#from John Stembridge E6 # point representatives from cells that are psd in all irreps face {1, 2, 3, 4} [0, 0, 0, 0, 0] face {2, 3, 4} [1, 0, 0, 0, 0, 1] {} {1} {23} [1/2, 0, 0, 0, 0, 1/2] {1} {23} {} [0, 0, 0, 0, 2] face {1, 3, 4} [0, 1, 0, 0, 0, 0] {} {2} {36} [0, 0, 0, 0, 1] face {3, 4} [1, 1, 0, 0, 0, 1] {} {1, 2} {17, 23} [1/2, 1, 0, 0, 0, 1/2] {1} {2, 23} {17} [1/2, 1/2, 0, 0, 0, 1/2] {1, 2} {17, 23} {27} [1/4, 3/4, 0, 0, 0, 1/4] {2, 23} {17} {27} [1/4, 1/2, 0, 0, 0, 1/4] {17, 23} {27} {36} [0, 0, 0, 2, 3] face {1, 2, 4} [0, 0, 1/2, 0, 1/2, 0] {3} {15} {29} [0, 0, 0, 0, 1] face {2, 4} [1/4, 0, 1/4, 0, 1/4, 1/4] {18} {23, 29} {32} [0, 0, 1/4, 0, 1/4, 0] {32} {34} {} [0, 0, 0, 1, 1] face {1, 4} [0, 1/2, 1/4, 0, 1/4, 0] {13, 15} {19} {29} [0, 0, 0, 1, 0] face {4} [1, 1, 1, 0, 1, 1] {} {1, 2, 3} {7, 13, 15} [1/2, 1, 1/2, 0, 1/2, 1/2] {1, 3} {2, 7, 15} {13, 18} [1/2, 1/2, 1/2, 0, 1/2, 1/2] {1, 2, 3} {7, 13, 15} {17, 18, 19} [5/8, 5/8, 3/8, 0, 3/8, 5/8] {1, 2, 15} {7, 13} {17, 18, 19} [1/3, 1/3, 1/3, 0, 1/3, 1/3] {7, 13, 15} {17, 18, 19} {22, 23} [1/4, 1/2, 1/4, 0, 1/4, 1/4] {13, 18} {17, 19, 23} {22} [1/4, 1/4, 1/4, 0, 1/4, 1/4] {17, 18, 19} {22, 23} {27, 29} [1/8, 1/4, 5/16, 0, 5/16, 1/8] {17, 19, 23} {22} {27, 29} [1/8, 1/2, 1/8, 0, 1/8, 1/8] {22, 23} {27, 29} {32} [0, 1/2, 1/8, 0, 1/8, 0] {32} {34} {36} [0, 0, 2, 3, 5] face {1, 2, 3} [0, 0, 0, 1, 0, 0] {} {4} {24} [0, 0, 0, 0, 1] face {2, 3} [1, 0, 0, 1, 0, 1] {} {1, 4} {12, 24} [1/2, 0, 0, 1/2, 0, 1/2] {1, 4} {12, 24} {23, 26} [5/8, 0, 0, 3/8, 0, 5/8] {1, 24} {12} {23, 26} [1/3, 0, 0, 1/3, 0, 1/3] {12, 24} {23, 26} {30} [0, 0, 0, 1, 3] face {1, 3} [0, 1, 0, 1, 0, 0] {} {2, 4} {8} [0, 1/2, 0, 1/4, 0, 0] {8} {24} {35} [0, 0, 0, 1, 1] face {3} [1, 1, 0, 1, 0, 1] {} {1, 2, 4} {8, 12} [1/4, 1/2, 0, 1/2, 0, 1/4] {2, 12} {8, 23} {17, 24} [1/3, 1/3, 0, 1/3, 0, 1/3] {8, 12} {17, 23, 24} {26, 27} [3/8, 1/8, 0, 1/4, 0, 3/8] {17, 24} {23, 26} {27} [1/4, 1/2, 0, 1/8, 0, 1/4] {17, 23, 24} {26} {27} [1/4, 1/4, 0, 1/4, 0, 1/4] {17, 23, 24} {26, 27} {30} [1/4, 0, 0, 1/4, 0, 1/4] {26, 27} {30} {35} [0, 0, 2, 3, 2] face {1, 2} [0, 0, 0, 0, 0] face {2} [1/8, 0, 5/16, 1/8, 5/16, 1/8] {18, 24} {23, 26} {29, 30} [9/32, 0, 5/32, 1/8, 5/32, 9/32] {26} {23, 29} {30} [0, 0, 0, 1/3, 0, 0] {34} {35} {} [0, 0, 1, 2, 0] face {1} [0, 1/4, 1/4, 1/2, 1/4, 0] {8, 9} {13, 15} {19} [0, 1/4, 1/4, 0, 1/4, 0] {24} {29} {34} [0, 0, 1, 1, 0] face {} [1, 1, 1, 1, 1, 1] {} {1, 2, 3, 