########################################################################### ########################################################################### ### ### ### Vertex-minimal triangulations of sphere bundles. ### ### ### ### Frank H. Lutz, Thom Sulanke, and Ed Swartz. ### ### f-vectors of 3-manifolds. ### ### Electron. J. Comb. 16, No. 2, Research Paper R13, 33 p. (2009). ### ### ### ########################################################################### ########################################################################### ## (S^2xS^1)#2 f = (12,58,92,46), g_2 = 20. ## deg = 7,8,9,9,9,9,10,11,11,11,11,11 facets:=[[1,2,3,4],[1,2,3,5],[1,2,4,5],[1,3,4,6],[1,3,5,6],[1,4,5,7], [1,4,6,7],[1,5,6,8],[1,5,7,8],[1,6,7,8],[2,3,4,9],[2,3,5,10],[2,3,7,8], [2,3,7,9],[2,3,8,10],[2,4,5,10],[2,4,9,10],[2,6,7,10],[2,6,7,11], [2,6,8,10],[2,6,8,11],[2,7,8,11],[2,7,9,10],[3,4,5,6],[3,4,5,10], [3,4,9,11],[3,4,10,12],[3,4,11,12],[3,7,8,10],[3,7,9,10],[3,9,10,12], [3,9,11,12],[4,5,6,7],[4,8,9,11],[4,8,9,12],[4,8,11,12],[4,9,10,12], [5,6,7,12],[5,6,8,12],[5,7,8,12],[6,7,8,10],[6,7,11,12],[6,8,9,11], [6,8,9,12],[6,9,11,12],[7,8,11,12]] ## (S^2twistS^1)#2 f = (12,58,92,46), g_2 = 20. ## deg = 8,8,9,9,10,10,10,10,10,10,11,11 facets=[[1,2,3,4],[1,2,3,5],[1,2,4,5],[1,3,4,6],[1,3,5,6],[1,4,5,7], [1,4,6,7],[1,5,6,8],[1,5,7,8],[1,6,7,9],[1,6,8,9],[1,7,8,9],[2,3,4,8], [2,3,5,10],[2,3,7,10],[2,3,7,11],[2,3,8,11],[2,4,5,10],[2,4,8,10], [2,7,8,9],[2,7,8,10],[2,7,9,11],[2,8,9,11],[3,4,5,6],[3,4,5,12], [3,4,8,10],[3,4,10,12],[3,5,10,12],[3,7,8,10],[3,7,8,11],[4,5,6,7], [4,5,9,10],[4,5,9,12],[4,9,10,11],[4,9,11,12],[4,10,11,12],[5,6,7,8], [5,9,10,12],[6,7,8,11],[6,7,9,11],[6,8,9,12],[6,8,11,12],[6,9,10,11], [6,9,10,12],[6,10,11,12],[8,9,11,12]] ## (S^2xS^1)#3 f = (13,72,118,59), g_2 = 30. ## deg = 10,10,10,11,11,11,11,11,11,12,12,12,12 facets=[[1,2,3,4],[1,2,3,5],[1,2,4,5],[1,3,4,6],[1,3,5,6],[1,4,5,7], [1,4,6,7],[1,5,6,8],[1,5,7,8],[1,6,7,9],[1,6,8,9],[1,7,8,10], [1,7,9,11],[1,7,10,11],[1,8,9,10],[1,9,10,12],[1,9,11,12],[1,10,11,12], [2,3,4,11],[2,3,5,13],[2,3,7,9],[2,3,7,13],[2,3,8,9],[2,3,8,12], [2,3,11,12],[2,4,5,11],[2,5,11,13],[2,6,11,12],[2,6,11,13],[2,6,12,13], [2,7,8,9],[2,7,8,13],[2,8,12,13],[3,4,5,6],[3,4,5,11],[3,5,11,13], [3,7,8,10],[3,7,8,13],[3,7,9,10],[3,8,9,10],[3,8,12,13],[3,11,12,13], [4,5,6,10],[4,5,7,12],[4,5,10,12],[4,6,7,12],[4,6,10,13],[4,6,12,13], [4,10,12,13],[5,6,7,8],[5,6,7,12],[5,6,10,12],[6,7,8,9],[6,10,11,12], [6,10,11,13],[7,9,10,11],[9,10,11,13],[9,10,12,13],[9,11,12,13]] ## (S^2twistS^1)#3 f = (13,72,118,59), g_2 = 30. ## deg = 8,9,10,10,11,12,12,12,12,12,12,12,12 facets=[[1,2,3,4],[1,2,3,5],[1,2,4,5],[1,3,4,6],[1,3,5,6],[1,4,5,7], [1,4,6,7],[1,5,6,8],[1,5,7,8],[1,6,7,9],[1,6,8,9],[1,7,8,10], [1,7,9,10],[1,8,9,11],[1,8,10,12],[1,8,11,13],[1,8,12,13],[1,9,10,11], [1,10,11,12],[1,11,12,13],[2,3,4,13],[2,3,5,9],[2,3,7,12],[2,3,7,13], [2,3,9,12],[2,4,5,9],[2,4,9,13],[2,7,11,12],[2,7,11,13],[2,8,11,12], [2,8,11,13],[2,8,12,13],[2,9,12,13],[3,4,5,6],[3,4,5,10],[3,4,8,9], [3,4,8,10],[3,4,9,13],[3,5,9,10],[3,7,12,13],[3,8,9,11],[3,8,10,11], [3,9,10,11],[3,9,12,13],[4,5,6,12],[4,5,7,11],[4,5,9,10],[4,5,11,12], [4,6,7,12],[4,7,11,12],[4,8,9,10],[5,6,7,8],[5,6,7,12],[5,7,11,13], [5,7,12,13],[5,11,12,13],[6,7,8,9],[7,8,9,10],[8,10,11,12]] ## (S^2xS^1)#4 f = (14,86,144,72), g_2 = 40. ## deg = 11,12,12,12,12,12,12,12,12,13,13,13,13,13 