## S^3 f = (5,10,10,5), g_2 = 0. ## deg = 4,4,4,4,4 ## n_4,... = 5 facets:=[[1,2,3,4],[1,2,3,5],[1,2,4,5],[1,3,4,5],[2,3,4,5]]; ## RP^3 f = (11,51,80,40), g_2 = 17. ## deg = 6,9,9,9,9,10,10,10,10,10,10 ## n_4,... = 0,0,1,0,0,4,6 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], [1,4,6,7],[1,5,6,7],[2,3,4,8],[2,3,5,9],[2,3,8,9],[2,4,6,10], [2,4,8,10],[2,5,6,11],[2,5,9,11],[2,6,10,11],[2,7,8,9],[2,7,8,10], [2,7,9,11],[2,7,10,11],[3,4,7,11],[3,4,8,11],[3,5,7,10],[3,5,9,10], [3,6,8,9],[3,6,8,11],[3,6,9,10],[3,6,10,11],[3,7,10,11],[4,5,8,10], [4,5,8,11],[4,5,9,10],[4,5,9,11],[4,6,7,9],[4,6,9,10],[4,7,9,11], [5,6,7,8],[5,6,8,11],[5,7,8,10],[6,7,8,9]]; ## L_3_1 f = (12,66,108,54), g_2 = 28. ## deg = 11,11,11,11,11,11,11,11,11,11,11,11 ## n_4,... = 0,0,0,0,0,0,0,12 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], [1,6,8,10],[1,7,9,11],[1,8,9,12],[1,8,10,12],[1,9,11,12],[1,10,11,12], [2,3,4,10],[2,3,5,9],[2,3,8,10],[2,3,8,11],[2,3,9,11],[2,4,6,12], [2,4,10,12],[2,5,6,9],[2,6,7,9],[2,6,7,12],[2,7,8,11],[2,7,8,12], [2,7,9,11],[2,8,10,12],[3,4,7,10],[3,5,7,12],[3,5,9,12],[3,6,7,10], [3,6,7,12],[3,6,8,10],[3,6,8,11],[3,6,11,12],[3,9,11,12],[4,5,8,9], [4,5,8,11],[4,5,9,10],[4,5,10,11],[4,6,8,11],[4,6,11,12],[4,7,9,10], [4,10,11,12],[5,6,9,10],[5,7,8,11],[5,7,8,12],[5,8,9,12],[6,7,9,10]]; ## L_4_1 f = (14,84,140,70), g_2 = 38. ## deg = 11,11,11,12,12,12,12,12,12,12,12,13,13,13 ## n_4,... = 0,0,0,0,0,0,0,3,8,3 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],[1,7,9,11],[1,8,9,12],[1,8,10,12],[1,9,11,12],[1,10,11,12], [2,3,4,10],[2,3,5,9],[2,3,9,10],[2,4,6,11],[2,4,10,11],[2,5,6,13], [2,5,9,14],[2,5,13,14],[2,6,11,12],[2,6,12,13],[2,9,10,14], [2,10,11,12],[2,10,12,14],[2,12,13,14],[3,4,7,14],[3,4,10,13], [3,4,13,14],[3,5,7,12],[3,5,9,12],[3,6,7,12],[3,6,7,14],[3,6,8,11], [3,6,8,14],[3,6,11,12],[3,8,11,13],[3,8,13,14],[3,9,10,13],[3,9,11,12], [3,9,11,13],[4,5,8,9],[4,5,8,11],[4,5,9,14],[4,5,10,11],[4,5,10,13], [4,5,13,14],[4,6,8,11],[4,7,9,14],[5,6,10,13],[5,7,8,11],[5,7,8,12], [5,8,9,12],[6,7,10,13],[6,7,10,14],[6,7,12,13],[6,8,10,14],[7,8,11,13], [7,8,12,13],[7,9,10,13],[7,9,10,14],[7,9,11,13],[8,10,12,14], [8,12,13,14]]; ## L_5_1 f = (15,97,164,82), g_2 = 47. ## deg = 11,12,12,13,13,13,13,13,13,13,13,13,14,14,14 ## n_4,... = 0,0,0,0,0,0,0,1,2,9,3 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],[1,5,10,12], [1,5,11,12],[1,6,8,10],[1,7,9,11],[1,8,9,13],[1,8,10,13],[1,9,11,14], [1,9,13,14],[1,10,12,13],[1,11,12,14],[1,12,13,14],[2,3,4,10], [2,3,5,9],[2,3,9,12],[2,3,10,11],[2,3,11,12],[2,4,6,13],[2,4,10,13], [2,5,6,15],[2,5,9,15],[2,6,13,15],[2,8,10,13],[2,8,10,14],[2,8,13,15], [2,8,14,15],[2,9,12,15],[2,10,11,14],[2,11,12,14],[2,12,14,15], [3,4,7,15],[3,4,10,15],[3,5,7,14],[3,5,9,14],[3,6,8,12],[3,6,8,14], [3,6,9,12],[3,6,9,14],[3,7,14,15],[3,8,11,12],[3,8,11,15],[3,8,14,15], [3,10,11,15],[4,5,8,9],[4,5,8,12],[4,5,9,15],[4,5,10,12],[4,5,10,15], [4,6,8,12],[4,6,12,13],[4,7,9,15],[4,10,12,13],[5,6,10,15],[5,7,11,13], [5,7,13,14],[5,8,9,13],[5,8,11,12],[5,8,11,13],[5,9,13,14],[6,7,9,11], [6,7,9,12],[6,7,11,13],[6,7,12,13],[6,8,10,14],[6,9,11,14], [6,10,11,14],[6,10,11,15],[6,11,13,15],[7,9,12,15],[7,12,13,14], [7,12,14,15],[8,11,13,15]]; ## L_5_2 f = (14,86,144,72), g_2 = 40. ## deg = 11,11,11,11,12,12,13,13,13,13,13,13,13,13 ## n_4,... = 0,0,0,0,0,0,0,4,2,8 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],[1,7,9,11],[1,8,9,12],[1,8,10,12],[1,9,11,12], [2,3,4,13],[2,3,5,8],[2,3,8,10],[2,3,10,11],[2,3,11,13],[2,4,6,14], [2,4,13,14],[2,5,6,9],[2,5,8,9],[2,6,7,12],[2,6,7,14],[2,6,9,12], [2,7,10,11],[2,7,10,12],[2,7,11,13],[2,7,13,14],[2,8,9,12],[2,8,10,12], [3,4,7,12],[3,4,12,13],[3,5,7,8],[3,6,7,12],[3,6,7,14],[3,6,11,13], [3,6,11,14],[3,6,12,13],[3,7,8,14],[3,8,10,14],[3,10,11,14],[4,5,8,9], [4,5,8,11],[4,5,9,10],[4,5,10,12],[4,5,11,12],[4,6,8,11],[4,6,11,14], [4,7,9,10],[4,7,10,12],[4,11,12,14],[4,12,13,14],[5,6,9,10],[5,7,8,11], [6,8,10,13],[6,8,11,13],[6,9,10,13],[6,9,12,13],[7,8,11,13], [7,8,13,14],[7,9,10,11],[8,10,13,14],[9,10,11,14],[9,10,13,14], [9,11,12,14],[9,12,13,14]]; ## L_6_1 f = (16,110,188,94), g_2 = 56. ## deg = 9,13,13,13,13,14,14,14,14,14,14,15,15,15,15,15 ## n_4,... = 0,0,0,0,0,1,0,0,0,4,6,5 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],[1,7,9,11],[1,8,9,13],[1,8,10,13],[1,9,11,14], [1,9,13,15],[1,9,14,15],[1,10,12,16],[1,10,13,16],[1,11,12,14], [1,12,14,16],[1,13,15,16],[1,14,15,16],[2,3,4,11],[2,3,5,8],[2,3,8,11], [2,4,6,16],[2,4,11,16],[2,5,6,9],[2,5,8,9],[2,6,9,16],[2,8,9,16], [2,8,11,16],[3,4,7,13],[3,4,11,13],[3,5,7,14],[3,5,8,15],[3,5,14,15], [3,6,7,13],[3,6,7,14],[3,6,9,14],[3,6,9,16],[3,6,13,16],[3,8,11,15], [3,9,12,15],[3,9,12,16],[3,9,14,15],[3,10,11,13],[3,10,11,15], [3,10,12,15],[3,10,12,16],[3,10,13,16],[4,5,8,9],[4,5,8,15],[4,5,9,10], [4,5,10,12],[4,5,11,12],[4,5,11,16],[4,5,15,16],[4,6,8,15],[4,6,15,16], [4,7,9,10],[4,7,10,12],[4,7,12,13],[4,11,12,13],[5,6,9,10],[5,7,11,16], [5,7,14,16],[5,14,15,16],[6,7,8,14],[6,7,8,15],[6,7,13,15],[6,8,10,14], [6,9,10,14],[6,13,15,16],[7,8,11,15],[7,8,11,16],[7,8,14,16], [7,9,10,11],[7,10,11,15],[7,10,12,15],[7,12,13,15],[8,9,12,13], [8,9,12,16],[8,10,13,14],[8,12,13,14],[8,12,14,16],[9,10,11,14], [9,12,13,15],[10,11,13,14],[11,12,13,14]]; ## L_7_1 f = (17,123,212,106), g_2 = 65. ## deg = 12,13,13,14,14,14,14,14,15,15,15,15,15,15,16,16,16 ## n_4,... = 0,0,0,0,0,0,0,0,1,2,5,6,3 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],[1,7,11,13],[1,7,12,13],[1,8,9,14],[1,8,10,14], [1,9,12,14],[1,10,11,15],[1,10,14,15],[1,11,13,15],[1,12,13,15], [1,12,14,15],[2,3,4,10],[2,3,5,9],[2,3,9,10],[2,4,6,16],[2,4,10,16], [2,5,6,12],[2,5,9,12],[2,6,7,11],[2,6,7,16],[2,6,11,12],[2,7,8,10], [2,7,8,11],[2,7,10,16],[2,8,10,17],[2,8,11,17],[2,9,10,17],[2,9,12,17], [2,11,12,17],[3,4,7,14],[3,4,10,12],[3,4,12,13],[3,4,13,14],[3,5,7,8], [3,5,8,15],[3,5,9,16],[3,5,15,17],[3,5,16,17],[3,6,9,10],[3,6,9,11], [3,6,10,12],[3,6,11,12],[3,7,8,14],[3,8,13,14],[3,8,13,15],[3,9,11,16], [3,11,12,17],[3,11,16,17],[3,12,13,15],[3,12,15,17],[4,5,8,11], [4,5,8,15],[4,5,10,11],[4,5,10,12],[4,5,12,13],[4,5,13,14],[4,5,14,15], [4,6,8,16],[4,7,9,15],[4,7,14,15],[4,8,9,15],[4,8,11,16],[4,10,11,16], [5,6,10,12],[5,7,8,11],[5,9,12,16],[5,12,13,16],[5,13,14,17], [5,13,16,17],[5,14,15,17],[6,7,11,13],[6,7,13,16],[6,8,10,17], [6,8,16,17],[6,9,10,17],[6,9,11,13],[6,9,13,17],[6,13,16,17], [7,8,10,14],[7,9,12,16],[7,9,15,16],[7,10,14,15],[7,10,15,16], [7,12,13,16],[8,9,13,14],[8,9,13,15],[8,11,16,17],[9,11,13,15], [9,11,15,16],[9,12,14,17],[9,13,14,17],[10,11,15,16],[12,14,15,17]]; ## L_7_2 f = (16,104,176,88), g_2 = 50. ## deg = 10,11,11,11,12,12,12,13,13,14,14,15,15,15,15,15 ## n_4,... = 0,0,0,0,0,0,1,3,3,2,2,5 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],[1,5,9,11],[1,5,10,11], [1,6,8,9],[1,7,8,12],[1,7,10,12],[1,8,9,13],[1,8,12,13],[1,9,11,13], [1,10,11,14],[1,10,12,14],[1,11,13,14],[1,12,13,14],[2,3,4,9], [2,3,5,14],[2,3,9,14],[2,4,6,11],[2,4,9,11],[2,5,6,15],[2,5,14,16], [2,5,15,16],[2,6,7,11],[2,6,7,15],[2,7,9,11],[2,7,9,12],[2,7,12,15], [2,9,12,16],[2,9,14,16],[2,12,15,16],[3,4,7,16],[3,4,9,15],[3,4,15,16], [3,5,7,13],[3,5,13,14],[3,7,11,13],[3,7,11,16],[3,9,14,15], [3,11,13,14],[3,11,14,15],[3,11,15,16],[4,5,9,11],[4,5,9,15], [4,5,11,12],[4,5,12,14],[4,5,14,16],[4,5,15,16],[4,6,8,10],[4,6,10,12], [4,6,11,12],[4,7,8,14],[4,7,14,16],[4,8,10,14],[4,10,12,14],[5,6,9,15], [5,7,10,13],[5,8,10,11],[5,8,10,13],[5,8,11,12],[5,8,12,13], [5,12,13,14],[6,7,11,16],[6,7,14,15],[6,7,14,16],[6,8,9,10], [6,9,10,12],[6,9,12,16],[6,9,14,15],[6,9,14,16],[6,11,12,16], [7,8,12,15],[7,8,14,15],[7,9,10,12],[7,9,10,13],[7,9,11,13], [8,9,10,13],[8,10,11,14],[8,11,12,15],[8,11,14,15],[11,12,15,16]]; ## L_8_1 f = (17,130,226,113), g_2 = 72. ## deg = 13,14,14,15,15,15,15,15,16,16,16,16,16,16,16,16,16 ## n_4,... = 0,0,0,0,0,0,0,0,0,1,2,5,9 