Classification of Cyclic Triangular Actions on Sufaces from Genus 2 to 13 

 
bdata:  2, 10, [ 2, 5, 10 ] 
G = cyclic group Z_10 
1  generating vector(s)
[ <<5, 4, 1>, true> ] 

 
bdata:  2,  8, [ 2, 8, 8 ] 
G = cyclic group Z_8  
1  generating vector(s)
[ <<4, 3, 1>, true> ] 

 
bdata:  2,  6, [ 3, 6, 6 ] 
G = cyclic group Z_6  
1  generating vector(s)
[ <<4, 1, 1>, true> ] 

 
bdata:  2,  5, [ 5, 5, 5 ] 
G = cyclic group Z_5  
1  generating vector(s)
[ <<2, 2, 1>, true> ] 

 
bdata:  3, 14, [ 2, 7, 14 ] 
G = cyclic group Z_14 
1  generating vector(s)
[ <<7, 6, 1>, true> ] 

 
bdata:  3, 12, [ 2, 12, 12 ] 
G = cyclic group Z_12 
1  generating vector(s)
[ <<6, 5, 1>, true> ] 

 
bdata:  3, 12, [ 3, 4, 12 ] 
G = cyclic group Z_12 
1  generating vector(s)
[ <<8, 3, 1>, true> ] 

 
bdata:  3,  9, [ 3, 9, 9 ] 
G = cyclic group Z_9  
1  generating vector(s)
[ <<6, 2, 1>, true> ] 

 
bdata:  3,  8, [ 4, 8, 8 ] 
G = cyclic group Z_8  
2  generating vector(s)
[ <<2, 5, 1>, true>, <<6, 1, 1>, true> ] 

 
bdata:  3,  7, [ 7, 7, 7 ] 
G = cyclic group Z_7  
2  generating vector(s)
[ <<3, 3, 1>, true>, <<2, 4, 1>, true> ] 

 
bdata:  4, 18, [ 2, 9, 18 ] 
G = cyclic group Z_18 
1  generating vector(s)
[ <<9, 8, 1>, true> ] 

 
bdata:  4, 16, [ 2, 16, 16 ] 
G = cyclic group Z_16 
1  generating vector(s)
[ <<8, 7, 1>, true> ] 

 
bdata:  4, 15, [ 3, 5, 15 ] 
G = cyclic group Z_15 
1  generating vector(s)
[ <<5, 9, 1>, true> ] 

 
bdata:  4, 12, [ 3, 12, 12 ] 
G = cyclic group Z_12 
1  generating vector(s)
[ <<4, 7, 1>, true> ] 

 
bdata:  4, 12, [ 4, 6, 12 ] 
G = cyclic group Z_12 
1  generating vector(s)
[ <<9, 2, 1>, true> ] 

 
bdata:  4, 10, [ 5, 10, 10 ] 
G = cyclic group Z_10 
2  generating vector(s)
[ <<2, 7, 1>, true>, <<8, 1, 1>, true> ] 

 
bdata:  4,  9, [ 9, 9, 9 ] 
G = cyclic group Z_9  
1  generating vector(s)
[ <<4, 4, 1>, true> ] 

 
bdata:  5, 22, [ 2, 11, 22 ] 
G = cyclic group Z_22 
1  generating vector(s)
[ <<11, 10, 1>, true> ] 

 
bdata:  5, 20, [ 2, 20, 20 ] 
G = cyclic group Z_20 
1  generating vector(s)
[ <<10, 9, 1>, true> ] 

 
bdata:  5, 15, [ 3, 15, 15 ] 
G = cyclic group Z_15 
1  generating vector(s)
[ <<10, 4, 1>, true> ] 

 
bdata:  5, 12, [ 6, 12, 12 ] 
G = cyclic group Z_12 
1  generating vector(s)
[ <<10, 1, 1>, true> ] 