4} {7, 8, 9} [1/4, 1, 1/4, 1/2, 1/4, 1/4] {7, 9} {2, 12, 15} {8, 18} [1, 1/4, 1/4, 1/2, 1/4, 1] {8, 9} {1, 13, 15} {7, 19} [1/8, 1/4, 1/4, 3/8, 1/4, 1/8] {12, 13, 15} {17, 18} {19, 23} [1/4, 1/4, 1/4, 1/4, 1/4, 1/4] {12, 13, 15} {17, 18, 19} {22, 23, 24} [1/4, 3/4, 1/4, 0, 1/4, 1/4] {8, 18} {13, 23} {17, 19} [1/8, 1/4, 1/8, 1/2, 1/8, 1/8] {13, 18} {17, 19, 23} {22, 24} [3/8, 1/4, 1/4, 1/8, 1/4, 3/8] {12, 19} {17, 18, 24} {22, 23} [1/2, 1/4, 1/4, 0, 1/4, 1/2] {12, 24} {17, 18} {22, 23} [9/32, 7/16, 5/32, 1/8, 5/32, 9/32] {18, 19} {17, 23, 24} {22} [1/8, 1/8, 5/16, 1/8, 5/16, 1/8] {17, 18, 19} {22, 23, 24} {26, 27} [1/4, 1/8, 3/16, 1/8, 3/16, 1/4] {22, 24} {23, 26} {27, 29} [1/4, 1/4, 1/8, 1/8, 1/8, 1/4] {22, 23, 24} {26} {27, 29} [1/8, 3/8, 1/8, 1/8, 1/8, 1/8] {22, 23, 24} {26, 27} {29, 30} [5/16, 1/8, 3/16, 0, 3/16, 5/16] {26} {23, 29} {27} [1/4, 3/8, 1/8, 0, 1/8, 1/4] {23, 26} {29} {27} [1/4, 1/8, 1/8, 1/8, 1/8, 1/4] {23, 26} {27, 29} {30} [1/8, 1/4, 1/8, 1/8, 1/8, 1/8] {26, 27} {29, 30} {32} [1/8, 0, 1/4, 1/16, 1/4, 1/8] {30} {29} {32} [1/8, 3/8, 1/8, 0, 1/8, 1/8] {29, 30} {32} {34} [0, 1/4, 1/8, 1/8, 1/8, 0] {32} {34} {35} [0, 0, 0, 3/8, 0, 0] {34} {} {35} [0, 1/4, 0, 1/4, 0, 0] {34} {35} {36} [0, 1/4, 0, 1/6, 0, 0] {35} {36} {} [0, 0, 0, 0, 0, 0] {36} {} {} [2, 7, 8, 7, 1] 2 3 4 2 + 7 q + 14 q + 22 q + 21 q # representatives from the maximal psd cells # Format: fund.wt.coords co-dim J <1 =1 >1 [0, 0, 0, 0, 0, 0] 0 {} {36} {} {} [0, 0, 0, 3/8, 0, 0] 0 {} {34} {} {35} [1/8, 3/8, 1/8, 0, 1/8, 1/8] 1 {} {29, 30} {32} {34} [1/8, 0, 1/4, 1/16, 1/4, 1/8] 1 {} {30} {29} {32} [1/4, 3/8, 1/8, 0, 1/8, 1/4] 1 {} {23, 26} {29} {27} [1/4, 1/4, 1/8, 1/8, 1/8, 1/4] 1 {} {22, 23, 24} {26} {27, 29} [1/8, 1/8, 5/16, 1/8, 5/16, 1/8] 3 {} {17, 18, 19} {22, 23, 24} {26, 27} [9/32, 7/16, 5/32, 1/8, 5/32, 9/32] 3 {} {18, 19} {17, 23, 24} {22} [1/2, 1/4, 1/4, 0, 1/4, 1/2] 2 {} {12, 24} {17, 18} {22, 23} [1/8, 1/4, 1/8, 1/2, 1/8, 1/8] 3 {} {13, 18} {17, 19, 23} {22, 24} [1/4, 3/4, 1/4, 0, 1/4, 1/4] 2 {} {8, 18} {13, 23} {17, 19} [1/8, 1/4, 1/4, 3/8, 1/4, 1/8] 2 {} {12, 13, 15} {17, 18} {19, 23} [1, 1/4, 1/4, 1/2, 1/4, 1] 3 {} {8, 9} {1, 13, 15} {7, 19} [1/4, 1, 1/4, 1/2, 1/4, 1/4] 3 {} {7, 9} {2, 12, 15} {8, 18} [1, 1, 1, 1, 1, 1] 4 {} {} {1, 2, 3, 4} {7, 8, 9} [1, 1, 0, 1, 0, 1] 4 {3} {} {1, 2, 4} {8, 12} [5/8, 5/8, 3/8, 0, 3/8, 5/8] 3 {4} {1, 2, 15} {7, 13} {17, 18, 19} [1, 1, 1, 0, 1, 1] 4 {4} {} {1, 2, 3} {7, 13, 15}