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],[1,8,10,14],[1,8,13,14], [1,9,12,13],[1,10,11,15],[1,10,14,15],[1,11,12,16],[1,11,15,16], [1,12,13,16],[1,13,14,15],[1,13,15,16],[2,3,4,14],[2,3,5,15], [2,3,9,12],[2,3,9,14],[2,3,12,15],[2,4,6,14],[2,5,6,15],[2,6,11,15], [2,6,11,17],[2,6,14,17],[2,8,9,13],[2,8,9,17],[2,8,11,13],[2,8,11,17], [2,9,12,13],[2,9,14,17],[2,10,11,13],[2,10,11,15],[2,10,12,13], [2,10,12,15],[3,4,7,10],[3,4,10,17],[3,4,11,14],[3,4,11,17],[3,5,7,16], [3,5,8,15],[3,5,8,16],[3,6,8,12],[3,6,8,16],[3,6,9,11],[3,6,9,12], [3,6,11,17],[3,6,13,16],[3,6,13,17],[3,7,10,16],[3,8,12,15], [3,9,11,14],[3,10,13,16],[3,10,13,17],[4,5,8,9],[4,5,8,16],[4,5,9,10], [4,5,10,17],[4,5,16,17],[4,6,8,16],[4,6,13,14],[4,6,13,16],[4,7,9,10], [4,11,12,14],[4,11,12,17],[4,12,14,15],[4,12,15,17],[4,13,14,15], [4,13,15,16],[4,15,16,17],[5,6,9,10],[5,6,9,15],[5,7,11,13], [5,7,13,14],[5,7,14,16],[5,8,9,15],[5,10,11,13],[5,10,13,17], [5,13,14,17],[5,14,16,17],[6,7,8,10],[6,7,8,12],[6,7,9,10],[6,7,9,12], [6,9,11,15],[6,13,14,17],[7,8,10,14],[7,8,11,12],[7,8,11,13], [7,8,13,14],[7,10,14,16],[8,9,15,17],[8,11,12,17],[8,12,15,17], [9,11,14,16],[9,11,15,16],[9,14,16,17],[9,15,16,17],[10,12,13,16], [10,12,14,15],[10,12,14,16],[11,12,14,16]]; ## L_8_3 f = (16,106,180,90), g_2 = 52. ## deg = 11,11,12,13,13,13,13,13,14,14,14,14,14,14,14,15 ## n_4,... = 0,0,0,0,0,0,0,2,1,5,7,1 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],[1,7,9,11],[1,8,9,12],[1,8,10,12],[1,9,11,12], [2,3,4,13],[2,3,5,8],[2,3,8,10],[2,3,10,14],[2,3,13,14],[2,4,6,15], [2,4,13,15],[2,5,6,9],[2,5,8,9],[2,6,7,12],[2,6,7,15],[2,6,9,12], [2,7,10,12],[2,7,10,14],[2,7,13,14],[2,7,13,15],[2,8,9,12],[2,8,10,12], [3,4,7,12],[3,4,12,13],[3,5,7,15],[3,5,8,15],[3,6,7,12],[3,6,7,15], [3,6,11,15],[3,6,11,16],[3,6,12,13],[3,6,13,14],[3,6,14,16], [3,8,10,11],[3,8,11,15],[3,10,11,16],[3,10,14,16],[4,5,8,9],[4,5,8,16], [4,5,9,10],[4,5,10,12],[4,5,11,12],[4,5,11,16],[4,6,8,16],[4,6,11,15], [4,6,11,16],[4,7,9,10],[4,7,10,12],[4,11,12,15],[4,12,13,15], [5,6,9,10],[5,7,11,16],[5,7,15,16],[5,8,15,16],[6,8,10,13],[6,8,13,14], [6,8,14,16],[6,9,10,13],[6,9,12,13],[7,9,10,14],[7,9,11,14], [7,11,13,14],[7,11,13,16],[7,13,15,16],[8,10,11,13],[8,11,13,14], [8,11,14,15],[8,14,15,16],[9,10,13,16],[9,10,14,16],[9,11,12,15], [9,11,14,15],[9,12,13,15],[9,13,15,16],[9,14,15,16],[10,11,13,16]]; ## L_9_1 f = (18,143,250,125), g_2 = 81. ## deg = 14,15,15,15,15,15,15,16,16,16,16,16,17,17,17,17,17,17 ## n_4,... = 0,0,0,0,0,0,0,0,0,0,1,6,5,6 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],[1,6,10,13],[1,6,12,13],[1,7,9,14],[1,7,11,15],[1,7,14,16], [1,7,15,16],[1,8,9,14],[1,8,12,14],[1,10,11,17],[1,10,13,18], [1,10,17,18],[1,11,15,17],[1,12,13,18],[1,12,14,16],[1,12,15,16], [1,12,15,18],[1,15,17,18],[2,3,4,15],[2,3,5,17],[2,3,13,15], [2,3,13,17],[2,4,6,11],[2,4,10,11],[2,4,10,15],[2,5,6,14],[2,5,9,14], [2,5,9,17],[2,6,11,14],[2,8,9,14],[2,8,9,16],[2,8,13,15],[2,8,13,16], [2,8,14,18],[2,8,15,18],[2,9,16,17],[2,10,11,12],[2,10,12,15], [2,11,12,18],[2,11,14,18],[2,12,15,18],[2,13,16,17],[3,4,7,12], [3,4,12,14],[3,4,14,15],[3,5,7,8],[3,5,8,17],[3,6,9,13],[3,6,9,18], [3,6,13,17],[3,6,17,18],[3,7,8,12],[3,8,12,14],[3,8,14,18],[3,8,17,18], [3,9,11,15],[3,9,11,18],[3,9,13,15],[3,11,14,15],[3,11,14,18], [4,5,8,11],[4,5,8,13],[4,5,10,11],[4,5,10,14],[4,5,13,14],[4,6,8,11], [4,7,9,12],[4,8,9,16],[4,8,13,16],[4,9,12,16],[4,10,14,15], [4,12,14,16],[4,13,14,16],[5,6,10,14],[5,7,8,11],[5,8,13,15], [5,8,15,17],[5,9,13,14],[5,9,13,15],[5,9,15,17],[6,7,8,11],[6,7,8,12], [6,7,11,15],[6,7,12,17],[6,7,15,16],[6,7,16,18],[6,7,17,18], [6,9,10,13],[6,9,10,16],[6,9,16,18],[6,10,14,15],[6,10,15,16], [6,11,14,15],[6,12,13,17],[7,9,10,12],[7,9,10,13],[7,9,13,14], [7,10,12,17],[7,10,13,18],[7,10,17,18],[7,13,14,16],[7,13,16,18], [8,15,17,18],[9,10,12,16],[9,11,15,17],[9,11,16,17],[9,11,16,18], [10,11,12,17],[10,12,15,16],[11,12,13,17],[11,12,13,18],[11,13,16,17], [11,13,16,18]]; ## L_9_2 f = (16,114,196,98), g_2 = 60. ## deg = 12,13,14,14,14,14,14,14,14,15,15,15,15,15,15,15 ## n_4,... = 0,0,0,0,0,0,0,0,1,1,7,7 