facets=[[1,2,3,4],[1,2,3,5],[1,2,4,5],[1,3,4,6],[1,3,5,6],[1,4,5,7], [1,4,6,7],[1,5,6,8],[1,5,7,8],[1,6,7,9],[1,6,8,9],[1,7,8,10], [1,7,9,10],[1,8,9,11],[1,8,10,12],[1,8,11,12],[1,9,10,12],[1,9,11,13], [1,9,12,13],[1,11,12,13],[2,3,4,14],[2,3,5,9],[2,3,8,9],[2,3,8,10], [2,3,10,13],[2,3,13,14],[2,4,5,9],[2,4,9,10],[2,4,10,14],[2,6,11,12], [2,6,11,13],[2,6,12,13],[2,7,8,9],[2,7,8,10],[2,7,9,10],[2,10,11,13], [2,10,11,14],[2,11,12,14],[2,12,13,14],[3,4,5,9],[3,4,5,12],[3,4,6,11], [3,4,9,10],[3,4,10,14],[3,4,11,12],[3,5,6,12],[3,6,11,12],[3,8,9,10], [3,10,13,14],[4,5,6,7],[4,5,6,12],[4,6,11,13],[4,6,12,13],[4,11,12,13], [5,6,7,14],[5,6,8,14],[5,7,8,13],[5,7,11,13],[5,7,11,14],[5,8,13,14], [5,10,11,13],[5,10,11,14],[5,10,13,14],[6,7,8,9],[6,7,8,14], [7,8,13,14],[7,11,13,14],[8,9,10,12],[8,9,11,12],[9,11,12,14], [9,11,13,14],[9,12,13,14]] ## (S^2twistS^1)#4 f = (14,86,144,72), g_2 = 40. ## deg = 10,11,12,12,12,12,12,13,13,13,13,13,13,13 facets=[[1,2,3,4],[1,2,3,5],[1,2,4,5],[1,3,4,6],[1,3,5,6],[1,4,5,7], [1,4,6,7],[1,5,6,8],[1,5,7,8],[1,6,7,9],[1,6,8,9],[1,7,8,10], [1,7,9,10],[1,8,9,11],[1,8,10,11],[1,9,10,11],[2,3,4,8],[2,3,5,12], [2,3,7,8],[2,3,7,13],[2,3,9,12],[2,3,9,13],[2,4,5,13],[2,4,8,13], [2,5,9,11],[2,5,9,13],[2,5,11,12],[2,6,7,8],[2,6,7,13],[2,6,8,13], [2,9,11,14],[2,9,12,14],[2,11,12,14],[3,4,5,6],[3,4,5,10],[3,4,8,13], [3,4,10,14],[3,4,11,13],[3,4,11,14],[3,5,9,12],[3,5,9,13],[3,5,10,13], [3,7,8,13],[3,10,11,13],[3,10,11,14],[4,5,6,7],[4,5,10,13],[4,9,10,11], [4,9,10,14],[4,9,11,14],[4,10,11,13],[5,6,7,14],[5,6,8,14],[5,7,8,14], [5,9,11,12],[6,7,8,9],[6,7,11,12],[6,7,11,14],[6,7,12,13],[6,8,13,14], [6,10,11,12],[6,10,11,14],[6,10,12,14],[6,12,13,14],[7,8,9,10], [7,8,13,14],[7,11,12,14],[7,12,13,14],[8,9,10,12],[8,9,11,12], [8,10,11,12],[9,10,12,14]] ## (S^2xS^1)#5 f = (15,100,170,85), g_2 = 50. ## deg = 11,12,12,13,13,13,14,14,14,14,14,14,14,14,14 facets=[[1,2,3,4],[1,2,3,5],[1,2,4,5],[1,3,4,6],[1,3,5,6],[1,4,5,7], [1,4,6,7],[1,5,6,8],[1,5,7,8],[1,6,7,9],[1,6,8,9],[1,7,8,10], [1,7,9,10],[1,8,9,11],[1,8,10,12],[1,8,11,13],[1,8,12,14],[1,8,13,14], [1,9,10,15],[1,9,11,14],[1,9,12,14],[1,9,12,15],[1,10,12,15], [1,11,13,14],[2,3,4,11],[2,3,5,12],[2,3,8,9],[2,3,8,12],[2,3,9,13], [2,3,11,13],[2,4,5,13],[2,4,10,13],[2,4,10,15],[2,4,11,14],[2,4,14,15], [2,5,9,12],[2,5,9,13],[2,6,7,11],[2,6,7,14],[2,6,11,14],[2,7,11,13], [2,7,13,14],[2,8,9,12],[2,10,13,15],[2,13,14,15],[3,4,5,6],[3,4,5,13], [3,4,11,13],[3,5,9,12],[3,5,9,13],[3,8,9,10],[3,8,10,12],[3,9,10,12], [4,5,6,7],[4,8,11,13],[4,8,11,14],[4,8,13,14],[4,9,10,12],[4,9,10,15], [4,9,12,15],[4,10,12,13],[4,12,13,15],[4,13,14,15],[5,6,7,14], [5,6,8,15],[5,6,11,14],[5,6,11,15],[5,7,8,15],[5,7,11,14],[5,7,11,15], [6,7,8,9],[6,7,8,15],[6,7,11,12],[6,7,12,15],[6,10,11,12],[6,10,11,15], [6,10,12,13],[6,10,13,15],[6,12,13,15],[7,8,9,10],[7,11,12,15], [7,11,13,14],[8,9,11,14],[8,9,12,14],[10,11,12,15]] ## (S^2twistS^1)#5 f = (15,100,170,85), g_2 = 50. ## deg = 12,12,13,13,13,13,13,13,14,14,14,14,14,14,14 facets=[[1,2,3,4],[1,2,3,5],[1,2,4,5],[1,3,4,6],[1,3,5,6],[1,4,5,7], [1,4,6,7],[1,5,6,8],[1,5,7,8],[1,6,7,9],[1,6,8,10],[1,6,9,10], [1,7,8,11],[1,7,9,10],[1,7,10,12],[1,7,11,13],[1,7,12,13],[1,8,10,12], [1,8,11,14],[1,8,12,13],[1,8,13,14],[1,11,13,14],[2,3,4,14],[2,3,5,9], [2,3,7,8],[2,3,7,15],[2,3,8,12],[2,3,9,10],[2,3,10,15],[2,3,12,14], [2,4,5,13],[2,4,13,14],[2,5,9,12],[2,5,12,14],[2,5,13,14],[2,6,9,10], [2,6,9,15],[2,6,10,15],[2,7,8,12],[2,7,12,15],[2,9,12,15],[3,4,5,6], [3,4,5,14],[3,5,9,12],[3,5,12,14],[3,7,8,13],[3,7,12,13],[3,7,12,15], [3,8,12,13],[3,9,10,15],[3,9,11,12],[3,9,11,15],[3,11,12,15],[4,5,6,7], [4,5,11,13],[4,5,11,14],[4,8,9,13],[4,8,9,15],[4,8,11,14],[4,8,11,15], [4,8,13,14],[4,9,11,12],[4,9,11,13],[4,9,12,15],[4,11,12,15],[5,6,7,8], [5,10,11,13],[5,10,11,14],[5,10,13,15],[5,10,14,15],[5,13,14,15], [6,7,8,10],[6,7,9,14],[6,7,10,14],[6,9,14,15],[6,10,13,14], [6,10,13,15],[6,13,14,15],[7,8,10,12],[7,8,11,13],[7,9,10,14], [8,9,11,13],[8,9,11,15],[9,10,14,15],[10,11,13,14]] ## (S^2xS^1)#6 