## Sigma_2_3_7 f = (16,117,202,101), g_2 = 63. ## deg = 13,13,14,14,15,15,15,15,15,15,15,15,15,15,15,15 ## n_4,... = 0,0,0,0,0,0,0,0,0,2,2,12 facets:=[[1,2,3,4],[1,2,3,5],[1,2,4,6],[1,2,5,6],[1,3,4,7],[1,3,5,7], [1,4,6,8],[1,4,7,9],[1,4,8,9],[1,5,6,10],[1,5,7,11],[1,5,10,11], [1,6,8,12],[1,6,10,12],[1,7,9,13],[1,7,11,13],[1,8,9,12],[1,9,12,14], [1,9,13,14],[1,10,11,14],[1,10,12,14],[1,11,13,14],[2,3,4,11], [2,3,5,8],[2,3,8,11],[2,4,6,15],[2,4,11,12],[2,4,12,15],[2,5,6,9], [2,5,8,13],[2,5,9,13],[2,6,9,15],[2,7,8,13],[2,7,8,14],[2,7,9,10], [2,7,9,13],[2,7,10,14],[2,8,11,16],[2,8,14,16],[2,9,10,15], [2,10,12,14],[2,10,12,15],[2,11,12,16],[2,12,14,16],[3,4,7,10], [3,4,10,11],[3,5,7,12],[3,5,8,12],[3,6,9,11],[3,6,9,16],[3,6,11,13], [3,6,13,16],[3,7,10,14],[3,7,12,16],[3,7,14,15],[3,7,15,16],[3,8,9,11], [3,8,9,12],[3,9,12,16],[3,10,11,14],[3,11,13,14],[3,13,14,15], [3,13,15,16],[4,5,10,11],[4,5,10,16],[4,5,11,12],[4,5,12,13], [4,5,13,14],[4,5,14,16],[4,6,8,14],[4,6,14,15],[4,7,9,10],[4,8,9,10], [4,8,10,16],[4,8,14,16],[4,12,13,15],[4,13,14,15],[5,6,9,16], [5,6,10,16],[5,7,11,12],[5,8,12,13],[5,9,13,14],[5,9,14,16],[6,7,8,13], [6,7,8,14],[6,7,11,13],[6,7,11,15],[6,7,14,15],[6,8,12,13],[6,9,11,15], [6,10,12,13],[6,10,13,16],[7,11,12,16],[7,11,15,16],[8,9,10,15], [8,9,11,15],[8,10,15,16],[8,11,15,16],[9,12,14,16],[10,12,13,15], [10,13,15,16]]; ## Sigma_2_5_7 f = (18,138,240,120), g_2 = 76. ## deg = 12,14,14,14,14,15,15,16,16,16,16,16,16,16,16,16,17,17 ## n_4,... = 0,0,0,0,0,0,0,0,1,0,4,2,9,2 facets:=[[1,2,3,4],[1,2,3,5],[1,2,4,6],[1,2,5,6],[1,3,4,7],[1,3,5,8], [1,3,7,8],[1,4,6,9],[1,4,7,9],[1,5,6,10],[1,5,8,10],[1,6,9,11], [1,6,10,12],[1,6,11,12],[1,7,8,13],[1,7,9,11],[1,7,11,13],[1,8,10,12], [1,8,12,13],[1,11,12,13],[2,3,4,10],[2,3,5,12],[2,3,10,14],[2,3,12,14], [2,4,6,8],[2,4,8,15],[2,4,10,15],[2,5,6,13],[2,5,12,16],[2,5,13,16], [2,6,8,13],[2,7,9,11],[2,7,9,15],[2,7,10,14],[2,7,10,15],[2,7,11,14], [2,8,9,13],[2,8,9,15],[2,9,11,17],[2,9,13,17],[2,11,14,18], [2,11,17,18],[2,12,14,16],[2,13,16,18],[2,13,17,18],[2,14,16,18], [3,4,7,16],[3,4,10,16],[3,5,8,18],[3,5,12,18],[3,6,7,8],[3,