Questions?
See the FAQ
or other info.

# Polytope of Type {2,10}

Atlas Canonical Name : {2,10}*40
if this polytope has a name.
Group : SmallGroup(40,13)
Rank : 3
Schlafli Type : {2,10}
Number of vertices, edges, etc : 2, 10, 10
Order of s0s1s2 : 10
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,10,2} of size 80
{2,10,4} of size 160
{2,10,5} of size 200
{2,10,3} of size 240
{2,10,3} of size 240
{2,10,5} of size 240
{2,10,5} of size 240
{2,10,6} of size 240
{2,10,8} of size 320
{2,10,4} of size 400
{2,10,10} of size 400
{2,10,10} of size 400
{2,10,10} of size 400
{2,10,12} of size 480
{2,10,4} of size 480
{2,10,4} of size 480
{2,10,6} of size 480
{2,10,6} of size 480
{2,10,3} of size 480
{2,10,5} of size 480
{2,10,6} of size 480
{2,10,6} of size 480
{2,10,6} of size 480
{2,10,6} of size 480
{2,10,10} of size 480
{2,10,10} of size 480
{2,10,10} of size 480
{2,10,10} of size 480
{2,10,14} of size 560
{2,10,3} of size 600
{2,10,6} of size 600
{2,10,15} of size 600
{2,10,16} of size 640
{2,10,5} of size 640
{2,10,4} of size 640
{2,10,4} of size 640
{2,10,5} of size 640
{2,10,18} of size 720
{2,10,3} of size 720
{2,10,15} of size 720
{2,10,20} of size 800
{2,10,20} of size 800
{2,10,20} of size 800
{2,10,4} of size 800
{2,10,22} of size 880
{2,10,24} of size 960
{2,10,6} of size 960
{2,10,4} of size 960
{2,10,4} of size 960
{2,10,12} of size 960
{2,10,12} of size 960
{2,10,12} of size 960
{2,10,12} of size 960
{2,10,20} of size 960
{2,10,20} of size 960
{2,10,4} of size 960
{2,10,6} of size 960
{2,10,6} of size 960
{2,10,10} of size 960
{2,10,25} of size 1000
{2,10,5} of size 1000
{2,10,10} of size 1000
{2,10,26} of size 1040
{2,10,28} of size 1120
{2,10,5} of size 1200
{2,10,15} of size 1200
{2,10,6} of size 1200
{2,10,6} of size 1200
{2,10,12} of size 1200
{2,10,30} of size 1200
{2,10,30} of size 1200
{2,10,30} of size 1200
{2,10,32} of size 1280
{2,10,5} of size 1280
{2,10,8} of size 1280
{2,10,8} of size 1280
{2,10,8} of size 1280
{2,10,8} of size 1280
{2,10,10} of size 1280
{2,10,10} of size 1280
{2,10,10} of size 1280
{2,10,4} of size 1280
{2,10,4} of size 1280
{2,10,10} of size 1280
{2,10,34} of size 1360
{2,10,35} of size 1400
{2,10,36} of size 1440
{2,10,3} of size 1440
{2,10,4} of size 1440
{2,10,5} of size 1440
{2,10,8} of size 1440
{2,10,8} of size 1440
{2,10,10} of size 1440
{2,10,10} of size 1440
{2,10,6} of size 1440
{2,10,12} of size 1440
{2,10,3} of size 1440
{2,10,6} of size 1440
{2,10,6} of size 1440
{2,10,15} of size 1440
{2,10,30} of size 1440
{2,10,30} of size 1440
{2,10,38} of size 1520
{2,10,40} of size 1600
{2,10,40} of size 1600
{2,10,40} of size 1600
{2,10,8} of size 1600
{2,10,21} of size 1680
{2,10,35} of size 1680
{2,10,42} of size 1680
{2,10,44} of size 1760
{2,10,9} of size 1800
{2,10,18} of size 1800
{2,10,45} of size 1800
{2,10,46} of size 1840
{2,10,48} of size 1920
{2,10,12} of size 1920
{2,10,15} of size 1920
{2,10,8} of size 1920
{2,10,8} of size 1920
{2,10,24} of size 1920
{2,10,24} of size 1920
{2,10,24} of size 1920
{2,10,24} of size 1920
{2,10,40} of size 1920