f = (16,114,196,98), g_2 = 60. ## deg = 13,13,13,14,14,14,14,14,14,15,15,15,15,15,15,15 facets=[[1,2,3,4],[1,2,3,5],[1,2,4,5],[1,3,4,6],[1,3,5,6],[1,4,5,7], [1,4,6,7],[1,5,6,8],[1,5,7,8],[1,6,7,9],[1,6,8,9],[1,7,8,10], [1,7,9,10],[1,8,9,11],[1,8,10,11],[1,9,10,12],[1,9,11,12],[1,10,11,13], [1,10,12,13],[1,11,12,14],[1,11,13,14],[1,12,13,14],[2,3,4,11], [2,3,5,14],[2,3,7,12],[2,3,7,14],[2,3,10,11],[2,3,10,15],[2,3,12,15], [2,4,5,10],[2,4,10,11],[2,5,10,14],[2,6,7,12],[2,6,7,14],[2,6,12,14], [2,8,9,15],[2,8,9,16],[2,8,12,14],[2,8,12,15],[2,8,14,16],[2,9,13,15], [2,9,13,16],[2,10,14,15],[2,13,15,16],[2,14,15,16],[3,4,5,10], [3,4,5,16],[3,4,6,16],[3,4,8,10],[3,4,8,11],[3,5,6,16],[3,5,10,14], [3,7,12,13],[3,7,13,14],[3,8,10,11],[3,10,14,15],[3,12,13,14], [3,12,14,15],[4,5,6,12],[4,5,6,13],[4,5,7,12],[4,5,13,16],[4,6,7,14], [4,6,12,14],[4,6,13,16],[4,7,12,14],[4,8,9,10],[4,8,9,11],[4,9,10,11], [5,6,7,8],[5,6,7,12],[5,6,11,13],[5,6,11,16],[5,9,13,15],[5,9,13,16], [5,9,15,16],[5,11,13,15],[5,11,15,16],[6,7,8,15],[6,7,9,15],[6,8,9,15], [6,10,11,13],[6,10,11,16],[6,10,13,16],[7,8,9,10],[7,8,9,16], [7,8,15,16],[7,9,15,16],[7,11,12,13],[7,11,12,14],[7,11,13,14], [8,12,14,15],[8,14,15,16],[9,10,11,12],[10,11,12,16],[10,12,13,16], [11,12,13,16],[11,13,15,16]] ## (S^2twistS^1)#6 f = (16,114,196,98), g_2 = 60. ## deg = 13,13,14,14,14,14,14,14,14,14,15,15,15,15,15,15 facets=[[1,2,3,4],[1,2,3,5],[1,2,4,5],[1,3,4,6],[1,3,5,6],[1,4,5,7], [1,4,6,7],[1,5,6,8],[1,5,7,8],[1,6,7,9],[1,6,8,9],[1,7,8,10], [1,7,9,11],[1,7,10,12],[1,7,11,13],[1,7,12,13],[1,8,9,13],[1,8,10,13], [1,9,11,13],[1,10,12,14],[1,10,13,15],[1,10,14,15],[1,12,13,15], [1,12,14,15],[2,3,4,12],[2,3,5,10],[2,3,10,16],[2,3,12,16],[2,4,5,12], [2,5,10,15],[2,5,12,16],[2,5,15,16],[2,6,8,11],[2,6,8,15],[2,6,10,13], [2,6,10,16],[2,6,11,16],[2,6,13,15],[2,8,11,14],[2,8,14,16], [2,8,15,16],[2,10,13,15],[2,11,14,16],[3,4,5,6],[3,4,5,11],[3,4,8,11], [3,4,8,12],[3,5,9,12],[3,5,9,14],[3,5,10,16],[3,5,11,12],[3,5,13,14], [3,5,13,16],[3,7,9,13],[3,7,9,14],[3,7,13,14],[3,8,11,12],[3,9,12,16], [3,9,13,16],[4,5,6,7],[4,5,11,12],[4,8,11,16],[4,8,12,14],[4,8,14,16], [4,9,10,11],[4,9,10,14],[4,9,11,13],[4,9,13,14],[4,10,11,12], [4,10,12,14],[4,11,13,14],[4,11,14,16],[5,6,7,8],[5,9,12,16], [5,9,13,14],[5,9,13,16],[5,10,15,16],[6,7,8,16],[6,7,9,15],[6,7,15,16], [6,8,9,15],[6,8,11,16],[6,10,12,13],[6,10,12,15],[6,10,15,16], [6,12,13,15],[7,8,9,13],[7,8,9,15],[7,8,10,13],[7,8,15,16],[7,9,11,14], [7,10,12,13],[7,11,13,14],[8,11,12,14],[9,10,11,14],[10,11,12,15], [10,11,14,15],[11,12,14,15]] ## (S^2xS^1)#7 f = (17,128,222,111), g_2 = 70. ## deg = 12,14,15,15,15,15,15,15,15,15,15,15,16,16,16,16,16 facets=[[1,2,3,4],[1,2,3,5],[1,2,4,5],[1,3,4,6],[1,3,5,6],[1,4,5,7], [1,4,6,7],[1,5,6,8],[1,5,7,8],[1,6,7,9],[1,6,8,9],[1,7,8,10], [1,7,9,11],[1,7,10,11],[1,8,9,12],[1,8,10,13],[1,8,11,14],[1,8,11,15], [1,8,12,14],[1,8,13,15],[1,9,11,16],[1,9,12,14],[1,9,14,16], [1,10,11,15],[1,10,13,17],[1,10,15,17],[1,11,14,16],[1,13,15,17], [2,3,4,10],[2,3,5,12],[2,3,9,11],[2,3,9,16],[2,3,10,16],[2,3,11,12], [2,4,5,10],[2,5,10,12],[2,6,11,12],[2,6,11,17],[2,6,12,14],[2,6,14,15], [2,6,15,16],[2,6,16,17],[2,7,12,14],[2,7,12,15],[2,7,14,15], [2,9,11,13],[2,9,13,16],[2,10,12,16],[2,11,13,16],[2,11,16,17], [2,12,15,16],[3,4,5,6],[3,4,5,10],[3,5,10,13],[3,5,12,17],[3,5,13,17], [3,7,13,15],[3,7,13,17],[3,7,15,17],[3,9,11,16],[3,10,12,16], [3,10,12,17],[3,10,13,15],[3,10,15,17],[3,11,12,16],[4,5,6,16], [4,5,7,16],[4,6,7,13],[4,6,11,16],[4,6,11,17],[4,6,13,17],[4,7,12,14], [4,7,12,15],[4,7,13,15],[4,7,14,17],[4,7,16,17],[4,8,9,12],[4,8,9,14], [4,8,12,14],[4,9,12,15],[4,9,14,15],[4,11,16,17],[4,13,15,17], [4,14,15,17],[5,6,7,8],[5,6,7,16],[5,9,10,14],[5,9,10,17],[5,9,11,13], [5,9,11,14],[5,9,13,17],[5,10,12,17],[5,10,13,14],[5,11,13,14], [6,7,8,9],[6,7,13,17],[6,7,16,17],[6,11,12,16],[6,12,14,15], [6,12,15,16],[7,8,9,11],[7,8,10,11],[7,14,15,17],[8,9,11,14], [8,10,11,15],[8,10,13,15],[9,10,13,14],[9,10,13,17],[9,12,14,15], [9,13,14,16],[11,13,14,16]] ## (S^2twistS^1)#7 