 
bdata:  5, 11, [ 11, 11, 11 ] 
G = cyclic group Z_11 
2  generating vector(s)
[ <<5, 5, 1>, true>, <<6, 4, 1>, true> ] 

 
bdata:  6, 26, [ 2, 13, 26 ] 
G = cyclic group Z_26 
1  generating vector(s)
[ <<13, 12, 1>, true> ] 

 
bdata:  6, 24, [ 2, 24, 24 ] 
G = cyclic group Z_24 
1  generating vector(s)
[ <<12, 11, 1>, true> ] 

 
bdata:  6, 21, [ 3, 7, 21 ] 
G = cyclic group Z_21 
1  generating vector(s)
[ <<14, 6, 1>, true> ] 

 
bdata:  6, 18, [ 3, 18, 18 ] 
G = cyclic group Z_18 
1  generating vector(s)
[ <<6, 11, 1>, true> ] 

 
bdata:  6, 20, [ 4, 5, 20 ] 
G = cyclic group Z_20 
1  generating vector(s)
[ <<15, 4, 1>, true> ] 

 
bdata:  6, 16, [ 4, 16, 16 ] 
G = cyclic group Z_16 
1  generating vector(s)
[ <<12, 3, 1>, true> ] 

 
bdata:  6, 15, [ 5, 15, 15 ] 
G = cyclic group Z_15 
2  generating vector(s)
[ <<12, 2, 1>, true>, <<3, 11, 1>, true> ] 

 
bdata:  6, 14, [ 7, 14, 14 ] 
G = cyclic group Z_14 
3  generating vector(s)
[ <<10, 3, 1>, true>, <<2, 11, 1>, true>, <<12, 1, 1>, true> ] 

 
bdata:  6, 13, [ 13, 13, 13 ] 
G = cyclic group Z_13 
3  generating vector(s)
[ <<6, 6, 1>, true>, <<7, 5, 1>, true>, <<9, 3, 1>, true> ] 

 
bdata:  7, 30, [ 2, 15, 30 ] 
G = cyclic group Z_30 
1  generating vector(s)
[ <<15, 14, 1>, true> ] 

 
bdata:  7, 28, [ 2, 28, 28 ] 
G = cyclic group Z_28 
1  generating vector(s)
[ <<14, 13, 1>, true> ] 

 
bdata:  7, 24, [ 3, 8, 24 ] 
G = cyclic group Z_24 
1  generating vector(s)
[ <<8, 15, 1>, true> ] 

 
bdata:  7, 21, [ 3, 21, 21 ] 
G = cyclic group Z_21 
1  generating vector(s)
[ <<7, 13, 1>, true> ] 

 
bdata:  7, 20, [ 4, 10, 20 ] 
G = cyclic group Z_20 
1  generating vector(s)
[ <<5, 14, 1>, true> ] 

 
bdata:  7, 18, [ 6, 9, 18 ] 
G = cyclic group Z_18 
2  generating vector(s)
[ <<15, 2, 1>, true>, <<3, 14, 1>, true> ] 

 
bdata:  7, 16, [ 8, 16, 16 ] 
G = cyclic group Z_16 
3  generating vector(s)
[ <<10, 5, 1>, true>, <<6, 9, 1>, true>, <<14, 1, 1>, true> ] 

 
bdata:  7, 15, [ 15, 15, 15 ] 
G = cyclic group Z_15 
1  generating vector(s)
[ <<7, 7, 1>, true> ] 

 
bdata:  8, 34, [ 2, 17, 34 ] 
G = cyclic group Z_34 
1  generating vector(s)
[ <<17, 16, 1>, true> ] 

 
bdata:  8, 32, [ 2, 32, 32 ] 
G = cyclic group Z_32 
1  generating vector(s)
[ <<16, 15, 1>, true> ] 

 
bdata:  8, 24, [ 3, 24, 24 ] 
G = cyclic group Z_24 
1  generating vector(s)
[ <<16, 7, 1>, true> ] 