{2,10,40} of size 1920
{2,10,4} of size 1920
{2,10,12} of size 1920
{2,10,12} of size 1920
{2,10,20} of size 1920
{2,10,6} of size 1920
{2,10,8} of size 1920
{2,10,8} of size 1920
{2,10,12} of size 1920
{2,10,12} of size 1920
{2,10,20} of size 1920
{2,10,6} of size 1920
{2,10,10} of size 1920
{2,10,4} of size 2000
{2,10,20} of size 2000
{2,10,20} of size 2000
{2,10,20} of size 2000
{2,10,20} of size 2000
{2,10,50} of size 2000
{2,10,50} of size 2000
{2,10,10} of size 2000
{2,10,10} of size 2000
{2,10,10} of size 2000
{2,10,20} of size 2000
{2,10,10} of size 2000
Vertex Figure Of :
{2,2,10} of size 80
{3,2,10} of size 120
{4,2,10} of size 160
{5,2,10} of size 200
{6,2,10} of size 240
{7,2,10} of size 280
{8,2,10} of size 320
{9,2,10} of size 360
{10,2,10} of size 400
{11,2,10} of size 440
{12,2,10} of size 480
{13,2,10} of size 520
{14,2,10} of size 560
{15,2,10} of size 600
{16,2,10} of size 640
{17,2,10} of size 680
{18,2,10} of size 720
{19,2,10} of size 760
{20,2,10} of size 800
{21,2,10} of size 840
{22,2,10} of size 880
{23,2,10} of size 920
{24,2,10} of size 960
{25,2,10} of size 1000
{26,2,10} of size 1040
{27,2,10} of size 1080
{28,2,10} of size 1120
{29,2,10} of size 1160
{30,2,10} of size 1200
{31,2,10} of size 1240
{32,2,10} of size 1280
{33,2,10} of size 1320
{34,2,10} of size 1360
{35,2,10} of size 1400
{36,2,10} of size 1440
{37,2,10} of size 1480
{38,2,10} of size 1520
{39,2,10} of size 1560
{40,2,10} of size 1600
{41,2,10} of size 1640
{42,2,10} of size 1680
{43,2,10} of size 1720
{44,2,10} of size 1760
{45,2,10} of size 1800
{46,2,10} of size 1840
{47,2,10} of size 1880
{48,2,10} of size 1920
{49,2,10} of size 1960
{50,2,10} of size 2000
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,5}*20
5-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,20}*80, {4,10}*80
3-fold covers : {6,10}*120, {2,30}*120
4-fold covers : {4,20}*160, {2,40}*160, {8,10}*160
5-fold covers : {2,50}*200, {10,10}*200a, {10,10}*200b
6-fold covers : {12,10}*240, {6,20}*240a, {2,60}*240, {4,30}*240a
7-fold covers : {14,10}*280, {2,70}*280
8-fold covers : {4,40}*320a, {4,20}*320, {4,40}*320b, {8,20}*320a, {8,20}*320b, {2,80}*320, {16,10}*320
9-fold covers : {18,10}*360, {2,90}*360, {6,30}*360a, {6,30}*360b, {6,30}*360c
10-fold covers : {2,100}*400, {4,50}*400, {10,20}*400a, {10,20}*400b, {20,10}*400a, {20,10}*400c
11-fold covers : {22,10}*440, {2,110}*440
12-fold covers : {24,10}*480, {6,40}*480, {12,20}*480, {4,60}*480a, {2,120}*480, {8,30}*480, {6,20}*480c, {6,30}*480, {4,30}*480
13-fold covers : {26,10}*520, {2,130}*520
14-fold covers : {14,20}*560, {28,10}*560, {2,140}*560, {4,70}*560
15-fold covers : {6,50}*600, {2,150}*600, {30,10}*600a, {10,30}*600b, {10,30}*600c, {30,10}*600b
16-fold covers : {4,40}*640a, {8,40}*640a, {8,40}*640b, {8,20}*640a, {8,40}*640c, {8,40}*640d, {4,80}*640a, {4,80}*640b, {4,20}*640a, {4,40}*640b, {8,20}*640b, {16,20}*640a, {16,20}*640b, {2,160}*640, {32,10}*640, {4,10}*640b
17-fold covers : {34,10}*680, {2,170}*680