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],[1,4,7,8],[1,5,6,9],[1,5,7,10],[1,5,9,10],[1,6,8,11], [1,6,9,11],[1,7,8,12],[1,7,10,13],[1,7,12,13],[1,8,11,12],[1,9,10,13], [1,9,11,14],[1,9,13,14],[1,11,12,14],[1,12,13,14],[2,3,4,11],[2,3,5,8], [2,3,8,10],[2,3,10,12],[2,3,11,12],[2,4,6,14],[2,4,11,13],[2,4,13,14], [2,5,6,15],[2,5,8,15],[2,6,14,15],[2,7,9,14],[2,7,9,16],[2,7,14,15], [2,7,15,16],[2,8,10,15],[2,9,13,14],[2,9,13,16],[2,10,12,16], [2,10,15,16],[2,11,12,16],[2,11,13,16],[3,4,7,15],[3,4,11,15], [3,5,7,14],[3,5,8,14],[3,6,8,10],[3,6,8,14],[3,6,10,13],[3,6,13,15], [3,6,14,15],[3,7,14,15],[3,9,10,12],[3,9,10,13],[3,9,12,15], [3,9,13,15],[3,11,12,15],[4,5,10,11],[4,5,10,12],[4,5,11,13], [4,5,12,13],[4,6,8,14],[4,7,8,16],[4,7,15,16],[4,8,14,16],[4,10,11,15], [4,10,12,16],[4,10,15,16],[4,12,13,14],[4,12,14,16],[5,6,9,12], [5,6,12,13],[5,6,13,15],[5,7,10,11],[5,7,11,14],[5,8,13,15], [5,8,13,16],[5,8,14,16],[5,9,10,12],[5,11,13,16],[5,11,14,16], [6,7,9,11],[6,7,9,12],[6,7,10,11],[6,7,10,13],[6,7,12,13],[6,8,10,11], [7,8,9,12],[7,8,9,16],[7,9,11,14],[8,9,12,15],[8,9,13,15],[8,9,13,16], [8,10,11,15],[8,11,12,15],[11,12,14,16]]; ## L_10_1 f = (19,155,272,136), g_2 = 89. ## deg = 7,15,15,15,15,16,17,17,17,17,17,17,17,18,18,18,18,18,18 ## n_4,... = 0,0,0,1,0,0,0,0,0,0,0,4,1,7,6 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],[1,5,6,8],[1,5,7,8],[2,3,4,9],[2,3,5,10], [2,3,9,10],[2,4,6,11],[2,4,9,11],[2,5,6,12],[2,5,10,12],[2,6,11,13], [2,6,12,14],[2,6,13,14],[2,7,9,10],[2,7,9,11],[2,7,10,15],[2,7,11,16], [2,7,15,16],[2,8,13,14],[2,8,13,17],[2,8,14,18],[2,8,15,17], [2,8,15,18],[2,10,12,15],[2,11,13,16],[2,12,14,18],[2,12,15,18], [2,13,16,17],[2,15,16,17],[3,4,7,16],[3,4,9,16],[3,5,7,19],[3,5,10,18], [3,5,15,18],[3,5,15,19],[3,6,11,13],[3,6,11,19],[3,6,13,15], [3,6,15,19],[3,7,16,19],[3,8,9,16],[3,8,9,17],[3,8,11,17],[3,8,11,19], [3,8,16,19],[3,9,10,18],[3,9,17,18],[3,11,12,13],[3,11,12,14], [3,11,14,17],[3,12,13,15],[3,12,14,18],[3,12,15,18],[3,14,17,18], [4,5,9,11],[4,5,9,16],[4,5,10,11],[4,5,10,12],[4,5,12,17],[4,5,16,17], [4,6,8,10],[4,6,10,11],[4,7,8,18],[4,7,13,15],[4,7,13,18],[4,7,15,16], [4,8,10,12],[4,8,12,19],[4,8,18,19],[4,12,17,19],[4,13,14,15], [4,13,14,19],[4,13,18,19],[4,14,15,17],[4,14,17,19],[4,15,16,17], [5,6,8,16],[5,6,12,17],[5,6,16,17],[5,7,8,14],[5,7,14,19],[5,8,9,13], [5,8,9,16],[5,8,13,14],[5,9,11,15],[5,9,13,19],[5,9,15,19], [5,10,11,18],[5,11,15,18],[5,13,14,19],[6,7,9,10],[6,7,9,12], [6,7,10,17],[6,7,12,17],[6,8,10,16],[6,9,10,18],[6,9,12,14], [6,9,14,15],[6,9,15,19],[6,9,18,19],[6,10,11,18],[6,10,16,17], [6,11,18,19],[6,13,14,15],[7,8,14,18],[7,9,11,12],[7,10,13,15], [7,10,13,17],[7,11,12,16],[7,12,16,19],[7,12,17,19],[7,13,17,18], [7,14,17,18],[7,14,17,19],[8,9,13,17],[8,10,12,16],[8,11,15,17], [8,11,15,18],[8,11,18,19],[8,12,16,19],[9,11,12,14],[9,11,14,15], [9,13,17,18],[9,13,18,19],[10,12,13,15],[10,12,13,16],[10,13,16,17], [11,12,13,16],[11,14,15,17]]; ## L_10_3 f = (17,118,202,101), g_2 = 60. ## deg = 11,11,12,12,13,13,13,13,14,15,15,15,15,16,16,16,16 ## n_4,... = 0,0,0,0,0,0,0,2,2,4,1,4,4 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],[1,4,7,9],[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],[1,8,9,15], [1,8,10,15],[1,9,13,16],[1,9,15,16],[1,10,12,15],[1,11,12,14], [1,12,14,16],[1,12,15,16],[1,13,14,16],[2,3,4,11],[2,3,5,16], [2,3,11,16],[2,4,6,17],[2,4,11,17],[2,5,6,9],[2,5,9,16],[2,6,9,13], [2,6,13,15],[2,6,15,17],[2,8,11,16],[2,8,11,17],[2,8,13,15], [2,8,13,16],[2,8,15,17],[2,9,13,16],[3,4,7,15],[3,4,11,15],[3,5,7,8], [3,5,8,17],[3,5,16,17],[3,6,7,8],[3,6,7,15],[3,6,8,10],[3,6,10,11], [3,6,11,15],[3,8,10,17],[3,10,11,16],[3,10,16,17],[4,5,11,15], [4,5,11,17],[4,5,15,16],[4,5,16,17],[4,6,8,16],[4,6,16,17],[4,7,9,12], [4,7,12,15],[4,8,9,14],[4,8,14,16],[4,9,12,14],[4,12,14,16], [4,12,15,16],[5,6,9,14],[5,6,10,14],[5,7,8,11],[5,8,11,17],[5,9,14,15], [5,9,15,16],[5,10,12,13],[5,10,13,14],[5,11,12,13],[5,11,13,15], [5,13,14,15],[6,7,8,16],[6,7,15,17],[6,7,16,17],[6,9,11,13], [6,9,11,14],[6,10,11,14],[6,11,13,15],[7,8,11,16],[7,9,12,13], [7,10,11,14],[7,10,11,16],[7,10,12,13],[7,10,12,15],[7,10,13,14], [7,10,15,17],[7,10,16,17],[8,9,14,15],[8,10,15,17],[8,13,14,15], [8,13,14,16],[9,11,12,13],[9,11,12,14]]; ## cube_space f = (15,90,150,75), g_2 = 40. ## deg = 12,12,12,12,12,12,12,12,12,12,12,12,12,12,12 ## n_4,... = 0,0,0,0,0,0,0,0,15 