D5 # point representatives from the cells that are positive # semi-definite in the reflection representation face {1, 3, 4, 5} [0, 0, 0, 0, 0] face {3, 4, 5} [1/2, 1/2, 0, 0, 0] {1} {10} {} [0, 0, 0, 0, 1] face {1, 4, 5} [0, 0, 1, 0, 0] {} {3} {17} [0, 0, 0, 0, 1] face {4, 5} [0, 0, 1/2, 0, 0] {10} {17} {} [0, 0, 0, 1, 0] face {1, 3, 5} [0, 0, 0, 1, 0] {} {4} {20} [0, 0, 0, 0, 1] face {3, 5} [1, 1, 0, 1, 0] {} {1, 4} {10, 11} [1/2, 1/2, 0, 1, 0] {1} {4, 10} {11} [1/4, 1/4, 0, 1, 0] {10} {4} {11} [1/4, 1/4, 0, 1/2, 0] {10, 11} {14} {20} [0, 0, 0, 2, 2] face {1, 5} [0, 0, 1, 1, 0] {} {3, 4} {8} [0, 0, 1/4, 3/4, 0] {3, 4} {8} {17} [0, 0, 0, 1, 1] face {5} [1, 1, 1, 1, 0] {} {1, 3, 4} {6, 8} [1, 1, 1/4, 1, 0] {3} {1, 4} {6, 8} [1/4, 1/4, 3/4, 1, 0] {1, 3} {4, 6} {8, 10} [1/4, 1/4, 1/2, 1, 0] {6} {4, 10} {8} [0, 0, 1/4, 1, 0] {10} {4} {8} [1/4, 1/4, 1/2, 1/4, 0] {6, 8} {10, 11} {14} [1/4, 1/4, 1/4, 1/2, 0] {8, 10} {11} {14} [0, 0, 1/4, 1/2, 0] {14} {17} {20} [0, 0, 3, 4, 1] face {1, 3, 4} [0, 0, 0, 0, 1] {} {5} {} [0, 0, 0, 0, 1] face {3, 4} [1/2, 1/2, 0, 0, 1/2] {1, 5} {10, 15} {18} [1/4, 1/4, 0, 0, 1/2] {10, 15} {18} {} [0, 0, 0, 1, 1] face {1, 4} [0, 0, 1, 0, 1] {} {3, 5} {13, 17} [0, 0, 0, 0, 1] face {4} [1, 1, 1, 0, 1] {} {1, 3, 5} {6, 13} [1/4, 1/4, 1/2, 0, 1/4] {6, 13} {10, 15} {17, 18} [0, 0, 1/4, 0, 1/2] {17, 18} {19} {} [0, 0, 1, 1, 1] face {1, 3} [0, 0, 0, 1, 1] {} {4, 5} {9} [0, 0, 0, 1, 1/4] {5} {4} {9} [0, 0, 0, 1/4, 3/4] {4, 5} {9} {20} [0, 0, 0, 2, 1] face {3} [1, 1, 0, 1, 1] {} {1, 4, 5} {9, 10, 11} [1, 1, 0, 1, 1/4] {5} {1, 4} {9, 10, 11} [1/2, 1/2, 0, 1, 1] {1} {4, 5, 10} {9, 11} [1/2, 1/2, 0, 1, 1/4] {1, 5} {4, 10} {9, 11} [1/4, 1/4, 0, 1, 1] {10} {4, 5} {9, 11} [1/4, 1/4, 0, 1, 1/4] {5, 10} {4} {9, 11} [1/2, 1/2, 0, 1/2, 1/2] {1, 4, 5} {9, 10, 11} {14, 15} [1/4, 1/4, 0, 3/4, 1/4] {4, 5, 10} {9, 11} {14, 15} [1/4, 1/4, 0, 1/2, 1/4] {9, 10, 11} {14, 15} {18} [1/4, 1/4, 0, 1/4, 1/4] {14, 15} {18} {20} [0, 0, 2, 5, 3] face {1} [0, 0, 1, 1, 1] {} {3, 4, 5} {8, 9} [0, 0, 1, 1/4, 1] {4} {3, 5} {8, 9} [0, 0, 1, 1, 1/4] {5} {3, 4} {8, 9} [0, 0, 1, 1/2, 3/4] {4, 5} {3} {8, 9} [0, 0, 3/4, 1/4, 1] {3, 4} {5, 8} {9, 17} [0, 0, 1/2, 1/2, 3/4] {3, 4, 5} {8} {9, 17} [0, 0, 1, 1/4, 3/4] {4, 5} {3, 9} {8} [0, 0, 3/4, 1/4, 3/4] {3, 4, 5} {8, 9} {13, 17} [0, 0, 1/4, 1/2, 1/4] {8, 9} {13, 17} {19} [0, 0, 1/4, 0, 3/4] {9, 17} {13} {19} [0, 0, 3, 6, 1] face {} [1, 1, 1, 1, 1] {} {1, 3, 4, 5} {6, 8, 9} [1, 1, 1/4, 1, 1] {3} {1, 4, 5} {6, 8, 9} [1, 1, 1, 1/4, 1] {4} {1, 3, 5} {6, 8, 9} [1, 1, 3/4, 1/2, 1] {3, 4} {1, 5} {6, 8, 9} [1, 1, 1, 1, 1/4] {5} {1, 3, 4} {6, 8, 9} [1, 1, 