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# Polytope of Type {4,60}

Atlas Canonical Name : {4,60}*480a
Also Known As : {4,60|2}. if this polytope has another name.
Group : SmallGroup(480,847)
Rank : 3
Schlafli Type : {4,60}
Number of vertices, edges, etc : 4, 120, 60
Order of s0s1s2 : 60
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,60,2} of size 960
{4,60,4} of size 1920
{4,60,4} of size 1920
{4,60,4} of size 1920
Vertex Figure Of :
{2,4,60} of size 960
{4,4,60} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,60}*240, {4,30}*240a
3-fold quotients : {4,20}*160
4-fold quotients : {2,30}*120
5-fold quotients : {4,12}*96a
6-fold quotients : {2,20}*80, {4,10}*80
8-fold quotients : {2,15}*60
10-fold quotients : {2,12}*48, {4,6}*48a
12-fold quotients : {2,10}*40
15-fold quotients : {4,4}*32
20-fold quotients : {2,6}*24
24-fold quotients : {2,5}*20
30-fold quotients : {2,4}*16, {4,2}*16
40-fold quotients : {2,3}*12
60-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,120}*960a, {4,60}*960a, {4,120}*960b, {8,60}*960a, {8,60}*960b
3-fold covers : {4,180}*1440a, {12,60}*1440b, {12,60}*1440c
4-fold covers : {8,60}*1920a, {4,120}*1920a, {8,120}*1920a, {8,120}*1920b, {8,120}*1920c, {8,120}*1920d, {16,60}*1920a, {4,240}*1920a, {16,60}*1920b, {4,240}*1920b, {4,60}*1920a, {4,120}*1920b, {8,60}*1920b, {4,60}*1920d
Permutation Representation (GAP) :
```s0 := ( 61, 76)( 62, 77)( 63, 78)( 64, 79)( 65, 80)( 66, 81)( 67, 82)( 68, 83)
( 69, 84)( 70, 85)( 71, 86)( 72, 87)( 73, 88)( 74, 89)( 75, 90)( 91,106)
( 92,107)( 93,108)( 94,109)( 95,110)( 96,111)( 97,112)( 98,113)( 99,114)
(100,115)(101,116)(102,117)(103,118)(104,119)(105,120);;
s1 := (  1, 61)(  2, 65)(  3, 64)(  4, 63)(  5, 62)(  6, 71)(  7, 75)(  8, 74)
(  9, 73)( 10, 72)( 11, 66)( 12, 70)( 13, 69)( 14, 68)( 15, 67)( 16, 76)
( 17, 80)( 18, 79)( 19, 78)( 20, 77)( 21, 86)( 22, 90)( 23, 89)( 24, 88)
( 25, 87)( 26, 81)( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31, 91)( 32, 95)
( 33, 94)( 34, 93)( 35, 92)( 36,101)( 37,105)( 38,104)( 39,103)( 40,102)
( 41, 96)( 42,100)( 43, 99)( 44, 98)( 45, 97)( 46,106)( 47,110)( 48,109)
( 49,108)( 50,107)( 51,116)( 52,120)( 53,119)( 54,118)( 55,117)( 56,111)
( 57,115)( 58,114)( 59,113)( 60,112);;
s2 := (  1,  7)(  2,  6)(  3, 10)(  4,  9)(  5,  8)( 11, 12)( 13, 15)( 16, 22)
( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 37)( 32, 36)
( 33, 40)( 34, 39)( 35, 38)( 41, 42)( 43, 45)( 46, 52)( 47, 51)( 48, 55)
( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61, 97)( 62, 96)( 63,100)( 64, 99)
( 65, 98)( 66, 92)( 67, 91)( 68, 95)( 69, 94)( 70, 93)( 71,102)( 72,101)
( 73,105)( 74,104)( 75,103)( 76,112)( 77,111)( 78,115)( 79,114)( 80,113)
( 81,107)( 82,106)( 83,110)( 84,109)( 85,108)( 86,117)( 87,116)( 88,120)
( 89,119)( 90,118);;
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*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, 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(120)!( 61, 76)( 62, 77)( 63, 78)( 64, 79)( 65, 80)( 66, 81)( 67, 82)
( 68, 83)( 69, 84)( 70, 85)( 71, 86)( 72, 87)( 73, 88)( 74, 89)( 75, 90)
( 91,106)( 92,107)( 93,108)( 94,109)( 95,110)( 96,111)( 97,112)( 98,113)
( 99,114)(100,115)(101,116)(102,117)(103,118)(104,119)(105,120);
s1 := Sym(120)!(  1, 61)(  2, 65)(  3, 64)(  4, 63)(  5, 62)(  6, 71)(  7, 75)
(  8, 74)(  9, 73)( 10, 72)( 11, 66)( 12, 70)( 13, 69)( 14, 68)( 15, 67)
( 16, 76)( 17, 80)( 18, 79)( 19, 78)( 20, 77)( 21, 86)( 22, 90)( 23, 89)
( 24, 88)( 25, 87)( 26, 81)( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31, 91)
( 32, 95)( 33, 94)( 34, 93)( 35, 92)( 36,101)( 37,105)( 38,104)( 39,103)
( 40,102)( 41, 96)( 42,100)( 43, 99)( 44, 98)( 45, 97)( 46,106)( 47,110)
( 48,109)( 49,108)( 50,107)( 51,116)( 52,120)( 53,119)( 54,118)( 55,117)
( 56,111)( 57,115)( 58,114)( 59,113)( 60,112);
s2 := Sym(120)!(  1,  7)(  2,  6)(  3, 10)(  4,  9)(  5,  8)( 11, 12)( 13, 15)
( 16, 22)( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 37)
( 32, 36)( 33, 40)( 34, 39)( 35, 38)( 41, 42)( 43, 45)( 46, 52)( 47, 51)
( 48, 55)( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61, 97)( 62, 96)( 63,100)
( 64, 99)( 65, 98)( 66, 92)( 67, 91)( 68, 95)( 69, 94)( 70, 93)( 71,102)
( 72,101)( 73,105)( 74,104)( 75,103)( 76,112)( 77,111)( 78,115)( 79,114)
( 80,113)( 81,107)( 82,106)( 83,110)( 84,109)( 85,108)( 86,117)( 87,116)
( 88,120)( 89,119)( 90,118);
poly := sub<Sym(120)|s0,s1,s2>;

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

```
References : None.
to this polytope