facets:=[[1,2,3,4],[1,2,3,5],[1,2,4,6],[1,2,5,7],[1,2,6,7],[1,3,4,8], [1,3,5,9],[1,3,8,9],[1,4,6,10],[1,4,8,10],[1,5,7,11],[1,5,9,11], [1,6,7,12],[1,6,10,12],[1,7,11,12],[1,8,9,13],[1,8,10,13],[1,9,11,13], [1,10,12,13],[1,11,12,13],[2,3,4,11],[2,3,5,14],[2,3,11,14],[2,4,6,13], [2,4,11,13],[2,5,7,8],[2,5,8,14],[2,6,7,15],[2,6,13,15],[2,7,8,15], [2,8,12,14],[2,8,12,15],[2,11,12,13],[2,11,12,14],[2,12,13,15], [3,4,8,15],[3,4,11,15],[3,5,6,9],[3,5,6,14],[3,6,9,12],[3,6,10,12], [3,6,10,14],[3,8,9,12],[3,8,12,15],[3,10,11,14],[3,10,11,15], [3,10,12,15],[4,6,10,14],[4,6,13,14],[4,7,8,10],[4,7,8,15],[4,7,9,14], [4,7,9,15],[4,7,10,14],[4,9,11,13],[4,9,11,15],[4,9,13,14],[5,6,9,15], [5,6,13,14],[5,6,13,15],[5,7,8,10],[5,7,10,11],[5,8,10,13],[5,8,13,14], [5,9,11,15],[5,10,11,15],[5,10,13,15],[6,7,9,12],[6,7,9,15], [7,9,12,14],[7,10,11,14],[7,11,12,14],[8,9,12,14],[8,9,13,14], [10,12,13,15]]; ## P_3 f = (15,97,164,82), g_2 = 47. ## deg = 10,11,12,12,12,12,13,14,14,14,14,14,14,14,14 ## n_4,... = 0,0,0,0,0,0,1,1,4,1,8 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], [1,10,11,13],[1,11,12,13],[2,3,4,11],[2,3,5,9],[2,3,9,11],[2,4,6,13], [2,4,11,13],[2,5,6,14],[2,5,9,14],[2,6,13,14],[2,9,10,11],[2,9,10,14], [2,10,11,13],[2,10,13,14],[3,4,7,10],[3,4,10,14],[3,4,11,14], [3,5,7,13],[3,5,9,13],[3,6,8,10],[3,6,8,11],[3,6,9,11],[3,6,9,12], [3,6,10,12],[3,7,10,15],[3,7,13,15],[3,8,10,14],[3,8,11,14], [3,9,12,13],[3,10,12,15],[3,12,13,15],[4,5,8,9],[4,5,8,15],[4,5,9,14], [4,5,12,14],[4,5,12,15],[4,6,8,15],[4,6,13,15],[4,7,9,10],[4,9,10,14], [4,11,12,13],[4,11,12,14],[4,12,13,15],[5,6,10,12],[5,6,12,14], [5,7,8,11],[5,7,8,13],[5,8,9,13],[5,8,11,15],[5,10,11,15],[5,10,12,15], [6,7,9,12],[6,7,9,15],[6,7,12,14],[6,7,13,14],[6,7,13,15],[6,8,11,15], [6,9,11,15],[7,8,11,14],[7,8,13,14],[7,9,10,15],[7,11,12,14], [8,10,13,14],[9,10,11,15]]; ## P_4 f = (15,104,178,89), g_2 = 54. ## deg = 13,13,14,14,14,14,14,14,14,14,14,14,14,14,14 ## n_4,... = 0,0,0,0,0,0,0,0,0,2,13 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],[1,9,12,14], [1,9,13,14],[1,10,11,15],[1,10,13,14],[1,10,14,15],[1,11,12,15], [1,12,14,15],[2,3,4,14],[2,3,5,14],[2,4,6,12],[2,4,12,13],[2,4,13,14], [2,5,6,15],[2,5,8,14],[2,5,8,15],[2,6,12,15],[2,7,8,11],[2,7,8,14], [2,7,10,12],[2,7,10,14],[2,7,11,12],[2,8,11,15],[2,10,12,13], [2,10,13,14],[2,11,12,15],[3,4,7,15],[3,4,11,14],[3,4,11,15], [3,5,7,13],[3,5,12,13],[3,5,12,14],[3,6,8,10],[3,6,8,11],[3,6,9,10], [3,6,9,11],[3,7,13,15],[3,8,10,13],[3,8,11,15],[3,8,13,15],[3,9,10,12], [3,9,11,14],[3,9,12,14],[3,10,12,13],[4,5,8,9],[4,5,8,12],[4,5,9,10], [4,5,10,11],[4,5,11,13],[4,5,12,13],[4,6,8,12],[4,7,9,10],[4,7,10,15], [4,10,11,15],[4,11,13,14],[5,6,9,10],[5,6,9,15],[5,7,11,13],[5,8,9,15], [5,8,12,14],[6,7,8,11],[6,7,8,14],[6,7,11,13],[6,7,13,15],[6,7,14,15], [6,8,12,14],[6,9,11,13],[6,9,13,15],[6,12,14,15],[7,9,10,12], [7,10,14,15],[8,9,13,15],[9,11,13,14]]; ## P_5 f = (17,122,210,105), g_2 = 64. ## deg = 7,13,13,13,14,15,15,15,15,15,15,15,15,16,16,16,16 ## n_4,... = 0,0,0,1,0,0,0,0,0,3,1,8,4 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],[1,5,6,8],[1,5,7,8],[2,3,4,9],[2,3,5,9],[2,4,6,10], [2,4,9,11],[2,4,10,11],[2,5,6,12],[2,5,9,13],[2,5,12,13],[2,6,7,10], [2,6,7,14],[2,6,12,15],[2,6,14,15],[2,7,8,14],[2,7,8,16],[2,7,10,16], [2,8,14,17],[2,8,16,17],[2,9,11,13],[2,10,11,16],[2,11,13,16], [2,12,13,15],[2,13,15,17],[2,13,16,17],[2,14,15,17],[3,4,7,17], [3,4,9,16],[3,4,16,17],[3,5,7,15],[3,5,9,10],[3,5,10,11],[3,5,11,15], [3,6,8,11],[3,6,8,13],[3,6,9,12],[3,6,9,16],[3,6,11,12],[3,6,13,16], [3,7,15,17],[3,8,11,15],[3,8,13,15],[3,9,10,14],[3,9,12,14], [3,10,11,14],[3,11,12,14],[3,13,15,17],[3,13,16,17],[4,5,10,11], [4,5,10,13],[4,5,11,15],[4,5,12,13],[4,5,12,17],[4,5,15,16], [4,5,16,17],[4,6,8,13],[4,6,10,13],[4,7,8,12],[4,7,12,17],[4,8,12,13], [4,9,11,15],[4,9,15,16],[5,6,8,17],[5,6,12,17],[5,7,8,16],[5,7,15,16], [5,8,16,17],[5,9,10,13],[6,7,10,13],[6,7,13,14],[6,8,11,17], [6,9,12,15],[6,9,15,16],[6,11,12,17],[6,13,14,16],[6,14,15,16], [7,8,12,14],[7,9,10,13],[7,9,10,17],[7,9,11,13],[7,9,11,17], [7,10,15,16],[7,10,15,17],[7,11,12,14],[7,11,12,17],[7,11,13,14], [8,9,11,15],[8,9,11,17],[8,9,12,14],[8,9,12,15],[8,9,14,17], [8,12,13,15],[9,10,14,17],[10,11,14,16],[10,14,15,16],[10,14,15,17], [11,13,14,16]]; ## P_6 