1/4, 1, 1/4] {3, 5} {1, 4} {6, 8, 9} [1, 1, 1, 1/2, 3/4] {4, 5} {1, 3} {6, 8, 9} [1, 1, 3/4, 1/2, 3/4] {3, 4, 5} {1} {6, 8, 9} [1/4, 1/4, 3/4, 1, 1] {1, 3} {4, 5, 6} {8, 9, 10} [1/4, 1/4, 3/4, 1/2, 1] {1, 3, 4} {5, 6} {8, 9, 10} [1/4, 1/4, 3/4, 1, 1/4] {1, 3, 5} {4, 6} {8, 9, 10} [1/4, 1/4, 3/4, 1/2, 3/4] {1, 3, 4, 5} {6} {8, 9, 10} [1, 1, 3/4, 1/4, 1] {3, 4} {1, 5, 8} {6, 9} [1, 1, 1/2, 1/2, 3/4] {3, 4, 5} {1, 8} {6, 9} [1/4, 1/4, 3/4, 1/4, 1] {1, 3, 4} {5, 6, 8} {9, 10, 11} [1/2, 1/2, 1/2, 1/2, 3/4] {1, 3, 4, 5} {6, 8} {9, 10, 11} [1, 1, 1, 1/4, 3/4] {4, 5} {1, 3, 9} {6, 8} [1, 1, 3/4, 1/2, 1/2] {3, 4, 5} {1, 9} {6, 8} [1/4, 1/4, 3/4, 1/2, 1/2] {1, 3, 4, 5} {6, 9} {8, 10} [1, 1, 3/4, 1/4, 3/4] {3, 4, 5} {1, 8, 9} {6, 13} [1/4, 1/4, 3/4, 1/4, 3/4] {1, 3, 4, 5} {6, 8, 9} {10, 11, 13} [1/4, 1/4, 1/2, 1, 1] {6} {4, 5, 10} {8, 9} [1/4, 1/4, 1/2, 3/4, 1] {4, 6} {5, 10} {8, 9} [1/4, 1/4, 1/2, 1, 1/4] {5, 6} {4, 10} {8, 9} [1/4, 1/4, 1/2, 3/4, 1/2] {4, 5, 6} {10} {8, 9} [0, 0, 1/4, 1, 1] {10} {4, 5} {8, 9} [0, 0, 3/4, 1/2, 1] {4, 10} {5} {8, 9} [0, 0, 1/4, 1, 1/4] {5, 10} {4} {8, 9} [0, 0, 3/4, 1/2, 3/4] {4, 5, 10} {} {8, 9} [1/4, 1/4, 1/2, 1/2, 1] {4, 6} {5, 8, 10} {9, 11} [1/4, 1/4, 1/2, 1/2, 3/4] {4, 5, 6} {8, 10} {9, 11} [1/4, 1/4, 1/4, 3/4, 1] {4, 10} {5, 8} {9, 11} [1/4, 1/4, 1/4, 3/4, 1/2] {4, 5, 10} {8} {9, 11} [1/4, 1/4, 1/2, 3/4, 1/4] {4, 5, 6} {9, 10} {8} [0, 0, 3/4, 1/2, 1/2] {4, 5, 10} {9} {8} [1/4, 1/4, 1/2, 1/2, 1/2] {4, 5, 6} {8, 9, 10} {11, 13} [1/4, 1/4, 1/4, 3/4, 1/4] {4, 5, 10} {8, 9} {11, 13} [1/4, 1/4, 1/2, 1/4, 1] {6, 8} {5, 10, 11} {9, 14} [1/2, 1/2, 0, 1/2, 3/4] {5, 6, 8} {10, 11} {9, 14} [1/4, 1/4, 1/4, 1/2, 1] {8, 10} {5, 11} {9, 14} [1/4, 1/4, 1/4, 1/2, 3/4] {5, 8, 10} {11} {9, 14} [1/4, 1/4, 1/2, 1/4, 3/4] {5, 6, 8} {9, 10, 11} {13, 14} [1/4, 1/4, 1/4, 1/2, 1/2] {5, 8, 10} {9, 11} {13, 14} [1/4, 1/4, 1/2, 1/4, 1/4] {6, 8, 9} {10, 11, 13} {14, 15} [1/4, 1/4, 1/4, 1/2, 1/4] {8, 9, 10} {11, 13} {14, 15} [1/2, 1/2, 0, 1/2, 1/4] {6, 13} {10, 11} {14, 15} [1/4, 1/4, 3/8, 3/8, 1/8] {10, 13} {11} {14, 15} [1/2, 1/2, 0, 1/4, 1/4] {11, 13} {10, 15} {14} [1/4, 1/4, 3/8, 1/4, 1/8] {10, 11, 13} {15} {14} [1/4, 1/4, 1/4, 1/4, 1/4] {10, 11, 13} {14, 15} {17, 18} [1/4, 1/4, 1/4, 0, 1/2] {13, 14} {15, 17} {18} [1/4, 1/4, 1/8, 0, 5/8] {13, 17} {15} {18} [1/4, 1/4, 1/4, 0, 1/4] {14, 15} {17, 18} {19} [1/8, 1/8, 1/8, 0, 5/8] {15, 17} {18} {19} [0, 0, 1/2, 0, 1/4] {18} {17} {19} [0, 0, 7/16, 0, 1/4] {17, 18} {} {19} [0, 0, 1/4, 1/4, 1/4] {17, 18} {19} {20} [0, 0, 0, 1/4, 1/2] {19} {20} {} [0, 0, 0, 0, 0] {20} {} {} [3, 15, 25, 15, 1] 2 3 4 3 + 15 q + 34 q + 38 q + 17 q