Classification of 2-generator Abelian Triangular Actions on Sufaces from Genus 2 to 13 bdata: 2 12 [ 2, 6, 6 ] G = 2 generator abelian group Z_2 x Z_6 1 generating vector(s) [ <<[ 1, 0 ], [ 1, 5 ], [ 0, 1 ]>, true> ] bdata: 3 16 [ 2, 8, 8 ] G = 2 generator abelian group Z_2 x Z_8 1 generating vector(s) [ <<[ 1, 0 ], [ 0, 1 ], [ 1, 7 ]>, true> ] bdata: 3 16 [ 4, 4, 4 ] G = 2 generator abelian group Z_4 x Z_4 1 generating vector(s) [ <<[ 1, 0 ], [ 3, 1 ], [ 0, 3 ]>, true> ] bdata: 4 20 [ 2, 10, 10 ] G = 2 generator abelian group Z_2 x Z_10 1 generating vector(s) [ <<[ 1, 0 ], [ 1, 1 ], [ 0, 9 ]>, true> ] bdata: 4 18 [ 3, 6, 6 ] G = 2 generator abelian group Z_3 x Z_6 1 generating vector(s) [ <<[ 1, 0 ], [ 2, 5 ], [ 0, 1 ]>, true> ] bdata: 4 12 [ 6, 6, 6 ] G = 2 generator abelian group Z_2 x Z_6 1 generating vector(s) [ <<[ 1, 2 ], [ 1, 5 ], [ 0, 5 ]>, true> ] bdata: 5 24 [ 2, 12, 12 ] G = 2 generator abelian group Z_2 x Z_12 1 generating vector(s) [ <<[ 1, 0 ], [ 0, 7 ], [ 1, 5 ]>, true> ] bdata: 5 16 [ 4, 8, 8 ] G = 2 generator abelian group Z_2 x Z_8 1 generating vector(s) [ <<[ 1, 2 ], [ 0, 1 ], [ 1, 5 ]>, true> ] bdata: 6 28 [ 2, 14, 14 ] G = 2 generator abelian group Z_2 x Z_14 1 generating vector(s) [ <<[ 1, 0 ], [ 0, 11 ], [ 1, 3 ]>, true> ] bdata: 6 25 [ 5, 5, 5 ] G = 2 generator abelian group Z_5 x Z_5 1 generating vector(s) [ <<[ 1, 0 ], [ 0, 3 ], [ 4, 2 ]>, true> ] bdata: 7 32 [ 2, 16, 16 ] G = 2 generator abelian group Z_2 x Z_16 1 generating vector(s) [ <<[ 1, 0 ], [ 0, 1 ], [ 1, 15 ]>, true> ] bdata: 7 27 [ 3, 9, 9 ] G = 2 generator abelian group Z_3 x Z_9 1 generating vector(s) [ <<[ 1, 0 ], [ 0, 1 ], [ 2, 8 ]>, true> ] bdata: 7 24 [ 4, 6, 12 ] G = 2 generator abelian group Z_2 x Z_12 1 generating vector(s) [ <<[ 0, 3 ], [ 1, 4 ], [ 1, 5 ]>, true> ] bdata: 8 36 [ 2, 18, 18 ] G = 2 generator abelian group Z_2 x Z_18 1 generating vector(s) [ <<[ 1, 0 ], [ 1, 13 ], [ 0, 5 ]>, true> ] bdata: 8 20 [ 10, 10, 10 ] G = 2 generator abelian group Z_2 x Z_10 1 generating vector(s) [ <<[ 1, 2 ], [ 0, 7 ], [ 1, 1 ]>, true> ] bdata: 9 40 [ 2, 20, 20 ] G = 2 generator abelian group Z_2 x Z_20 1 generating vector(s) [ <<[ 1, 0 ], [ 0, 9 ], [ 1, 11 ]>, true> ] bdata: 9 32 [ 4, 8, 8 ] G = 2 generator abelian group Z_4 x Z_8 1 generating vector(s) [ <<[ 1, 0 ], [ 0, 1 ], [ 3, 7 ]>, true> ] bdata: 9 24 [ 6, 12, 12 ] G = 2 generator abelian group Z_2 x Z_12 1 generating vector(s) [ <<[ 1, 4 ], [ 0, 7 ], [ 1, 1 ]>, true> ] bdata: 10 44 [ 2, 22, 22 ] G = 2 generator abelian group Z_2 x Z_22 1 generating vector(s) [ <<[ 1, 0 ], [ 1, 1 ], [ 0, 21 ]>, true> ] bdata: 10 36 [ 3, 12, 12 ] G = 2 generator abelian group Z_3 x Z_12 1 generating vector(s) [ <<[ 1, 0 ], [ 0, 5 ], [ 2, 7 ]>, true> ] bdata: 10 36 [ 6, 6, 6 ] G = 2 generator abelian group Z_6 x Z_6 1 generating vector(s) [ <<[ 5, 0 ], [ 4, 1 ], [ 3, 5 ]>, true> ] bdata: 10 27 [ 9, 9, 9 ] G = 2 generator abelian group Z_3 x Z_9 1 generating vector(s) [ <<[ 0, 1 ], [ 2, 4 ], [ 1, 4 ]>, true> ] bdata: 11 48 [ 2, 24, 24 ] G = 2 generator abelian group Z_2 x Z_24 1 generating vector(s) [ <<[ 1, 0 ], [ 0, 11 ], [ 1, 13 ]>, true> ] bdata: 11 32 [ 4, 16, 16 ] G = 2 generator abelian group Z_2 x Z_16 1 generating vector(s) [ <<[ 1, 4 ], [ 0, 1 ], [ 1, 11 ]>, true> ] bdata: 12 52 [ 2, 26, 26 ] G = 2 generator abelian group Z_2 x Z_26 1 generating vector(s) [ <<[ 1, 0 ], [ 1, 9 ], [ 0, 17 ]>, true> ] bdata: 12 28 [ 14, 14, 14 ] G = 2 generator abelian group Z_2 x Z_14 2 generating vector(s) [ <<[ 1, 2 ], [ 0, 13 ], [ 1, 13 ]>, true>, <<[ 1, 2 ], [ 0, 11 ], [ 1, 1 ]>, true> ] bdata: 13 56 [ 2, 28, 28 ] G = 2 generator abelian group Z_2 x Z_28 1 generating vector(s) [ <<[ 1, 0 ], [ 0, 11 ], [ 1, 17 ]>, true> ] bdata: 13 45 [ 3, 15, 15 ] G = 2 generator abelian group Z_3 x Z_15 1 generating vector(s) [ <<[ 1, 0 ], [ 0, 11 ], [ 2, 4 ]>, true> ] bdata: 13 40 [ 4, 10, 20 ] G = 2 generator abelian group Z_2 x Z_20 1 generating vector(s) [ <<[ 0, 5 ], [ 1, 4 ], [ 1, 11 ]>, true> ] bdata: 13 36 [ 6, 12, 12 ] G = 2 generator abelian group Z_3 x Z_12 1 generating vector(s) [ <<[ 1, 6 ], [ 0, 5 ], [ 2, 1 ]>, true> ] bdata: 13 32 [ 8, 16, 16 ] G = 2 generator abelian group Z_2 x Z_16 2 generating vector(s) [ <<[ 1, 2 ], [ 0, 1 ], [ 1, 13 ]>, true>, <<[ 1, 2 ], [ 1, 15 ], [ 0, 15 ]>, true> ] ### summary #### total groupBDpairs: 31 total actions: 33 total kaleidoscopic actions: 33 total non kaleidoscopic actions: 0 multiple actions: [ [ 1, 29 ], [ 2, 2 ] ] groupBDpairs in genus: [ undef, [ 2, 1 ], [ 3, 2 ], [ 4, 3 ], [ 5, 2 ], [ 6, 2 ], [ 7, 3 ], [ 8, 2 ], [ 9, 3 ], [ 10, 4 ], [ 11, 2 ], [ 12, 2 ], [ 13, 5 ] ] actions in genus: [ undef, [ 2, 1 ], [ 3, 2 ], [ 4, 3 ], [ 5, 2 ], [ 6, 2 ], [ 7, 3 ], [ 8, 2 ], [ 9, 3 ], [ 10, 4 ], [ 11, 2 ], [ 12, 3 ], [ 13, 6 ] ] kaleidoscopic actions in genus: [ undef, [ 2, 1 ], [ 3, 2 ], [ 4, 3 ], [ 5, 2 ], [ 6, 2 ], [ 7, 3 ], [ 8, 2 ], [ 9, 3 ], [ 10, 4 ], [ 11, 2 ], [ 12, 3 ], [ 13, 6 ] ] non-kaleidoscopic actions in genus: [ undef, [ 2, 0 ], [ 3, 0 ], [ 4, 0 ], [ 5, 0 ], [ 6, 0 ], [ 7, 0 ], [ 8, 0 ], [ 9, 0 ], [ 10, 0 ], [ 11, 0 ], [ 12, 0 ], [ 13, 0 ] ]