f = (17,128,222,111), g_2 = 70. ## deg = 12,13,14,14,15,15,15,15,15,16,16,16,16,16,16,16,16 facets=[[1,2,3,4],[1,2,3,5],[1,2,4,5],[1,3,4,6],[1,3,5,6],[1,4,5,7], [1,4,6,7],[1,5,6,8],[1,5,7,8],[1,6,7,9],[1,6,8,9],[1,7,8,10], [1,7,9,10],[1,8,9,11],[1,8,10,12],[1,8,11,12],[1,9,10,13],[1,9,11,14], [1,9,12,14],[1,9,12,15],[1,9,13,16],[1,9,15,16],[1,10,12,13], [1,11,12,14],[1,12,13,16],[1,12,15,17],[1,12,16,17],[1,15,16,17], [2,3,4,10],[2,3,5,11],[2,3,10,11],[2,4,5,11],[2,4,9,11],[2,4,9,14], [2,4,10,14],[2,8,13,14],[2,8,13,17],[2,8,14,17],[2,9,11,12], [2,9,12,14],[2,10,11,17],[2,10,13,14],[2,10,13,17],[2,11,12,14], [2,11,14,17],[3,4,5,11],[3,4,5,16],[3,4,6,13],[3,4,8,15],[3,4,8,16], [3,4,10,11],[3,4,13,17],[3,4,15,17],[3,5,6,13],[3,5,9,13],[3,5,9,17], [3,5,16,17],[3,7,8,14],[3,7,8,16],[3,7,14,15],[3,7,15,16],[3,8,14,15], [3,9,13,17],[3,12,15,16],[3,12,15,17],[3,12,16,17],[4,5,6,7], [4,5,6,13],[4,5,13,17],[4,5,16,17],[4,8,15,16],[4,9,11,14], [4,10,11,14],[4,15,16,17],[5,6,7,15],[5,6,8,15],[5,7,8,15],[5,9,10,12], [5,9,10,17],[5,9,12,13],[5,10,12,13],[5,10,13,14],[5,10,14,17], [5,13,14,17],[6,7,8,9],[6,7,8,16],[6,7,11,15],[6,7,11,16],[6,8,15,16], [6,10,11,15],[6,10,11,17],[6,10,14,16],[6,10,14,17],[6,10,15,16], [6,11,14,16],[6,11,14,17],[7,8,9,10],[7,8,13,15],[7,8,13,17], [7,8,14,17],[7,11,15,16],[7,13,14,15],[7,13,14,17],[8,9,10,12], [8,9,11,12],[8,13,14,15],[9,10,13,17],[9,12,13,16],[9,12,15,16], [10,11,14,16],[10,11,15,16]] ## (S^2xS^1)#8 f = (18,142,248,124), g_2 = 80. ## deg = 13,13,14,15,15,16,16,16,16,16,16,16,17,17,17,17,17,17 facets=[[1,2,3,4],[1,2,3,5],[1,2,4,5],[1,3,4,6],[1,3,5,6],[1,4,5,7], [1,4,6,7],[1,5,6,8],[1,5,7,8],[1,6,7,9],[1,6,8,9],[1,7,8,10], [1,7,9,11],[1,7,10,12],[1,7,11,12],[1,8,9,10],[1,9,10,11],[1,10,11,13], [1,10,12,14],[1,10,13,14],[1,11,12,13],[1,12,13,14],[2,3,4,15], [2,3,5,15],[2,4,5,16],[2,4,8,12],[2,4,8,16],[2,4,9,15],[2,4,9,17], [2,4,12,17],[2,5,15,16],[2,6,11,13],[2,6,11,17],[2,6,13,17],[2,7,9,10], [2,7,9,16],[2,7,10,16],[2,8,11,13],[2,8,11,17],[2,8,12,14],[2,8,13,16], [2,8,14,18],[2,8,17,18],[2,9,10,17],[2,9,15,16],[2,10,16,17], [2,12,14,18],[2,12,17,18],[2,13,16,17],[3,4,5,11],[3,4,5,14], [3,4,6,11],[3,4,13,14],[3,4,13,18],[3,4,15,18],[3,5,6,17],[3,5,11,17], [3,5,14,15],[3,6,11,17],[3,7,8,15],[3,7,8,18],[3,7,13,15],[3,7,13,18], [3,8,15,18],[3,9,12,13],[3,9,12,16],[3,9,13,14],[3,9,14,16], [3,10,12,13],[3,10,12,14],[3,10,13,15],[3,10,14,15],[3,12,14,16], [4,5,6,7],[4,5,6,11],[4,5,14,15],[4,5,15,16],[4,8,12,17],[4,8,16,17], [4,9,15,16],[4,9,16,17],[4,13,14,15],[4,13,15,18],[5,6,7,18], [5,6,8,18],[5,6,10,11],[5,6,10,13],[5,6,13,17],[5,7,8,18],[5,10,11,12], [5,10,12,13],[5,11,12,13],[5,11,13,17],[6,7,8,9],[6,7,8,15], [6,7,15,18],[6,8,12,14],[6,8,12,15],[6,8,14,18],[6,10,11,13], [6,12,14,16],[6,12,15,18],[6,12,16,18],[6,14,16,18],[7,8,9,10], [7,9,11,14],[7,9,14,16],[7,10,11,12],[7,10,11,16],[7,11,14,16], [7,13,15,18],[8,11,13,17],[8,12,15,18],[8,12,17,18],[8,13,16,17], [9,10,11,16],[9,10,16,17],[9,11,14,18],[9,11,16,18],[9,12,13,14], [9,12,14,18],[9,12,16,18],[10,13,14,15],[11,14,16,18]] ## (S^2twistS^1)#8 f = (18,142,248,124), g_2 = 80. ## deg = 11,14,15,15,16,16,16,16,16,16,16,16,16,17,17,17,17,17 