f = (17,130,226,113), g_2 = 72. ## deg = 13,14,14,15,15,15,15,15,16,16,16,16,16,16,16,16,16 ## n_4,... = 0,0,0,0,0,0,0,0,0,1,2,5,9 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],[1,7,11,13],[1,7,12,13],[1,8,9,12],[1,8,10,14], [1,8,12,14],[1,10,11,15],[1,10,14,15],[1,11,13,15],[1,12,13,14], [1,13,14,15],[2,3,4,16],[2,3,5,8],[2,3,8,16],[2,4,6,14],[2,4,14,16], [2,5,6,13],[2,5,8,13],[2,6,11,14],[2,6,11,15],[2,6,12,13],[2,6,12,15], [2,7,8,13],[2,7,8,16],[2,7,9,12],[2,7,9,16],[2,7,12,13],[2,9,12,17], [2,9,16,17],[2,10,11,15],[2,10,11,16],[2,10,15,17],[2,10,16,17], [2,11,14,16],[2,12,15,17],[3,4,7,10],[3,4,10,12],[3,4,11,12], [3,4,11,15],[3,4,15,16],[3,5,7,17],[3,5,8,17],[3,6,8,16],[3,6,8,17], [3,6,11,14],[3,6,11,15],[3,6,14,17],[3,6,15,16],[3,7,10,17], [3,10,12,13],[3,10,13,17],[3,11,12,14],[3,12,13,14],[3,13,14,17], [4,5,8,9],[4,5,8,17],[4,5,9,10],[4,5,10,12],[4,5,12,17],[4,6,8,17], [4,6,14,17],[4,7,9,10],[4,11,12,17],[4,11,13,15],[4,11,13,17], [4,13,14,15],[4,13,14,17],[4,14,15,16],[5,6,9,10],[5,6,9,13], [5,7,11,14],[5,7,14,15],[5,7,15,17],[5,8,9,13],[5,10,11,16], [5,10,12,16],[5,11,14,16],[5,12,15,16],[5,12,15,17],[5,14,15,16], [6,7,8,10],[6,7,8,16],[6,7,9,10],[6,7,9,16],[6,9,13,16],[6,12,13,16], [6,12,15,16],[7,8,10,14],[7,8,11,13],[7,8,11,14],[7,10,14,15], [7,10,15,17],[8,9,11,12],[8,9,11,13],[8,11,12,14],[9,11,12,17], [9,11,13,17],[9,13,16,17],[10,12,13,16],[10,13,16,17]]; ## P_7 f = (18,143,250,125), g_2 = 81. ## deg = 13,14,15,15,16,16,16,16,16,16,16,16,16,17,17,17,17,17 ## n_4,... = 0,0,0,0,0,0,0,0,0,1,1,2,9,5 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],[1,5,6,8],[1,5,7,10],[1,5,8,11], [1,5,10,11],[1,7,9,12],[1,7,10,12],[1,8,9,13],[1,8,11,13],[1,9,12,14], [1,9,13,15],[1,9,14,15],[1,10,11,16],[1,10,12,16],[1,11,13,17], [1,11,16,17],[1,12,14,18],[1,12,16,18],[1,13,15,17],[1,14,15,17], [1,14,17,18],[1,16,17,18],[2,3,4,18],[2,3,5,13],[2,3,8,12],[2,3,8,13], [2,3,12,18],[2,4,6,11],[2,4,11,18],[2,5,6,14],[2,5,13,14],[2,6,7,10], [2,6,7,11],[2,6,10,17],[2,6,14,17],[2,7,10,15],[2,7,11,18],[2,7,15,18], [2,8,12,16],[2,8,13,14],[2,8,14,16],[2,9,14,15],[2,9,14,16], [2,9,15,18],[2,9,16,18],[2,10,15,17],[2,12,16,18],[2,14,15,17], [3,4,7,14],[3,4,14,18],[3,5,7,16],[3,5,13,16],[3,7,14,16],[3,8,9,13], [3,8,9,17],[3,8,12,17],[3,9,10,13],[3,9,10,17],[3,10,11,15], [3,10,11,16],[3,10,13,16],[3,10,15,17],[3,11,12,14],[3,11,12,15], [3,11,14,16],[3,12,14,18],[3,12,15,17],[4,5,11,15],[4,5,11,18], [4,5,13,14],[4,5,13,16],[4,5,14,18],[4,5,15,16],[4,6,8,15],[4,6,11,15], [4,7,9,17],[4,7,13,14],[4,7,13,17],[4,8,9,17],[4,8,12,16],[4,8,12,17], [4,8,15,16],[4,12,13,16],[4,12,13,17],[5,6,8,18],[5,6,14,18], [5,7,10,15],[5,7,15,16],[5,8,11,18],[5,10,11,15],[6,7,10,12], [6,7,11,12],[6,8,15,18],[6,9,10,13],[6,9,10,17],[6,9,13,15], [6,9,15,18],[6,9,17,18],[6,10,12,13],[6,11,12,15],[6,12,13,15], [6,14,17,18],[7,8,11,13],[7,8,11,18],[7,8,13,14],[7,8,14,16], [7,8,15,16],[7,8,15,18],[7,9,11,12],[7,9,11,17],[7,11,13,17], [9,11,12,14],[9,11,14,16],[9,11,16,17],[9,16,17,18],[10,12,13,16], [12,13,15,17]]; ## P_8 f = (19,155,272,136), g_2 = 89. ## deg = 7,16,16,16,16,16,16,16,16,17,17,17,17,17,18,18,18,18,18 ## n_4,... = 0,0,0,1,0,0,0,0,0,0,0,0,8,5,5 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],[1,5,6,8],[1,5,7,8],[2,3,4,9],[2,3,5,10],[2,3,8,9], [2,3,8,10],[2,4,6,11],[2,4,9,11],[2,5,6,12],[2,5,10,13],[2,5,12,13], [2,6,11,12],[2,7,10,14],[2,7,10,15],[2,7,12,14],[2,7,12,16], [2,7,15,16],[2,8,9,17],[2,8,10,17],[2,9,11,17],[2,10,13,14], [2,10,15,17],[2,11,12,16],[2,11,15,16],[2,11,15,17],[2,12,13,14], [3,4,7,16],[3,4,9,18],[3,4,16,18],[3,5,7,11],[3,5,10,11],[3,6,13,14], [3,6,13,17],[3,6,14,15],[3,6,15,19],[3,6,17,19],[3,7,11,13], [3,7,13,16],[3,8,9,19],[3,8,10,11],[3,8,11,19],[3,9,12,15],[3,9,12,18], [3,9,15,19],[3,11,13,17],[3,11,17,19],[3,12,13,14],[3,12,13,18], [3,12,14,15],[3,13,16,18],[4,5,9,11],[4,5,9,18],[4,5,10,11], [4,5,10,13],[4,5,13,19],[4,5,14,15],[4,5,14,19],[4,5,15,18],[4,6,8,13], [4,6,10,11],[4,6,10,13