6,7,16], [3,6,8,18],[3,6,9,17],[3,6,9,18],[3,6,16,17],[3,9,12,17],[3,9,12,18], [3,10,14,17],[3,10,16,17],[3,12,14,17],[4,5,7,9],[4,5,7,16],[4,5,9,14], [4,5,13,14],[4,5,13,16],[4,6,8,18],[4,6,9,18],[4,8,11,15],[4,8,11,18], [4,9,14,18],[4,10,13,15],[4,10,13,16],[4,11,13,14],[4,11,13,15], [4,11,14,18],[5,6,10,14],[5,6,13,14],[5,7,9,15],[5,7,12,16], [5,7,12,18],[5,7,15,18],[5,8,10,17],[5,8,17,18],[5,9,14,15], [5,10,14,17],[5,14,15,17],[5,15,17,18],[6,7,8,13],[6,7,10,12], [6,7,10,14],[6,7,12,16],[6,7,13,14],[6,9,11,17],[6,11,12,16], [6,11,16,17],[7,10,12,18],[7,10,15,18],[7,11,13,14],[8,9,10,12], [8,9,10,16],[8,9,12,13],[8,9,15,16],[8,10,16,17],[8,11,15,16], [8,11,16,17],[8,11,17,18],[9,10,12,18],[9,10,16,18],[9,12,13,17], [9,14,15,16],[9,14,16,18],[10,13,15,18],[10,13,16,18],[11,12,13,15], [11,12,15,16],[12,13,15,17],[12,14,15,16],[12,14,15,17],[13,15,17,18]]; ## Sigma_3_4_5 f = (18,139,242,121), g_2 = 77. ## deg = 13,13,13,14,15,15,15,16,16,16,16,16,16,16,17,17,17,17 ## n_4,... = 0,0,0,0,0,0,0,0,0,3,1,3,7,4 facets:=[[1,2,3,4],[1,2,3,5],[1,2,4,6],[1,2,5,6],[1,3,4,7],[1,3,5,7], [1,4,6,8],[1,4,7,8],[1,5,6,9],[1,5,7,10],[1,5,9,10],[1,6,8,11], [1,6,9,11],[1,7,8,12],[1,7,10,12],[1,8,11,12],[1,9,10,13],[1,9,11,13], [1,10,12,14],[1,10,13,14],[1,11,12,14],[1,11,13,14],[2,3,4,11], [2,3,5,8],[2,3,8,9],[2,3,9,14],[2,3,11,14],[2,4,6,15],[2,4,11,15], [2,5,6,16],[2,5,8,16],[2,6,13,15],[2,6,13,16],[2,7,9,12],[2,7,9,14], [2,7,12,15],[2,7,14,17],[2,7,15,17],[2,8,9,18],[2,8,13,16],[2,8,13,18], [2,9,12,18],[2,11,14,17],[2,11,15,17],[2,12,13,15],[2,12,13,18], [3,4,7,17],[3,4,11,12],[3,4,12,17],[3,5,7,13],[3,5,8,15],[3,5,13,15], [3,6,12,14],[3,6,12,18],[3,6,13,15],[3,6,13,16],[3,6,14,15], [3,6,16,18],[3,7,13,16],[3,7,16,18],[3,7,17,18],[3,8,9,15],[3,9,14,15], [3,11,12,14],[3,12,17,18],[4,5,9,17],[4,5,9,18],[4,5,12,16], [4,5,12,17],[4,5,16,18],[4,6,8,14],[4,6,14,15],[4,7,8,17],[4,8,9,17], [4,8,9,18],[4,8,14,18],[4,11,12,16],[4,11,15,16],[4,14,15,16], [4,14,16,18],[5,6,9,18],[5,6,16,18],[5,7,10,11],[5,7,11,13], [5,8,12,15],[5,8,12,16],[5,9,10,17],[5,10,11,17],[5,11,13,17], [5,12,13,15],[5,12,13,17],