facets=[[1,2,3,4],[1,2,3,5],[1,2,4,5],[1,3,4,6],[1,3,5,6],[1,4,5,7], [1,4,6,7],[1,5,6,8],[1,5,7,8],[1,6,7,9],[1,6,8,9],[1,7,8,10], [1,7,9,11],[1,7,10,12],[1,7,11,12],[1,8,9,10],[1,9,10,11],[1,10,11,13], [1,10,12,14],[1,10,13,15],[1,10,14,15],[1,11,12,14],[1,11,13,16], [1,11,14,15],[1,11,15,16],[1,13,15,17],[1,13,16,17],[1,15,16,17], [2,3,4,12],[2,3,5,9],[2,3,9,14],[2,3,12,16],[2,3,14,16],[2,4,5,13], [2,4,9,12],[2,4,9,13],[2,5,9,13],[2,6,7,9],[2,6,7,17],[2,6,8,9], [2,6,8,18],[2,6,17,18],[2,7,8,14],[2,7,8,18],[2,7,9,14],[2,7,17,18], [2,8,9,12],[2,8,12,14],[2,10,11,12],[2,10,11,14],[2,10,12,16], [2,10,14,16],[2,11,12,14],[3,4,5,9],[3,4,5,10],[3,4,6,11],[3,4,8,17], [3,4,8,18],[3,4,9,12],[3,4,10,17],[3,4,11,18],[3,5,6,11],[3,5,10,17], [3,5,11,17],[3,7,8,13],[3,7,8,18],[3,7,13,18],[3,8,11,15],[3,8,11,17], [3,8,13,15],[3,9,12,14],[3,11,13,15],[3,11,13,18],[3,12,14,16], [4,5,6,7],[4,5,6,11],[4,5,9,15],[4,5,10,14],[4,5,11,17],[4,5,13,15], [4,5,14,17],[4,8,11,17],[4,8,11,18],[4,9,13,15],[4,10,14,16], [4,10,16,17],[4,14,16,17],[5,6,7,8],[5,9,13,16],[5,9,15,16], [5,10,14,17],[5,12,13,15],[5,12,13,16],[5,12,15,16],[6,7,8,13], [6,7,13,18],[6,7,15,17],[6,7,15,18],[6,8,13,18],[6,10,12,16], [6,10,12,17],[6,10,16,17],[6,12,15,16],[6,12,15,18],[6,12,17,18], [6,15,16,17],[7,8,9,10],[7,8,9,14],[7,9,10,11],[7,10,11,12], [7,15,17,18],[8,9,12,14],[8,11,13,16],[8,11,13,18],[8,11,15,16], [8,13,15,16],[9,13,15,16],[10,11,13,15],[10,11,14,15],[10,12,14,17], [12,13,15,17],[12,13,16,17],[12,14,16,17],[12,15,17,18]] ## (S^2xS^1)#10 f = (19,166,294,147), g_2 = 100. ## deg = 15,16,16,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18 facets=[[1,2,3,4],[1,2,3,5],[1,2,4,5],[1,3,4,6],[1,3,5,6],[1,4,5,7], [1,4,6,7],[1,5,6,8],[1,5,7,8],[1,6,7,9],[1,6,8,9],[1,7,8,10], [1,7,9,11],[1,7,10,12],[1,7,11,13],[1,7,12,14],[1,7,13,15],[1,7,14,15], [1,8,9,15],[1,8,10,15],[1,9,11,16],[1,9,13,15],[1,9,13,16], [1,10,12,17],[1,10,14,15],[1,10,14,18],[1,10,17,18],[1,11,13,16], [1,12,14,19],[1,12,17,19],[1,14,17,18],[1,14,17,19],[2,3,4,12], [2,3,5,13],[2,3,7,8],[2,3,7,19],[2,3,8,16],[2,3,12,16],[2,3,13,19], [2,4,5,15],[2,4,11,12],[2,4,11,15],[2,5,12,15],[2,5,12,16],[2,5,13,16], [2,6,10,17],[2,6,10,19],[2,6,17,18],[2,6,18,19],[2,7,8,16],[2,7,16,19], [2,9,10,13],[2,9,10,18],[2,9,13,16],[2,9,16,19],[2,9,18,19], [2,10,13,19],[2,10,14,17],[2,10,14,18],[2,11,12,15],[2,14,17,18], [3,4,5,6],[3,4,5,14],[3,4,12,14],[3,5,12,14],[3,5,12,16],[3,5,13,16], [3,7,8,9],[3,7,9,15],[3,7,15,16],[3,7,16,19],[3,8,9,15],[3,8,15,17], [3,8,16,17],[3,13,16,19],[3,15,16,17],[4,5,6,18],[4,5,7,18],[4,5,9,12], [4,5,9,14],[4,5,12,15],[4,6,7,18],[4,8,11,12],[4,8,11,19],[4,8,12,15], [4,8,13,17],[4,8,13,19],[4,8,15,16],[4,8,16,17],[4,9,12,14], [4,11,15,19],[4,13,17,19],[4,15,16,17],[4,15,17,19],[5,6,7,8], [5,6,7,17],[5,6,10,11],[5,6,10,17],[5,6,11,18],[5,7,17,18],[5,9,12,19], [5,9,14,19],[5,10,11,18],[5,10,17,18],[5,12,14,19],[6,7,8,9], [6,7,17,18],[6,10,11,16],[6,10,16,18],[6,10,18,19],[6,11,12,13], [6,11,12,15],[6,11,13,14],[6,11,14,16],[6,11,15,18],[6,12,13,18], [6,12,15,18],[6,13,14,16],[6,13,16,18],[7,8,10,15],[7,8,15,16], [7,9,11,13],[7,9,13,15],[7,10,12,14],[7,10,14,15],[8,11,12,18], [8,11,15,18],[8,11,15,19],[8,12,15,18],[8,13,14,17],[8,13,14,19], [8,14,17,19],[8,15,17,19],[9,10,13,19],[9,10,18,19],[9,11,13,14], [9,11,14,16],[9,12,14,17],[9,12,17,19],[9,13,14,17],[9,13,17,19], [9,14,16,19],[10,11,16,18],[10,12,14,17],[11,12,13,18],[11,13,16,18], [13,14,16,19]] ## (S^2twistS^1)#10 f = (19,166,294,147), g_2 = 100. ## deg = 16,16,16,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18 