],[4,7,8,14],[4,7,12,14],[4,7,12,16],[4,8,13,19], [4,8,14,19],[4,12,14,15],[4,12,15,17],[4,12,16,17],[4,15,17,18], [4,16,17,18],[5,6,8,17],[5,6,12,19],[5,6,17,19],[5,7,8,18],[5,7,9,11], [5,7,9,18],[5,8,15,16],[5,8,15,18],[5,8,16,17],[5,12,13,19], [5,14,15,16],[5,14,16,17],[5,14,17,19],[6,7,9,16],[6,7,9,18], [6,7,15,16],[6,7,15,19],[6,7,18,19],[6,8,13,17],[6,9,10,12], [6,9,10,16],[6,9,12,18],[6,10,11,12],[6,10,13,14],[6,10,14,16], [6,12,18,19],[6,14,15,16],[7,8,14,18],[7,9,11,13],[7,9,13,16], [7,10,14,18],[7,10,15,19],[7,10,18,19],[8,9,13,17],[8,9,13,19], [8,10,11,12],[8,10,12,17],[8,11,12,16],[8,11,14,18],[8,11,14,19], [8,11,15,16],[8,11,15,18],[8,12,16,17],[9,10,12,15],[9,10,15,19], [9,10,16,19],[9,11,13,17],[9,13,16,19],[10,12,15,17],[10,14,16,18], [10,16,18,19],[11,14,17,18],[11,14,17,19],[11,15,17,18],[12,13,18,19], [13,16,18,19],[14,16,17,18]]; ## P_9 f = (19,163,288,144), g_2 = 97. ## deg = 15,16,16,16,17,17,17,17,17,17,17,18,18,18,18,18,18,18,18 ## n_4,... = 0,0,0,0,0,0,0,0,0,0,0,1,3,7,8 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],[1,7,11,13],[1,7,12,13],[1,8,9,14],[1,8,10,14], [1,9,12,14],[1,10,11,15],[1,10,14,15],[1,11,13,16],[1,11,15,16], [1,12,13,16],[1,12,14,17],[1,12,16,17],[1,14,15,17],[1,15,16,17], [2,3,4,18],[2,3,5,9],[2,3,9,18],[2,4,6,15],[2,4,11,18],[2,4,11,19], [2,4,15,19],[2,5,6,14],[2,5,9,16],[2,5,14,16],[2,6,14,15],[2,7,14,15], [2,7,14,16],[2,7,15,19],[2,7,16,17],[2,7,17,19],[2,8,10,13], [2,8,10,16],[2,8,11,13],[2,8,11,17],[2,8,16,17],[2,9,10,13], [2,9,10,16],[2,9,13,18],[2,11,13,18],[2,11,17,19],[3,4,7,17], [3,4,12,13],[3,4,12,18],[3,4,13,17],[3,5,7,8],[3,5,8,9],[3,6,9,18], [3,6,9,19],[3,6,12,18],[3,6,12,19],[3,7,8,14],[3,7,14,16],[3,7,16,17], [3,8,9,14],[3,9,11,14],[3,9,11,15],[3,9,15,19],[3,11,14,16], [3,11,15,16],[3,12,13,19],[3,13,15,17],[3,13,15,19],[3,15,16,17], [4,5,8,9],[4,5,8,15],[4,5,9,16],[4,5,14,16],[4,5,14,19],[4,5,15,19], [4,6,8,15],[4,7,9,17],[4,9,10,13],[4,9,10,16],[4,9,13,17],[4,10,12,13], [4,10,12,18],[4,10,16,18],[4,11,14,16],[4,11,14,19],[4,11,16,18], [5,6,10,17],[5,6,13,14],[5,6,13,17],[5,7,8,11],[5,8,11,12],[5,8,12,18], [5,8,15,18],[5,10,11,12],[5,10,12,18],[5,10,17,18],[5,13,14,19], [5,13,15,17],[5,13,15,19],[5,15,17,18],[6,8,10,19],[6,8,12,18], [6,8,12,19],[6,8,15,18],[6,9,13,17],[6,9,13,18],[6,9,17,19], [6,10,17,19],[6,13,14,18],[6,14,15,18],[7,8,10,13],[7,8,10,14], [7,8,11,13],[7,9,12,15],[7,9,15,19],[7,9,17,19],[7,10,12,13], [7,10,12,15],[7,10,14,15],[8,10,16,19],[8,11,12,17],[8,12,16,17], [8,12,16,19],[9,11,12,14],[9,11,12,15],[10,11,12,15],[10,16,18,19], [10,17,18,19],[11,12,14,17],[11,13,16,18],[11,14,17,19],[12,13,16,19], [13,14,18,19],[13,16,18,19],[14,15,17,18],[14,17,18,19]]; ## P_10 f = (20,175,310,155), g_2 = 105. ## deg = 9,16,16,17,17,17,18,18,18,18,18,18,18,18,19,19,19,19,19,19 ## n_4,... = 0,0,0,0,0,1,0,0,0,0,0,0,2,3,8,6 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],[1,7,11,13],[1,7,12,13],[1,8,9,14],[1,8,10,14], [1,9,12,15],[1,9,14,15],[1,10,11,16],[1,10,14,15],[1,10,15,17], [1,10,16,17],[1,11,13,18],[1,11,16,18],[1,12,13,19],[1,12,15,17], [1,12,17,19],[1,13,18,19],[1,16,17,18],[1,17,18,19],[2,3,4,14], [2,3,5,9],[2,3,9,19],[2,3,14,19],[2,4,6,11],[2,4,11,14],[2,5,6,9], [2,6,9,16],[2,6,11,15],[2,6,15,16],[2,7,12,13],[2,7,12,16],[2,7,13,20], [2,7,15,16],[2,7,15,18],[2,7,18,20],[2,8,10,14],[2,8,10,18], [2,8,11,14],[2,8,11,15],[2,8,15,18],[2,9,16,19],[2,10,13,19], [2,10,13,20],[2,10,14,19],[2,10,18,20],[2,12,13,19],[2,12,16,19], [3,4,7,10],[3,4,10,18],[3,4,12,14],[3,4,12,18],[3,5,7,8],[3,5,8,13], [3,5,9,15],[3,5,13,16],[3,5,15,16],[3,6,11,15],[3,6,11,19],[3,6,12,14], [3,6,12,18],[3,6,13,16],[3,6,13,18],[3,6,14,19],[3,6,15,16],[3,7,8,10], [3,8,10,18],[3,8,13,18],[3,9,11,15],[3,9,11,19],[4,5,8,13],[4,5,8,19], [4,5,12,18],[4,5,12,19],[4,5,13,20],[4,5,18,20],[4,6,8,19],[4,6,11,19], [4,7,9,10],[4,8,9,17],[4,8,13,15],[4,8,15,17],[4,9,10,17],[4,10,13,15], [4,10,13,20],[4,10,15,17],[4,10,18,20],[4,11,14,16],[4,11,16,19], [4,12,14,16],[4,12,16,19],[5,6,9,18],[5,6,10,12],[5,6,12,18], [5,7,8,19],[5,7,11,17],[5,7,17,19],[5,9,14,15],[5,9,14,18], [5,10,11,12],[5,11,12,17],[5,12,17,19],[5,13,16,20],[5,14,15,16], [5,14,16,18],[5,16,18,20],[6,7,8,10],[6,7,8,19],[6,7,10,12], [6,7,12,14],[6,7,14,19],[6,9,13,16],[6,9,13,18],[7,9,10,12], [7,11,13,17],[7,12,14,16],[7,13,17,20],[7,14,15,16],[7,14,15,19], [7,15,18,19],[7,17,18,19],[7,17,18,20],[8,9,14,17],[8,11,14,17], [8,11,15,17],[8,13,15,18],[9,10,11,12],[9,10,11,16],[9,10,16,17], [9,11,12,15],[9,11,16,19],[9,13,14,17],[9,13,14,18],[9,13,16,17], [10,13,15,19],[10,14,15,19],[11,12,15,17],[11,13,14,17],[11,13,14,18], [11,14,16,18],[13,15,18,19],[13,16,17,20],[16,17,18,20]]; ## octahedron_space