 
bdata:  8, 20, [ 5, 20, 20 ] 
G = cyclic group Z_20 
2  generating vector(s)
[ <<12, 7, 1>, true>, <<8, 11, 1>, true> ] 

 
bdata:  8, 18, [ 9, 18, 18 ] 
G = cyclic group Z_18 
2  generating vector(s)
[ <<4, 13, 1>, true>, <<16, 1, 1>, true> ] 

 
bdata:  8, 17, [ 17, 17, 17 ] 
G = cyclic group Z_17 
3  generating vector(s)
[ <<8, 8, 1>, true>, <<11, 5, 1>, true>, <<13, 3, 1>, true> ] 

 
bdata:  9, 38, [ 2, 19, 38 ] 
G = cyclic group Z_38 
1  generating vector(s)
[ <<19, 18, 1>, true> ] 

 
bdata:  9, 36, [ 2, 36, 36 ] 
G = cyclic group Z_36 
1  generating vector(s)
[ <<18, 17, 1>, true> ] 

 
bdata:  9, 30, [ 3, 10, 30 ] 
G = cyclic group Z_30 
1  generating vector(s)
[ <<20, 9, 1>, true> ] 

 
bdata:  9, 27, [ 3, 27, 27 ] 
G = cyclic group Z_27 
1  generating vector(s)
[ <<18, 8, 1>, true> ] 

 
bdata:  9, 28, [ 4, 7, 28 ] 
G = cyclic group Z_28 
1  generating vector(s)
[ <<7, 20, 1>, true> ] 

 
bdata:  9, 24, [ 4, 24, 24 ] 
G = cyclic group Z_24 
2  generating vector(s)
[ <<18, 5, 1>, true>, <<6, 17, 1>, true> ] 

 
bdata:  9, 24, [ 6, 8, 24 ] 
G = cyclic group Z_24 
1  generating vector(s)
[ <<20, 3, 1>, true> ] 

 
bdata:  9, 21, [ 7, 21, 21 ] 
G = cyclic group Z_21 
3  generating vector(s)
[ <<3, 17, 1>, true>, <<18, 2, 1>, true>, <<12, 8, 1>, true> ] 

 
bdata:  9, 20, [ 10, 20, 20 ] 
G = cyclic group Z_20 
2  generating vector(s)
[ <<2, 17, 1>, true>, <<18, 1, 1>, true> ] 

 
bdata:  9, 19, [ 19, 19, 19 ] 
G = cyclic group Z_19 
4  generating vector(s)
[ <<9, 9, 1>, true>, <<11, 7, 1>, true>, <<13, 5, 1>, true>, <<10, 8, 1>, true> ] 

 
bdata: 10, 42, [ 2, 21, 42 ] 
G = cyclic group Z_42 
1  generating vector(s)
[ <<21, 20, 1>, true> ] 

 
bdata: 10, 40, [ 2, 40, 40 ] 
G = cyclic group Z_40 
1  generating vector(s)
[ <<20, 19, 1>, true> ] 

 
bdata: 10, 33, [ 3, 11, 33 ] 
G = cyclic group Z_33 
1  generating vector(s)
[ <<11, 21, 1>, true> ] 

 
bdata: 10, 30, [ 3, 30, 30 ] 
G = cyclic group Z_30 
1  generating vector(s)
[ <<10, 19, 1>, true> ] 

 
bdata: 10, 28, [ 4, 14, 28 ] 
G = cyclic group Z_28 
1  generating vector(s)
[ <<21, 6, 1>, true> ] 

 
bdata: 10, 30, [ 5, 6, 30 ] 
G = cyclic group Z_30 
1  generating vector(s)
[ <<24, 5, 1>, true> ] 

 
bdata: 10, 25, [ 5, 25, 25 ] 
G = cyclic group Z_25 
2  generating vector(s)
[ <<20, 4, 1>, true>, <<15, 9, 1>, true> ] 