facets=[[1,2,3,4],[1,2,3,5],[1,2,4,5],[1,3,4,6],[1,3,5,6],[1,4,5,7], [1,4,6,7],[1,5,6,8],[1,5,7,8],[1,6,7,9],[1,6,8,10],[1,6,9,10], [1,7,8,9],[1,8,9,11],[1,8,10,12],[1,8,11,13],[1,8,12,13],[1,9,10,14], [1,9,11,13],[1,9,12,13],[1,9,12,15],[1,9,14,15],[1,10,12,16], [1,10,14,17],[1,10,16,17],[1,12,14,15],[1,12,14,17],[1,12,16,17], [2,3,4,9],[2,3,5,18],[2,3,9,17],[2,3,13,17],[2,3,13,18],[2,4,5,17], [2,4,9,17],[2,5,17,18],[2,6,7,12],[2,6,7,17],[2,6,11,17],[2,6,11,18], [2,6,12,18],[2,7,12,18],[2,7,17,18],[2,8,13,16],[2,8,13,19], [2,8,14,15],[2,8,14,19],[2,8,15,16],[2,10,11,17],[2,10,11,18], [2,10,13,18],[2,10,13,19],[2,10,17,19],[2,13,15,16],[2,13,15,17], [2,14,15,19],[2,15,17,19],[3,4,5,15],[3,4,5,17],[3,4,6,19],[3,4,8,12], [3,4,8,17],[3,4,9,12],[3,4,15,19],[3,5,6,19],[3,5,10,11],[3,5,10,16], [3,5,11,14],[3,5,14,15],[3,5,16,19],[3,5,17,18],[3,7,10,11], [3,7,10,16],[3,7,11,16],[3,8,9,12],[3,8,9,17],[3,11,14,19], [3,11,16,19],[3,13,17,18],[3,14,15,19],[4,5,6,13],[4,5,6,19], [4,5,7,13],[4,5,15,19],[4,6,7,18],[4,6,13,16],[4,6,14,16],[4,6,14,18], [4,7,11,13],[4,7,11,16],[4,7,14,16],[4,7,14,18],[4,8,9,10],[4,8,9,17], [4,8,10,12],[4,9,10,12],[4,11,13,16],[5,6,7,8],[5,6,7,13],[5,9,14,15], [5,9,14,19],[5,9,15,19],[5,10,11,12],[5,10,12,16],[5,11,12,16], [5,11,14,19],[5,11,16,19],[6,7,8,9],[6,7,12,14],[6,7,13,16], [6,7,14,16],[6,7,17,18],[6,8,9,10],[6,11,17,18],[6,12,14,15], [6,12,15,18],[6,14,15,18],[7,10,11,15],[7,10,15,16],[7,11,13,15], [7,12,14,18],[7,13,15,16],[8,9,11,16],[8,9,12,13],[8,9,13,16], [8,11,13,15],[8,11,15,16],[8,13,15,19],[8,14,15,18],[8,14,18,19], [8,15,18,19],[9,10,12,14],[9,11,13,16],[9,12,14,19],[9,12,15,19], [10,11,12,17],[10,11,15,16],[10,11,16,18],[10,12,14,17],[10,13,17,18], [10,13,17,19],[10,16,17,18],[11,12,16,17],[11,16,17,18],[12,14,18,19], [12,15,18,19],[13,15,17,19]] ## (S^2xS^1)#11 f = (20,180,320,160), g_2 = 110. ## deg = 16,16,16,17,17,17,18,18,18,18,18,19,19,19,19,19,19,19,19,19 facets=[[1,2,3,4],[1,2,3,5],[1,2,4,5],[1,3,4,6],[1,3,5,6],[1,4,5,7], [1,4,6,7],[1,5,6,8],[1,5,7,8],[1,6,7,9],[1,6,8,9],[1,7,8,10], [1,7,9,11],[1,7,10,11],[1,8,9,10],[1,9,10,12],[1,9,11,13],[1,9,12,14], [1,9,13,15],[1,9,14,15],[1,10,11,16],[1,10,12,14],[1,10,14,15], [1,10,15,17],[1,10,16,18],[1,10,17,18],[1,11,13,15],[1,11,15,16], [1,15,16,17],[1,16,17,18],[2,3,4,19],[2,3,5,14],[2,3,7,13],[2,3,7,14], [2,3,13,19],[2,4,5,19],[2,5,13,14],[2,5,13,18],[2,5,18,19],[2,6,8,17], [2,6,8,18],[2,6,12,17],[2,6,12,19],[2,6,18,19],[2,7,13,14],[2,8,17,18], [2,9,11,13],[2,9,11,15],[2,9,13,15],[2,11,13,18],[2,11,15,18], [2,12,15,18],[2,12,15,19],[2,12,17,18],[2,13,15,19],[3,4,5,6], [3,4,5,15],[3,4,9,10],[3,4,9,19],[3,4,10,20],[3,4,15,20],[3,5,9,10], [3,5,9,17],[3,5,10,20],[3,5,13,14],[3,5,13,19],[3,5,15,20],[3,5,16,17], [3,5,16,19],[3,7,12,13],[3,7,12,14],[3,8,16,17],[3,8,16,18], [3,8,17,18],[3,9,16,18],[3,9,16,19],[3,9,17,18],[3,12,13,14],[4,5,6,7], [4,5,9,12],[4,5,9,19],[4,5,10,12],[4,5,10,20],[4,5,11,15],[4,5,11,20], [4,8,13,14],[4,8,13,16],[4,8,14,16],[4,9,10,14],[4,9,12,14], [4,10,12,13],[4,10,13,14],[4,11,15,18],[4,11,18,20],[4,12,13,16], [4,12,14,16],[4,15,18,20],[5,6,7,8],[5,9,10,12],[5,9,16,17], [5,9,16,19],[5,11,15,20],[5,13,18,19],[6,7,8,17],[6,7,9,20], [6,7,17,20],[6,8,9,20],[6,8,11,14],[6,8,11,15],[6,8,14,16],[6,8,15,20], [6,8,16,18],[6,10,16,17],[6,10,16,18],[6,10,17,18],[6,11,13,15], [6,11,13,20],[6,11,14,17],[6,11,17,20],[6,12,17,18],[6,12,18,19], [6,13,15,20],[6,14,16,17],[7,8,9,10],[7,8,9,20],[7,8,12,19], [7,8,12,20],[7,8,17,19],[7,9,10,11],[7,12,13,16],[7,12,14,18], [7,12,15,18],[7,12,15,19],[7,12,16,20],[7,13,14,16],[7,14,16,20], [7,14,18,19],[7,14,19,20],[7,15,18,19],[7,17,19,20],[8,11,14,17], [8,11,15,20],[8,11,17,20],[8,12,19,20],[8,13,14,17],[8,13,16,17], [8,17,19,20],[9,10,11,15],[9,10,14,15],[9,16,17,18],[10,11,15,16], [10,12,13,14],[10,15,16,17],[11,13,18,20],[12,14,16,20],[12,14,18,19], [12,14,19,20],[13,14,16,17],[13,15,18,19],[13,15,18,20]] ## (S^2twistS^1)#11 