[6,7,9,11],[6,7,9,12],[6,7,10,11], [6,7,10,12],[6,8,10,11],[6,8,10,14],[6,9,12,18],[6,10,12,14], [7,8,12,15],[7,8,15,17],[7,9,11,13],[7,9,13,16],[7,9,14,16], [7,14,16,18],[7,14,17,18],[8,9,15,17],[8,10,11,16],[8,10,13,14], [8,10,13,16],[8,11,12,16],[8,13,14,18],[9,10,13,16],[9,10,15,16], [9,10,15,17],[9,14,15,16],[10,11,15,16],[10,11,15,17],[11,13,14,17], [12,13,17,18],[13,14,17,18]]; ## Sigma_3_4_7 f = (18,151,266,133), g_2 = 89. ## deg = 16,16,16,16,17,17,17,17,17,17,17,17,17,17,17,17,17,17 ## n_4,... = 0,0,0,0,0,0,0,0,0,0,0,0,4,14 facets:=[[1,2,3,4],[1,2,3,5],[1,2,4,6],[1,2,5,6],[1,3,4,7],[1,3,5,7], [1,4,6,8],[1,4,7,9],[1,4,8,9],[1,5,6,10],[1,5,7,11],[1,5,10,12], [1,5,11,12],[1,6,8,10],[1,7,9,13],[1,7,11,14],[1,7,13,14],[1,8,9,13], [1,8,10,15],[1,8,13,15],[1,10,12,15],[1,11,12,16],[1,11,14,16], [1,12,15,17],[1,12,16,17],[1,13,14,17],[1,13,15,17],[1,14,16,17], [2,3,4,13],[2,3,5,16],[2,3,13,16],[2,4,6,12],[2,4,12,18],[2,4,13,18], [2,5,6,15],[2,5,15,16],[2,6,9,12],[2,6,9,15],[2,7,8,16],[2,7,8,17], [2,7,11,14],[2,7,11,17],[2,7,13,14],[2,7,13,16],[2,8,10,15], [2,8,10,17],[2,8,15,16],[2,9,10,15],[2,9,10,17],[2,9,11,14], [2,9,11,17],[2,9,12,18],[2,9,14,18],[2,13,14,18],[3,4,7,10], [3,4,10,13],[3,5,7,8],[3,5,8,9],[3,5,9,16],[3,6,11,14],[3,6,11,17], [3,6,12,13],[3,6,12,14],[3,6,13,16],[3,6,16,17],[3,7,8,18],[3,7,10,15], [3,7,15,18],[3,8,9,18],[3,9,11,14],[3,9,11,17],[3,9,14,18],[3,9,16,17], [3,10,12,13],[3,10,12,15],[3,12,14,15],[3,14,15,18],[4,5,8,9], [4,5,8,14],[4,5,9,16],[4,5,14,15],[4,5,15,16],[4,6,8,14],[4,6,12,14], [4,7,9,10],[4,9,10,16],[4,10,11,16],[4,10,11,18],[4,10,13,18], [4,11,15,16],[4,11,15,17],[4,11,17,18],[4,12,14,15],[4,12,15,17], [4,12,17,18],[5,6,10,18],[5,6,15,18],[5,7,8,17],[5,7,11,17], [5,8,14,17],[5,10,12,13],[5,10,13,18],[5,11,12,13],[5,11,13,17], [5,13,14,17],[5,13,14,18],[5,14,15,18],[6,7,9,13],[6,7,9,15], [6,7,13,16],[6,7,15,18],[6,7,16,18],[6,8,10,14],[6,9,12,13], [6,10,11,14],[6,10,11,18],[6,11,17,18],[6,16,17,18],[7,8,16,18], [7,9,10,15],[8,9,12,13],[8,9,12,18],[8,10,14,17],[8,11,12,13], [8,11,12,16],[8,11,13,15],[8,11,15,16],[8,12,16,18],[9,10,16,17], [10,11,14,16],[10,14,16,17],[11,13,15,17],[12,16,17,18]]; ## Sigma_3_5_7 