18-fold covers : {36,10}*720, {18,20}*720a, {2,180}*720, {4,90}*720a, {6,60}*720a, {12,30}*720a, {12,30}*720b, {6,60}*720b, {6,60}*720c, {12,30}*720c, {4,20}*720, {4,30}*720, {6,20}*720
19-fold covers : {38,10}*760, {2,190}*760
20-fold covers : {4,100}*800, {2,200}*800, {8,50}*800, {10,40}*800a, {10,40}*800b, {40,10}*800a, {20,20}*800a, {20,20}*800b, {40,10}*800c
21-fold covers : {14,30}*840, {42,10}*840, {6,70}*840, {2,210}*840
22-fold covers : {22,20}*880, {44,10}*880, {2,220}*880, {4,110}*880
23-fold covers : {46,10}*920, {2,230}*920
24-fold covers : {48,10}*960, {6,80}*960, {12,20}*960a, {24,20}*960a, {12,40}*960a, {24,20}*960b, {12,40}*960b, {4,120}*960a, {4,60}*960a, {4,120}*960b, {8,60}*960a, {8,60}*960b, {2,240}*960, {16,30}*960, {12,20}*960b, {6,20}*960e, {6,60}*960a, {12,30}*960a, {6,30}*960, {6,40}*960d, {6,40}*960e, {6,60}*960b, {12,20}*960c, {12,30}*960b, {4,60}*960b, {4,30}*960b, {4,60}*960c, {8,30}*960b, {8,30}*960c
25-fold covers : {2,250}*1000, {10,50}*1000a, {10,50}*1000b, {50,10}*1000a, {10,10}*1000b, {10,10}*1000c, {10,10}*1000d
26-fold covers : {26,20}*1040, {52,10}*1040, {2,260}*1040, {4,130}*1040
27-fold covers : {54,10}*1080, {2,270}*1080, {18,30}*1080a, {6,30}*1080a, {6,90}*1080a, {6,90}*1080b, {18,30}*1080b, {6,30}*1080b, {6,30}*1080c, {6,30}*1080d
28-fold covers : {14,40}*1120, {56,10}*1120, {28,20}*1120, {4,140}*1120, {2,280}*1120, {8,70}*1120
29-fold covers : {58,10}*1160, {2,290}*1160
30-fold covers : {12,50}*1200, {6,100}*1200a, {2,300}*1200, {4,150}*1200a, {30,20}*1200a, {60,10}*1200a, {20,30}*1200b, {30,20}*1200b, {10,60}*1200b, {10,60}*1200c, {60,10}*1200b, {20,30}*1200c
31-fold covers : {62,10}*1240, {2,310}*1240
32-fold covers : {8,40}*1280a, {8,20}*1280a, {8,40}*1280b, {4,40}*1280a, {8,40}*1280c, {8,40}*1280d, {16,20}*1280a, {4,80}*1280a, {16,20}*1280b, {4,80}*1280b, {8,80}*1280a, {16,40}*1280a, {8,80}*1280b, {16,40}*1280b, {16,40}*1280c, {8,80}*1280c, {8,80}*1280d, {16,40}*1280d, {16,40}*1280e, {8,80}*1280e, {8,80}*1280f, {16,40}*1280f, {32,20}*1280a, {4,160}*1280a, {32,20}*1280b, {4,160}*1280b, {4,20}*1280a, {4,40}*1280b, {8,20}*1280b, {8,20}*1280c, {8,40}*1280e, {4,40}*1280c, {4,40}*1280d, {8,20}*1280d, {8,40}*1280f, {8,40}*1280g, {8,40}*1280h, {64,10}*1280, {2,320}*1280, {4,10}*1280a, {4,20}*1280b, {4,20}*1280c, {8,10}*1280c, {4,10}*1280b, {4,20}*1280d, {8,10}*1280d, {4,20}*1280e, {4,10}*1280c, {8,10}*1280e, {8,10}*1280f
33-fold covers : {22,30}*1320, {66,10}*1320, {6,110}*1320, {2,330}*1320
34-fold covers : {34,20}*1360, {68,10}*1360, {2,340}*1360, {4,170}*1360
35-fold covers : {14,50}*1400, {2,350}*1400, {70,10}*1400a, {10,70}*1400b, {10,70}*1400c, {70,10}*1400b
36-fold covers : {72,10}*1440, {18,40}*1440, {36,20}*1440, {4,180}*1440a, {2,360}*1440, {8,90}*1440, {6,120}*1440a, {24,30}*1440a, {12,60}*1440a, {24,30}*1440b, {6,120}*1440b, {6,120}*1440c, {12,60}*1440b, {12,60}*1440c, {24,30}*1440c, {18,20}*1440, {4,90}*1440, {4,20}*1440, {4,60}*1440, {8,30}*1440, {6,40}*1440, {12,20}*1440, {6,30}*1440g, {6,60}*1440c, {12,30}*1440a, {12,30}*1440b, {6,30}*1440h, {6,60}*1440d
37-fold covers : {74,10}*1480, {2,370}*1480
38-fold covers : {38,20}*1520, {76,10}*1520, {2,380}*1520, {4,190}*1520