f = (20,180,320,160), g_2 = 110. ## deg = 16,16,17,17,17,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19 facets=[[1,2,3,4],[1,2,3,5],[1,2,4,5],[1,3,4,6],[1,3,5,6],[1,4,5,7], [1,4,6,7],[1,5,6,8],[1,5,7,8],[1,6,7,9],[1,6,8,9],[1,7,8,10], [1,7,9,11],[1,7,10,12],[1,7,11,12],[1,8,9,10],[1,9,10,11],[1,10,11,13], [1,10,12,14],[1,10,13,15],[1,10,14,15],[1,11,12,13],[1,12,13,16], [1,12,14,16],[1,13,14,16],[1,13,14,17],[1,13,15,18],[1,13,17,18], [1,14,15,18],[1,14,17,18],[2,3,4,14],[2,3,5,14],[2,4,5,19],[2,4,9,12], [2,4,9,14],[2,4,12,19],[2,5,9,12],[2,5,9,14],[2,5,12,15],[2,5,15,18], [2,5,18,19],[2,6,12,15],[2,6,12,18],[2,6,13,15],[2,6,13,18],[2,7,8,16], [2,7,8,19],[2,7,16,19],[2,8,12,16],[2,8,12,19],[2,10,11,19], [2,10,11,20],[2,10,16,17],[2,10,16,18],[2,10,17,20],[2,10,18,19], [2,11,16,17],[2,11,16,19],[2,11,17,20],[2,12,16,18],[2,13,15,18], [3,4,5,14],[3,4,5,20],[3,4,6,13],[3,4,13,20],[3,5,6,10],[3,5,10,20], [3,6,10,11],[3,6,11,20],[3,6,13,20],[3,7,10,11],[3,7,10,12], [3,7,11,12],[3,8,11,18],[3,8,11,20],[3,8,15,16],[3,8,15,18], [3,8,16,19],[3,8,19,20],[3,9,15,17],[3,9,15,20],[3,9,17,20], [3,10,12,17],[3,10,17,20],[3,11,12,17],[3,11,15,17],[3,11,15,18], [3,15,16,20],[3,16,19,20],[4,5,6,7],[4,5,6,20],[4,5,9,12],[4,5,9,17], [4,5,12,19],[4,5,14,17],[4,6,13,15],[4,6,15,18],[4,6,18,20], [4,8,13,15],[4,8,13,18],[4,8,15,18],[4,9,14,17],[4,13,18,20],[5,6,7,8], [5,6,10,20],[5,9,13,14],[5,9,13,17],[5,12,15,18],[5,12,18,19], [5,13,14,17],[6,7,8,16],[6,7,9,14],[6,7,14,17],[6,7,16,19],[6,7,17,19], [6,8,9,19],[6,8,16,19],[6,9,14,17],[6,9,17,19],[6,10,11,20], [6,12,15,18],[6,13,18,20],[7,8,9,10],[7,8,9,19],[7,9,10,11], [7,9,14,18],[7,9,15,19],[7,9,15,20],[7,9,17,18],[7,9,17,20], [7,14,17,18],[7,15,17,19],[7,15,17,20],[8,11,14,15],[8,11,14,18], [8,11,15,20],[8,12,16,20],[8,12,19,20],[8,13,14,15],[8,13,14,18], [8,15,16,20],[9,13,14,18],[9,13,17,18],[9,15,17,19],[10,11,12,13], [10,11,12,17],[10,11,16,17],[10,11,16,19],[10,12,13,14],[10,13,14,15], [10,16,18,19],[11,14,15,18],[11,15,17,20],[12,13,14,19],[12,13,16,19], [12,14,16,20],[12,14,19,20],[12,16,18,19],[13,14,16,19],[14,16,19,20]] ## (S^2xS^1)#14 f = (22,218,392,196), g_2 = 140. ## deg = 17,17,19,19,19,19,20,20,20,20,20,20,20,20,20,20,21,21,21,21,21,21 facets=[[1,2,3,4],[1,2,3,5],[1,2,4,5],[1,3,4,6],[1,3,5,6],[1,4,5,7], [1,4,6,7],[1,5,6,8],[1,5,7,8],[1,6,7,9],[1,6,8,9],[1,7,8,10], [1,7,9,10],[1,8,9,11],[1,8,10,12],[1,8,11,13],[1,8,12,14],[1,8,13,15], [1,8,14,16],[1,8,15,17],[1,8,16,18],[1,8,17,18],[1,9,10,13], [1,9,11,19],[1,9,13,19],[1,10,12,16],[1,10,13,15],[1,10,15,16], [1,11,13,19],[1,12,14,16],[1,15,16,18],[1,15,17,20],[1,15,18,20], [1,17,18,20],[2,3,4,17],[2,3,5,21],[2,3,17,21],[2,4,5,21],[2,4,15,17], [2,4,15,21],[2,6,11,15],[2,6,11,17],[2,6,15,20],[2,6,17,20], [2,7,11,13],[2,7,11,21],[2,7,13,19],[2,7,16,17],[2,7,16,22], [2,7,17,21],[2,7,19,22],[2,8,12,14],[2,8,12,16],[2,8,14,16], [2,9,11,13],[2,9,11,19],[2,9,13,19],[2,11,15,21],[2,11,17,19], [2,12,14,22],[2,12,16,22],[2,14,16,17],[2,14,17,22],[2,15,17,20], [2,17,19,22],[3,4,5,6],[3,4,5,9],[3,4,8,10],[3,4,8,21],[3,4,9,16], [3,4,10,18],[3,4,16,19],[3,4,17,21],[3,4,18,19],[3,5,9,16],[3,5,16,21], [3,7,11,13],[3,7,11,19],[3,7,13,18],[3,7,14,18],[3,7,14,19], [3,8,10,15],[3,8,15,22],[3,8,21,22],[3,10,14,18],[3,10,14,19], [3,10,15,22],[3,10,19,21],[3,10,20,21],[3,10,20,22],[3,11,13,19], [3,13,18,19],[3,16,19,21],[3,20,21,22],[4,5,6,7],[4,5,9,11], [4,5,11,16],[4,5,16,21],[4,8,10,21],[4,9,11,22],[4,9,13,16], [4,9,13,20],[4,9,20,22],[4,10,18,19],[4,10,19,21],[4,11,13,16], [4,11,13,20],[4,11,20,22],[4,12,15,17],[4,12,15,21],[4,12,17,21], [4,16,19,21],[5,6,7,12],