f = (15,102,174,87), g_2 = 52. ## deg = 12,13,13,13,13,14,14,14,14,14,14,14,14,14,14 ## n_4,... = 0,0,0,0,0,0,0,0,1,4,10 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],[1,7,10,13],[1,7,12,13],[1,8,11,12],[1,9,10,13], [1,9,11,14],[1,9,13,14],[1,11,12,14],[1,12,13,14],[2,3,4,15],[2,3,5,8], [2,3,8,15],[2,4,6,12],[2,4,12,15],[2,5,6,13],[2,5,8,11],[2,5,11,13], [2,6,12,13],[2,7,10,13],[2,7,10,14],[2,7,12,13],[2,7,12,15], [2,7,14,15],[2,8,10,11],[2,8,10,14],[2,8,14,15],[2,10,11,13], [3,4,7,11],[3,4,11,13],[3,4,13,15],[3,5,7,14],[3,5,8,12],[3,5,12,14], [3,6,7,11],[3,6,7,14],[3,6,10,11],[3,6,10,12],[3,6,12,14],[3,8,9,12], [3,8,9,13],[3,8,13,15],[3,9,10,12],[3,9,10,13],[3,10,11,13], [4,5,10,14],[4,5,10,15],[4,5,11,13],[4,5,11,14],[4,5,13,15],[4,6,8,10], [4,6,10,12],[4,7,8,9],[4,7,9,11],[4,8,9,14],[4,8,10,14],[4,9,11,14], [4,10,12,15],[5,6,9,15],[5,6,13,15],[5,7,10,14],[5,8,11,12], [5,9,10,15],[5,11,12,14],[6,7,9,11],[6,7,9,15],[6,7,14,15],[6,8,10,11], [6,12,13,14],[6,13,14,15],[7,8,9,12],[7,9,12,15],[8,9,13,14], [8,13,14,15],[9,10,12,15]]; ## truncated_cube_space f = (16,109,186,93), g_2 = 55. ## deg = 8,12,13,13,14,14,14,14,14,14,14,14,15,15,15,15 ## n_4,... = 0,0,0,0,1,0,0,0,1,2,8,4 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],[1,5,7,9],[1,6,8,9],[1,7,8,9],[2,3,4,9], [2,3,5,10],[2,3,9,10],[2,4,6,11],[2,4,9,11],[2,5,6,12],[2,5,8,12], [2,5,8,13],[2,5,10,13],[2,6,11,14],[2,6,12,14],[2,8,12,14],[2,8,13,15], [2,8,14,15],[2,9,10,13],[2,9,11,16],[2,9,13,16],[2,11,14,15], [2,11,15,16],[2,13,15,16],[3,4,7,16],[3,4,9,15],[3,4,14,15], [3,4,14,16],[3,5,7,11],[3,5,10,11],[3,7,11,13],[3,7,13,16],[3,8,9,10], [3,8,9,15],[3,8,10,11],[3,8,11,12],[3,8,12,14],[3,8,14,15], [3,11,12,13],[3,12,13,14],[3,13,14,16],[4,5,8,13],[4,5,8,16], [4,5,10,13],[4,5,10,15],[4,5,14,15],[4,5,14,16],[4,6,8,13],[4,6,11,13], [4,7,8,16],[4,9,11,12],[4,9,12,15],[4,10,12,13],[4,10,12,15], [4,11,12,13],[5,6,9,12],[5,7,9,14],[5,7,11,14],[5,8,12,16],[5,9,12,16], [5,9,14,16],[5,10,11,15],[5,11,14,15],[6,7,11,13],[6,7,11,14], [6,7,12,14],[6,7,12,15],[6,7,13,15],[6,8,9,15],[6,8,13,15],[6,9,12,15], [7,8,9,10],[7,8,10,16],[7,9,10,14],[7,10,12,14],[7,10,12,15], [7,10,15,16],[7,13,15,16],[8,10,11,16],[8,11,12,16],[9,10,13,14], [9,11,12,16],[9,13,14,16],[10,11,15,16],[10,12,13,14]]; ## Poincare_sphere f = (16,106,180,90), g_2 = 52. ## deg = 6,11,11,12,13,14,14,14,14,14,14,15,15,15,15,15 ## n_4,... = 0,0,1,0,0,0,0,2,1,1,6,5 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], [1,4,6,7],[1,5,6,7],[2,3,4,8],[2,3,5,9],[2,3,8,9],[2,4,6,10], [2,4,8,10],[2,5,6,11],[2,5,9,11],[2,6,10,12],[2,6,11,12],[2,7,8,10], [2,7,8,13],[2,7,10,12],[2,7,12,14],[2,7,13,14],[2,8,9,13],[2,9,11,14], [2,9,13,14],[2,11,12,14],[3,4,7,11],[3,4,8,15],[3,4,11,15],[3,5,7,14], [3,5,9,16],[3,5,14,16],[3,6,10,12],[3,6,10,13],[3,6,12,16],[3,6,13,14], [3,6,14,16],[3,7,11,13],[3,7,13,14],[3,8,9,12],[3,8,12,15],[3,9,12,16], [3,10,11,13],[3,10,11,15],[3,10,12,15],[4,5,10,13],[4,5,10,14], [4,5,12,13],[4,5,12,14],[4,6,7,9],[4,6,9,13],[4,6,10,13],[4,7,9,16], [4,7,11,16],[4,8,10,14],[4,8,14,15],[4,9,12,13],[4,9,12,16], [4,11,12,14],[4,11,12,16],[4,11,14,15],[5,6,7,15],[5,6,8,11], [5,6,8,15],[5,7,12,14],[5,7,12,15],[5,8,11,13],[5,8,12,13],[5,8,12,15], [5,9,10,11],[5,9,10,16],[5,10,11,13],[5,10,14,16],[6,7,9,15], [6,8,11,16],[6,8,14,15],[6,8,14,16],[6,9,13,14],[6,9,14,15], [6,11,12,16],[7,8,10,16],[7,8,11,13],[7,8,11,16],[7,9,10,15], [7,9,10,16],[7,10,12,15],[8,9,12,13],[8,10,14,16],[9,10,11,15], [9,11,14,15]];