 
bdata: 10, 24, [ 6, 24, 24 ] 
G = cyclic group Z_24 
1  generating vector(s)
[ <<4, 19, 1>, true> ] 

 
bdata: 10, 24, [ 8, 12, 24 ] 
G = cyclic group Z_24 
2  generating vector(s)
[ <<21, 2, 1>, true>, <<9, 14, 1>, true> ] 

 
bdata: 10, 22, [ 11, 22, 22 ] 
G = cyclic group Z_22 
5  generating vector(s)
[ <<16, 5, 1>, true>, <<14, 7, 1>, true>, <<20, 1, 1>, true>, <<18, 3, 1>, true>, <<4, 17, 1>, true> ] 

 
bdata: 10, 21, [ 21, 21, 21 ] 
G = cyclic group Z_21 
2  generating vector(s)
[ <<10, 10, 1>, true>, <<16, 4, 1>, true> ] 

 
bdata: 11, 46, [ 2, 23, 46 ] 
G = cyclic group Z_46 
1  generating vector(s)
[ <<23, 22, 1>, true> ] 

 
bdata: 11, 44, [ 2, 44, 44 ] 
G = cyclic group Z_44 
1  generating vector(s)
[ <<22, 21, 1>, true> ] 

 
bdata: 11, 33, [ 3, 33, 33 ] 
G = cyclic group Z_33 
1  generating vector(s)
[ <<22, 10, 1>, true> ] 

 
bdata: 11, 30, [ 6, 10, 15 ] 
G = cyclic group Z_30 
1  generating vector(s)
[ <<5, 9, 16>, true> ] 

 
bdata: 11, 24, [ 12, 24, 24 ] 
G = cyclic group Z_24 
2  generating vector(s)
[ <<10, 13, 1>, true>, <<22, 1, 1>, true> ] 

 
bdata: 11, 23, [ 23, 23, 23 ] 
G = cyclic group Z_23 
4  generating vector(s)
[ <<11, 11, 1>, true>, <<13, 9, 1>, true>, <<20, 2, 1>, true>, <<17, 5, 1>, true> ] 

 
bdata: 12, 50, [ 2, 25, 50 ] 
G = cyclic group Z_50 
1  generating vector(s)
[ <<25, 24, 1>, true> ] 

 
bdata: 12, 48, [ 2, 48, 48 ] 
G = cyclic group Z_48 
1  generating vector(s)
[ <<24, 23, 1>, true> ] 

 
bdata: 12, 39, [ 3, 13, 39 ] 
G = cyclic group Z_39 
1  generating vector(s)
[ <<26, 12, 1>, true> ] 

 
bdata: 12, 36, [ 3, 36, 36 ] 
G = cyclic group Z_36 
1  generating vector(s)
[ <<24, 11, 1>, true> ] 

 
bdata: 12, 36, [ 4, 9, 36 ] 
G = cyclic group Z_36 
1  generating vector(s)
[ <<27, 8, 1>, true> ] 

 
bdata: 12, 32, [ 4, 32, 32 ] 
G = cyclic group Z_32 
1  generating vector(s)
[ <<24, 7, 1>, true> ] 

 
bdata: 12, 35, [ 5, 7, 35 ] 
G = cyclic group Z_35 
1  generating vector(s)
[ <<14, 20, 1>, true> ] 

 
bdata: 12, 30, [ 5, 30, 30 ] 
G = cyclic group Z_30 
2  generating vector(s)
[ <<12, 17, 1>, true>, <<18, 11, 1>, true> ] 

 
bdata: 12, 30, [ 6, 15, 30 ] 
G = cyclic group Z_30 
1  generating vector(s)
[ <<25, 4, 1>, true> ] 

 
bdata: 12, 28, [ 7, 28, 28 ] 
G = cyclic group Z_28 
3  generating vector(s)
[ <<24, 3, 1>, true>, <<16, 11, 1>, true>, <<12, 15, 1>, true> ] 