[5,6,8,19],[5,6,12,14],[5,6,14,20],[5,6,19,20], [5,7,8,19],[5,7,12,18],[5,7,15,18],[5,7,15,19],[5,9,11,16], [5,12,14,20],[5,12,18,19],[5,12,19,20],[5,15,18,19],[6,7,8,9], [6,7,8,19],[6,7,12,19],[6,10,20,21],[6,10,20,22],[6,10,21,22], [6,11,15,17],[6,12,13,14],[6,12,13,16],[6,12,16,22],[6,12,19,20], [6,12,20,22],[6,13,14,16],[6,14,15,18],[6,14,15,20],[6,14,16,22], [6,14,18,22],[6,15,17,18],[6,17,18,20],[6,18,20,21],[6,18,21,22], [7,8,9,10],[7,11,17,19],[7,11,17,21],[7,12,18,19],[7,13,18,19], [7,14,15,19],[7,14,15,20],[7,14,18,20],[7,15,18,20],[7,16,17,22], [7,17,19,22],[8,9,10,13],[8,9,11,20],[8,9,13,20],[8,10,12,16], [8,10,13,22],[8,10,15,16],[8,10,21,22],[8,11,13,20],[8,13,15,22], [8,15,16,18],[8,15,17,18],[9,11,12,13],[9,11,12,16],[9,11,18,20], [9,11,18,22],[9,12,13,17],[9,12,14,16],[9,12,14,21],[9,12,15,17], [9,12,15,21],[9,13,14,16],[9,13,14,21],[9,13,17,21],[9,15,17,21], [9,18,20,22],[10,13,15,22],[10,14,18,19],[11,12,13,16],[11,14,18,20], [11,14,18,22],[11,14,20,22],[11,15,17,21],[12,13,14,21],[12,13,17,21], [12,14,20,22],[14,15,18,19],[14,16,17,22],[18,20,21,22]] ## (S^2twistS^1)#14 f = (22,218,392,196), g_2 = 140. ## deg = 18,18,19,19,19,19,19,19,19,20,20,20,20,20,20,21,21,21,21,21,21,21 facets=[[1,2,3,4],[1,2,3,5],[1,2,4,5],[1,3,4,6],[1,3,5,6],[1,4,5,7], [1,4,6,7],[1,5,6,8],[1,5,7,8],[1,6,7,9],[1,6,8,9],[1,7,8,10], [1,7,9,10],[1,8,9,11],[1,8,10,12],[1,8,11,12],[1,9,10,11],[1,10,11,13], [1,10,12,14],[1,10,13,15],[1,10,14,16],[1,10,15,17],[1,10,16,18], [1,10,17,19],[1,10,18,19],[1,11,12,13],[1,12,13,19],[1,12,14,18], [1,12,18,19],[1,13,15,19],[1,14,16,18],[1,15,17,20],[1,15,19,21], [1,15,20,21],[1,17,19,20],[1,19,20,21],[2,3,4,12],[2,3,5,12], [2,4,5,10],[2,4,10,13],[2,4,12,13],[2,5,10,12],[2,6,7,18],[2,6,7,20], [2,6,11,12],[2,6,11,14],[2,6,12,20],[2,6,14,18],[2,7,11,13], [2,7,11,14],[2,7,12,13],[2,7,12,15],[2,7,14,21],[2,7,15,20], [2,7,18,21],[2,8,9,15],[2,8,9,17],[2,8,15,22],[2,8,17,22],[2,9,12,15], [2,9,12,22],[2,9,17,22],[2,10,11,12],[2,10,11,13],[2,12,20,22], [2,14,16,18],[2,14,16,21],[2,15,19,20],[2,15,19,22],[2,16,18,21], [2,19,20,22],[3,4,5,9],[3,4,5,12],[3,4,6,19],[3,4,8,18],[3,4,8,19], [3,4,9,20],[3,4,18,20],[3,5,6,19],[3,5,9,19],[3,7,8,10],[3,7,8,22], [3,7,9,10],[3,7,9,22],[3,8,9,10],[3,8,9,18],[3,8,13,14],[3,8,13,16], [3,8,14,17],[3,8,16,19],[3,8,17,22],[3,9,17,19],[3,9,17,22], [3,9,18,20],[3,11,15,16],[3,11,15,17],[3,11,16,17],[3,13,14,21], [3,13,16,17],[3,13,17,21],[3,14,17,21],[3,15,16,19],[3,15,17,19], [4,5,6,11],[4,5,6,19],[4,5,7,11],[4,5,9,19],[4,5,10,12],[4,6,7,11], [4,8,9,18],[4,8,9,19],[4,9,16,18],[4,9,16,20],[4,10,12,21], [4,10,13,22],[4,10,21,22],[4,12,13,21],[4,13,21,22],[4,15,16,17], [4,15,16,18],[4,15,17,20],[4,15,18,20],[4,16,17,20],[5,6,7,8], [5,6,7,14],[5,6,11,21],[5,6,13,21],[5,6,13,22],[5,6,14,15],[5,6,15,16], [5,6,16,22],[5,7,11,14],[5,11,14,15],[5,11,15,16],[5,11,16,22], [5,11,20,21],[5,11,20,22],[5,13,17,18],[5,13,17,21],[5,13,18,22], [5,17,18,21],[5,18,21,22],[5,20,21,22],[6,7,8,9],[6,7,11,12], [6,7,12,20],[6,7,14,18],[6,10,13,21],[6,10,13,22],[6,10,21,22], [6,11,14,15],[6,11,15,17],[6,11,16,17],[6,11,16,22],[6,11,21,22], [6,15,16,17],[7,8,9,22],[7,11,12,13],[7,12,15,20],[7,14,18,21], [8,9,10,11],[8,9,15,22],[8,9,17,19],[8,10,11,12],[8,13,14,17], [8,13,16,17],[8,16,17,19],[9,12,15,22],[9,13,14,18],[9,13,14,21], [9,13,18,21],[9,14,16,20],[9,14,16,21],[9,14,18,20],[9,16,18,21], [10,12,13,19],[10,12,13,21],[10,12,14,18],[10,12,18,19],[10,13,15,19], [10,14,16,20],[10,14,18,20],[10,15,17,19],[10,16,18,20],[11,19,20,21], [11,19,20,22],[11,19,21,22],[12,15,20,22],[13,14,17,18],[13,18,21,22], [14,17,18,21],[15,16,18,20],[15,16,19,20],[15,19,21,22],[15,20,21,22], [16,17,19,20]]