,+,+,+,+,+> [16(87)] 1 (13/8,11/8,5/8,-3/8) {1/4,1,3/4,1/4} <-,1,-,-,1,+,1,+,+,+,+,+> [17(86)] 1 (2,1,1/4,0) {1/4,1/4,3/4,1} <-,-,-,1,1,1,+,+,+,+,+,+> [18(89)] 1 (1,3/4,1/4,0) {1/4,1/4,1/2,1/4} <-,-,-,-,-,-,-,1,1,1,+,+> [19(21)] 1 (1/2,1/2,1/2,-1/4) {1/4,3/4,0,0} <-,-,-,-,-,-,-,1,-,-,1,1> [20(53)] 1 (7/8,1/8,1/8,1/8) {1/4,0,0,3/4} <-,-,-,-,-,-,-,-,1,-,1,1> [21(58)] 1 (5/8,3/8,3/8,-3/8) {0,3/4,0,1/4} <-,-,-,-,-,-,-,-,-,1,1,1> [22(85)] 0 (3,2,1,0) {1,1,1,1} <1,1,1,1,+,+,+,+,+,+,+,+> [23(63)] 0 (2,1,1,0) {1,1,0,1} <1,1,-,1,1,1,1,+,+,+,+,+> [24(31)] 0 (3/2,3/2,1/2,1/2) {1,0,1,0} <1,-,1,-,+,1,1,+,+,1,+,+> [25(11)] 0 (1/2,1/2,1/2,1/2) {1,0,0,0} <1,-,-,-,1,-,-,1,1,-,1,1> [26(37)] 0 (3/2,3/2,1/2,-1/2) {0,1,1,0} <-,1,1,-,1,+,1,+,1,+,+,+> [27(16)] 0 (1/2,1/2,1/2,-1/2) {0,1,0,0} <-,1,-,-,-,1,-,1,-,1,1,1> [28(69)] 0 (2,1,0,0) {0,0,1,1} <-,-,1,1,1,1,+,1,+,+,+,+> [29(26)] 0 (1,1,0,0) {0,0,1,0} <-,-,1,-,1,1,1,1,1,1,1,+> [30(48)] 0 (1,0,0,0) {0,0,0,1} <-,-,-,1,-,-,1,-,1,1,1,1> [31(32)] 0 (7/8,7/8,1/8,1/8) {1/4,0,3/4,0} <-,-,-,-,1,-,-,1,1,-,1,+> [32(38)] 0 (7/8,7/8,1/8,-1/8) {0,1/4,3/4,0} <-,-,-,-,-,1,-,1,-,1,1,+> [33(70)] 0 (1,1/4,0,0) {0,0,1/4,3/4} <-,-,-,-,-,-,1,-,1,1,1,+> Facet Closures [Facet number/dimension] Maximal Facets: [1/4]:[1/4][7/3][14/2][19/1][20/1][21/1][25/0][27/0][30/0] [2/4]:[2/4][3/3][4/3][5/3][6/3][8/2][9/2][10/2][11/2][12/2][13/2][14/2][18/1][19/1][20/1][21/1][25/0][27/0][29/0][30/0][31/0][32/0][33/0] [15/1]:[15/1][23/0][24/0] [16/1]:[16/1][23/0][26/0] [17/1]:[17/1][23/0][28/0] [22/0]:[22/0] Other Facets: [3/3]:[3/3][8/2][9/2][10/2][18/1][19/1][25/0][27/0][29/0][31/0][32/0] [4/3]:[4/3][8/2][11/2][12/2][18/1][20/1][25/0][29/0][30/0][31/0][33/0] [5/3]:[5/3][9/2][11/2][13/2][18/1][21/1][27/0][29/0][30/0][32/0][33/0] [6/3]:[6/3][10/2][12/2][13/2][14/2][19/1][20/1][21/1][25/0][27/0][29/0][30/0][31/0][32/0][33/0] [7/3]:[7/3][14/2][19/1][20/1][21/1][25/0][27/0][30/0] [8/2]:[8/2][18/1][25/0][29/0][31/0] [9/2]:[9/2][18/1][27/0][29/0][32/0] [10/2]:[10/2][19/1][25/0][27/0][29/0][31/0][32/0] [11/2]:[11/2][18/1][29/0][30/0][33/0] [12/2]:[12/2][20/1][25/0][29/0][30/0][31/0][33/0] [13/2]:[13/2][21/1][27/0][29/0][30/0][32/0][33/0] [14/2]:[14/2][19/1][20/1][21/1][25/0][27/0][30/0] [18/1]:[18/1][29/0] [19/1]:[19/1][25/0][27/0] [20/1]:[20/1][25/0][30/0] [21/1]:[21/1][27/0][30/0] [23/0]:[23/0] [24/0]:[24/0] [25/0]:[25/0] [26/0]:[26/0] [27/0]:[27/0] [28/0]:[28/0] [29/0]:[29/0] [30/0]:[30/0] [31/0]:[25/0][29/0][31/0] [32/0]:[27/0][29/0][32/0] [33/0]:[29/0][30/0][33/0] 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,+