Questions?
See the FAQ
or other info.

# Polytope of Type {2,130}

Atlas Canonical Name : {2,130}*520
if this polytope has a name.
Group : SmallGroup(520,48)
Rank : 3
Schlafli Type : {2,130}
Number of vertices, edges, etc : 2, 130, 130
Order of s0s1s2 : 130
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,130,2} of size 1040
Vertex Figure Of :
{2,2,130} of size 1040
{3,2,130} of size 1560
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,65}*260
5-fold quotients : {2,26}*104
10-fold quotients : {2,13}*52
13-fold quotients : {2,10}*40
26-fold quotients : {2,5}*20
65-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,260}*1040, {4,130}*1040
3-fold covers : {6,130}*1560, {2,390}*1560
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)(  9, 10)( 16, 55)( 17, 67)
( 18, 66)( 19, 65)( 20, 64)( 21, 63)( 22, 62)( 23, 61)( 24, 60)( 25, 59)
( 26, 58)( 27, 57)( 28, 56)( 29, 42)( 30, 54)( 31, 53)( 32, 52)( 33, 51)
( 34, 50)( 35, 49)( 36, 48)( 37, 47)( 38, 46)( 39, 45)( 40, 44)( 41, 43)
( 69, 80)( 70, 79)( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 81,120)( 82,132)
( 83,131)( 84,130)( 85,129)( 86,128)( 87,127)( 88,126)( 89,125)( 90,124)
( 91,123)( 92,122)( 93,121)( 94,107)( 95,119)( 96,118)( 97,117)( 98,116)
( 99,115)(100,114)(101,113)(102,112)(103,111)(104,110)(105,109)(106,108);;
s2 := (  3, 82)(  4, 81)(  5, 93)(  6, 92)(  7, 91)(  8, 90)(  9, 89)( 10, 88)
( 11, 87)( 12, 86)( 13, 85)( 14, 84)( 15, 83)( 16, 69)( 17, 68)( 18, 80)
( 19, 79)( 20, 78)( 21, 77)( 22, 76)( 23, 75)( 24, 74)( 25, 73)( 26, 72)
( 27, 71)( 28, 70)( 29,121)( 30,120)( 31,132)( 32,131)( 33,130)( 34,129)
( 35,128)( 36,127)( 37,126)( 38,125)( 39,124)( 40,123)( 41,122)( 42,108)
( 43,107)( 44,119)( 45,118)( 46,117)( 47,116)( 48,115)( 49,114)( 50,113)
( 51,112)( 52,111)( 53,110)( 54,109)( 55, 95)( 56, 94)( 57,106)( 58,105)
( 59,104)( 60,103)( 61,102)( 62,101)( 63,100)( 64, 99)( 65, 98)( 66, 97)
( 67, 96);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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(132)!(1,2);
s1 := Sym(132)!(  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)(  9, 10)( 16, 55)
( 17, 67)( 18, 66)( 19, 65)( 20, 64)( 21, 63)( 22, 62)( 23, 61)( 24, 60)
( 25, 59)( 26, 58)( 27, 57)( 28, 56)( 29, 42)( 30, 54)( 31, 53)( 32, 52)
( 33, 51)( 34, 50)( 35, 49)( 36, 48)( 37, 47)( 38, 46)( 39, 45)( 40, 44)
( 41, 43)( 69, 80)( 70, 79)( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 81,120)
( 82,132)( 83,131)( 84,130)( 85,129)( 86,128)( 87,127)( 88,126)( 89,125)
( 90,124)( 91,123)( 92,122)( 93,121)( 94,107)( 95,119)( 96,118)( 97,117)
( 98,116)( 99,115)(100,114)(101,113)(102,112)(103,111)(104,110)(105,109)
(106,108);
s2 := Sym(132)!(  3, 82)(  4, 81)(  5, 93)(  6, 92)(  7, 91)(  8, 90)(  9, 89)
( 10, 88)( 11, 87)( 12, 86)( 13, 85)( 14, 84)( 15, 83)( 16, 69)( 17, 68)
( 18, 80)( 19, 79)( 20, 78)( 21, 77)( 22, 76)( 23, 75)( 24, 74)( 25, 73)
( 26, 72)( 27, 71)( 28, 70)( 29,121)( 30,120)( 31,132)( 32,131)( 33,130)
( 34,129)( 35,128)( 36,127)( 37,126)( 38,125)( 39,124)( 40,123)( 41,122)
( 42,108)( 43,107)( 44,119)( 45,118)( 46,117)( 47,116)( 48,115)( 49,114)
( 50,113)( 51,112)( 52,111)( 53,110)( 54,109)( 55, 95)( 56, 94)( 57,106)
( 58,105)( 59,104)( 60,103)( 61,102)( 62,101)( 63,100)( 64, 99)( 65, 98)
( 66, 97)( 67, 96);
poly := sub<Sym(132)|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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

```

to this polytope