 
bdata: 12, 27, [ 9, 27, 27 ] 
G = cyclic group Z_27 
3  generating vector(s)
[ <<6, 20, 1>, true>, <<21, 5, 1>, true>, <<24, 2, 1>, true> ] 

 
bdata: 12, 26, [ 13, 26, 26 ] 
G = cyclic group Z_26 
6  generating vector(s)
[ <<6, 19, 1>, true>, <<8, 17, 1>, true>, <<18, 7, 1>, true>, <<20, 5, 1>, true>, <<22, 3, 1>, true>, <<24, 1, 1>, true> ] 

 
bdata: 12, 25, [ 25, 25, 25 ] 
G = cyclic group Z_25 
3  generating vector(s)
[ <<12, 12, 1>, true>, <<2, 22, 1>, true>, <<3, 21, 1>, true> ] 

 
bdata: 13, 54, [ 2, 27, 54 ] 
G = cyclic group Z_54 
1  generating vector(s)
[ <<27, 26, 1>, true> ] 

 
bdata: 13, 52, [ 2, 52, 52 ] 
G = cyclic group Z_52 
1  generating vector(s)
[ <<26, 25, 1>, true> ] 

 
bdata: 13, 42, [ 3, 14, 42 ] 
G = cyclic group Z_42 
1  generating vector(s)
[ <<14, 27, 1>, true> ] 

 
bdata: 13, 39, [ 3, 39, 39 ] 
G = cyclic group Z_39 
1  generating vector(s)
[ <<13, 25, 1>, true> ] 

 
bdata: 13, 36, [ 4, 18, 36 ] 
G = cyclic group Z_36 
1  generating vector(s)
[ <<9, 26, 1>, true> ] 

 
bdata: 13, 30, [ 10, 15, 30 ] 
G = cyclic group Z_30 
3  generating vector(s)
[ <<27, 2, 1>, true>, <<21, 8, 1>, true>, <<3, 26, 1>, true> ] 

 
bdata: 13, 28, [ 14, 28, 28 ] 
G = cyclic group Z_28 
3  generating vector(s)
[ <<10, 17, 1>, true>, <<2, 25, 1>, true>, <<26, 1, 1>, true> ] 

 
bdata: 13, 27, [ 27, 27, 27 ] 
G = cyclic group Z_27 
2  generating vector(s)
[ <<13, 13, 1>, true>, <<22, 4, 1>, true> ] 
 
 ### summary #### 
total  groupBDpairs: 93 

total actions: 144 

total kaleidoscopic actions: 144 

total non-kaleidoscopic actions: 0 

multiple actions: [
[ 1, 63 ],
[ 2, 16 ],
[ 3, 10 ],
[ 4, 2 ],
[ 5, 1 ],
[ 6, 1 ]
] 

groupBDpairs in genus: [
undef,
[ 2, 4 ],
[ 3, 6 ],
[ 4, 7 ],
[ 5, 5 ],
[ 6, 9 ],
[ 7, 8 ],
[ 8, 6 ],
[ 9, 10 ],
[ 10, 11 ],
[ 11, 6 ],
[ 12, 13 ],
[ 13, 8 ]
] 

actions in genus: [
undef,
[ 2, 4 ],
[ 3, 8 ],
[ 4, 8 ],
[ 5, 6 ],
[ 6, 14 ],
[ 7, 11 ],
[ 8, 10 ],
[ 9, 17 ],
[ 10, 18 ],
[ 11, 10 ],
[ 12, 25 ],
[ 13, 13 ]
] 

kaleidoscopic actions in genus: [
undef,
[ 2, 4 ],
[ 3, 8 ],
[ 4, 8 ],
[ 5, 6 ],
[ 6, 14 ],
[ 7, 11 ],
[ 8, 10 ],
[ 9, 17 ],
[ 10, 18 ],
[ 11, 10 ],
[ 12, 25 ],
[ 13, 13 ]
] 

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 ]
]