f = (20,171,302,151), g_2 = 101. ## deg = 14,15,15,16,16,16,16,17,17,17,18,18,18,18,18,18,18,19,19,19 ## n_4,... = 0,0,0,0,0,0,0,0,0,0,1,2,4,3,7,3 facets:=[[1,2,3,4],[1,2,3,5],[1,2,4,6],[1,2,5,6],[1,3,4,7],[1,3,5,7], [1,4,6,8],[1,4,7,9],[1,4,8,9],[1,5,6,10],[1,5,7,11],[1,5,10,11], [1,6,8,10],[1,7,9,12],[1,7,11,12],[1,8,9,13],[1,8,10,13],[1,9,12,13], [1,10,11,14],[1,10,13,15],[1,10,14,15],[1,11,12,16],[1,11,14,16], [1,12,13,17],[1,12,16,17],[1,13,15,17],[1,14,15,17],[1,14,16,17], [2,3,4,10],[2,3,5,13],[2,3,10,16],[2,3,13,18],[2,3,16,18],[2,4,6,12], [2,4,10,12],[2,5,6,13],[2,6,12,19],[2,6,13,18],[2,6,18,20],[2,6,19,20], [2,7,8,10],[2,7,8,11],[2,7,10,12],[2,7,11,12],[2,8,10,16],[2,8,11,17], [2,8,16,17],[2,9,16,17],[2,9,16,18],[2,9,17,19],[2,9,18,20], [2,9,19,20],[2,11,12,19],[2,11,17,19],[3,4,7,17],[3,4,10,17], [3,5,7,14],[3,5,12,13],[3,5,12,14],[3,6,10,16],[3,6,10,17],[3,6,11,15], [3,6,11,20],[3,6,15,17],[3,6,16,19],[3,6,19,20],[3,7,14,17], [3,9,11,13],[3,9,11,15],[3,9,12,13],[3,9,12,15],[3,11,13,20], [3,12,14,15],[3,13,18,19],[3,13,19,20],[3,14,15,17],[3,16,18,19], [4,5,12,14],[4,5,12,18],[4,5,14,20],[4,5,16,18],[4,5,16,20],[4,6,8,12], [4,7,9,17],[4,8,9,19],[4,8,12,18],[4,8,18,19],[4,9,17,19],[4,10,12,14], [4,10,14,20],[4,10,17,20],[4,11,16,19],[4,11,16,20],[4,11,17,19], [4,11,17,20],[4,16,18,19],[5,6,10,17],[5,6,13,17],[5,7,8,11], [5,7,8,14],[5,8,11,15],[5,8,14,20],[5,8,15,20],[5,9,10,11],[5,9,10,18], [5,9,11,15],[5,9,15,16],[5,9,16,18],[5,10,17,18],[5,12,13,17], [5,12,17,18],[5,15,16,20],[6,8,10,16],[6,8,12,16],[6,11,15,18], [6,11,18,20],[6,12,16,19],[6,13,15,17],[6,13,15,18],[7,8,10,13], [7,8,13,14],[7,9,12,15],[7,9,15,16],[7,9,16,17],[7,10,12,15], [7,10,13,15],[7,13,14,16],[7,13,15,16],[7,14,16,17],[8,9,13,14], [8,9,14,20],[8,9,19,20],[8,11,15,18],[8,11,17,18],[8,12,16,17], [8,12,17,18],[8,15,18,19],[8,15,19,20],[9,10,11,14],[9,10,14,20], [9,10,18,20],[9,11,13,14],[10,12,14,15],[10,17,18,20],[11,12,16,19], [11,13,14,16],[11,13,16,20],[11,17,18,20],[13,15,16,20],[13,15,18,19], [13,15,19,20]]; ## Sigma_4_5_7 