39-fold covers : {26,30}*1560, {78,10}*1560, {6,130}*1560, {2,390}*1560
40-fold covers : {4,200}*1600a, {4,100}*1600, {4,200}*1600b, {8,100}*1600a, {8,100}*1600b, {2,400}*1600, {16,50}*1600, {10,80}*1600a, {10,80}*1600b, {80,10}*1600a, {40,20}*1600a, {20,20}*1600a, {20,20}*1600b, {40,20}*1600b, {20,40}*1600c, {20,40}*1600d, {40,20}*1600c, {20,40}*1600e, {20,40}*1600f, {40,20}*1600e, {80,10}*1600c
41-fold covers : {82,10}*1640, {2,410}*1640
42-fold covers : {14,60}*1680, {28,30}*1680a, {42,20}*1680a, {84,10}*1680, {12,70}*1680, {6,140}*1680a, {2,420}*1680, {4,210}*1680a
43-fold covers : {86,10}*1720, {2,430}*1720
44-fold covers : {22,40}*1760, {88,10}*1760, {44,20}*1760, {4,220}*1760, {2,440}*1760, {8,110}*1760
45-fold covers : {18,50}*1800, {2,450}*1800, {6,150}*1800a, {6,150}*1800b, {6,150}*1800c, {90,10}*1800a, {10,90}*1800b, {10,90}*1800c, {90,10}*1800b, {30,30}*1800a, {30,30}*1800b, {30,30}*1800c, {30,30}*1800d, {30,30}*1800g, {30,30}*1800h
46-fold covers : {46,20}*1840, {92,10}*1840, {2,460}*1840, {4,230}*1840
47-fold covers : {94,10}*1880, {2,470}*1880
48-fold covers : {8,60}*1920a, {4,120}*1920a, {12,40}*1920a, {24,20}*1920a, {8,120}*1920a, {8,120}*1920b, {8,120}*1920c, {24,40}*1920a, {24,40}*1920b, {24,40}*1920c, {8,120}*1920d, {24,40}*1920d, {16,60}*1920a, {4,240}*1920a, {12,80}*1920a, {48,20}*1920a, {16,60}*1920b, {4,240}*1920b, {12,80}*1920b, {48,20}*1920b, {4,60}*1920a, {4,120}*1920b, {8,60}*1920b, {12,40}*1920b, {24,20}*1920b, {12,20}*1920a, {32,30}*1920, {2,480}*1920, {96,10}*1920, {6,160}*1920, {6,30}*1920a, {6,40}*1920a, {12,40}*1920e, {12,40}*1920f, {12,60}*1920a, {12,60}*1920b, {6,40}*1920b, {6,60}*1920, {6,20}*1920a, {6,30}*1920b, {6,30}*1920c, {6,40}*1920c, {24,20}*1920c, {24,20}*1920d, {6,40}*1920d, {6,120}*1920a, {6,20}*1920b, {6,120}*1920b, {12,20}*1920b, {12,20}*1920c, {12,60}*1920c, {24,30}*1920a, {12,30}*1920, {12,40}*1920g, {12,40}*1920h, {12,60}*1920d, {24,20}*1920e, {24,20}*1920f, {24,30}*1920b, {4,60}*1920d, {8,60}*1920e, {8,60}*1920f, {4,30}*1920a, {8,30}*1920d, {8,30}*1920e, {8,30}*1920f, {8,60}*1920g, {8,60}*1920h, {4,120}*1920c, {4,120}*1920d, {8,30}*1920g, {4,60}*1920e, {4,120}*1920e, {4,30}*1920b, {4,120}*1920f, {12,10}*1920a, {4,30}*1920d
49-fold covers : {98,10}*1960, {2,490}*1960, {14,70}*1960a, {14,70}*1960b, {14,70}*1960c
50-fold covers : {2,500}*2000, {4,250}*2000, {20,50}*2000a, {50,20}*2000a, {10,100}*2000a, {10,100}*2000b, {100,10}*2000a, {10,20}*2000a, {10,20}*2000b, {20,10}*2000b, {20,50}*2000b, {20,10}*2000c, {10,20}*2000h, {20,10}*2000h, {4,10}*2000b, {4,20}*2000b, {10,20}*2000j
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 5, 6)( 7, 8)( 9,10)(11,12);;
s2 := ( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,12);;
poly := Group([s0,s1,s2]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(12)!(1,2);
s1 := Sym(12)!( 5, 6)( 7, 8)( 9,10)(11,12);
s2 := Sym(12)!( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,12);
poly := sub<Sym(12)|s0,s1,s2>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

```

to this polytope