f = (20,177,314,157), g_2 = 107. ## deg = 15,15,15,16,17,17,18,18,18,18,18,18,18,19,19,19,19,19,19,19 ## n_4,... = 0,0,0,0,0,0,0,0,0,0,0,3,1,2,7,7 facets:=[[1,2,3,4],[1,2,3,5],[1,2,4,6],[1,2,5,6],[1,3,4,7],[1,3,5,7], [1,4,6,8],[1,4,7,9],[1,4,8,9],[1,5,6,10],[1,5,7,11],[1,5,10,11], [1,6,8,12],[1,6,10,12],[1,7,9,13],[1,7,11,14],[1,7,13,14],[1,8,9,15], [1,8,12,15],[1,9,13,15],[1,10,11,16],[1,10,12,16],[1,11,14,16], [1,12,15,16],[1,13,14,15],[1,14,15,16],[2,3,4,10],[2,3,5,8],[2,3,8,10], [2,4,6,13],[2,4,10,13],[2,5,6,17],[2,5,8,9],[2,5,9,17],[2,6,13,16], [2,6,16,18],[2,6,17,18],[2,7,8,10],[2,7,8,11],[2,7,10,13],[2,7,11,14], [2,7,13,14],[2,8,9,11],[2,9,11,12],[2,9,12,19],[2,9,17,18],[2,9,18,19], [2,11,12,14],[2,12,14,20],[2,12,19,20],[2,13,14,20],[2,13,16,19], [2,13,19,20],[2,16,18,19],[3,4,7,19],[3,4,10,15],[3,4,15,19], [3,5,7,12],[3,5,8,13],[3,5,12,13],[3,6,9,19],[3,6,9,20],[3,6,15,17], [3,6,15,19],[3,6,17,20],[3,7,12,18],[3,7,18,19],[3,8,10,17], [3,8,13,17],[3,9,14,16],[3,9,14,18],[3,9,16,20],[3,9,18,19], [3,10,15,17],[3,11,12,13],[3,11,12,14],[3,11,13,20],[3,11,14,16], [3,11,16,20],[3,12,14,18],[3,13,17,20],[4,5,8,9],[4,5,8,13],[4,5,9,17], [4,5,12,13],[4,5,12,16],[4,5,14,18],[4,5,14,19],[4,5,16,18], [4,5,17,19],[4,6,8,13],[4,7,9,17],[4,7,17,19],[4,10,11,15], [4,10,11,16],[4,10,12,13],[4,10,12,16],[4,11,15,20],[4,11,16,20], [4,14,15,19],[4,14,15,20],[4,14,18,20],[4,16,18,20],[5,6,10,20], [5,6,17,20],[5,7,11,15],[5,7,12,15],[5,10,11,15],[5,10,14,18], [5,10,14,19],[5,10,15,18],[5,10,19,20],[5,12,15,16],[5,15,16,18], [5,17,19,20],[6,8,12,19],[6,8,13,16],[6,8,14,16],[6,8,14,19], [6,9,10,12],[6,9,10,20],[6,9,12,19],[6,14,15,16],[6,14,15,19], [6,15,16,18],[6,15,17,18],[7,8,10,20],[7,8,11,15],[7,8,12,15], [7,8,12,20],[7,9,10,13],[7,9,10,20],[7,9,16,17],[7,9,16,20], [7,12,18,20],[7,16,17,19],[7,16,18,19],[7,16,18,20],[8,9,11,15], [8,10,14,17],[8,10,14,19],[8,10,19,20],[8,12,19,20],[8,13,16,17], [8,14,16,17],[9,10,12,13],[9,11,12,13],[9,11,13,15],[9,14,16,17], [9,14,17,18],[10,14,17,18],[10,15,17,18],[11,13,15,20],[12,14,18,20], [13,14,15,20],[13,16,17,19],[13,17,19,20]];