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# Polytope of Type {20,6}

Atlas Canonical Name : {20,6}*480c
if this polytope has a name.
Group : SmallGroup(480,1193)
Rank : 3
Schlafli Type : {20,6}
Number of vertices, edges, etc : 40, 120, 12
Order of s0s1s2 : 30
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{20,6,2} of size 960
{20,6,3} of size 1920
{20,6,4} of size 1920
{20,6,4} of size 1920
Vertex Figure Of :
{2,20,6} of size 960
{4,20,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {20,6}*240b
4-fold quotients : {10,6}*120
5-fold quotients : {4,6}*96
10-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
12-fold quotients : {10,2}*40
20-fold quotients : {4,3}*24, {2,6}*24
24-fold quotients : {5,2}*20
40-fold quotients : {2,3}*12
60-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {20,12}*960b, {20,6}*960e, {40,6}*960d, {40,6}*960e, {20,12}*960c
3-fold covers : {20,18}*1440, {60,6}*1440c, {60,6}*1440d
4-fold covers : {40,6}*1920a, {40,12}*1920e, {40,12}*1920f, {40,6}*1920b, {20,6}*1920a, {40,6}*1920c, {20,24}*1920c, {20,24}*1920d, {40,6}*1920d, {20,6}*1920b, {20,12}*1920b, {20,12}*1920c, {40,12}*1920g, {40,12}*1920h, {20,24}*1920e, {20,24}*1920f
Permutation Representation (GAP) :
```s0 := (  1,  3)(  2,  4)(  5, 19)(  6, 20)(  7, 17)(  8, 18)(  9, 15)( 10, 16)
( 11, 13)( 12, 14)( 21, 23)( 22, 24)( 25, 39)( 26, 40)( 27, 37)( 28, 38)
( 29, 35)( 30, 36)( 31, 33)( 32, 34)( 41, 43)( 42, 44)( 45, 59)( 46, 60)
( 47, 57)( 48, 58)( 49, 55)( 50, 56)( 51, 53)( 52, 54)( 61, 63)( 62, 64)
( 65, 79)( 66, 80)( 67, 77)( 68, 78)( 69, 75)( 70, 76)( 71, 73)( 72, 74)
( 81, 83)( 82, 84)( 85, 99)( 86,100)( 87, 97)( 88, 98)( 89, 95)( 90, 96)
( 91, 93)( 92, 94)(101,103)(102,104)(105,119)(106,120)(107,117)(108,118)
(109,115)(110,116)(111,113)(112,114);;
s1 := (  1,  5)(  2,  7)(  3,  6)(  4,  8)(  9, 17)( 10, 19)( 11, 18)( 12, 20)
( 14, 15)( 21, 45)( 22, 47)( 23, 46)( 24, 48)( 25, 41)( 26, 43)( 27, 42)
( 28, 44)( 29, 57)( 30, 59)( 31, 58)( 32, 60)( 33, 53)( 34, 55)( 35, 54)
( 36, 56)( 37, 49)( 38, 51)( 39, 50)( 40, 52)( 61, 65)( 62, 67)( 63, 66)
( 64, 68)( 69, 77)( 70, 79)( 71, 78)( 72, 80)( 74, 75)( 81,105)( 82,107)
( 83,106)( 84,108)( 85,101)( 86,103)( 87,102)( 88,104)( 89,117)( 90,119)
( 91,118)( 92,120)( 93,113)( 94,115)( 95,114)( 96,116)( 97,109)( 98,111)
( 99,110)(100,112);;
s2 := (  1,101)(  2,104)(  3,103)(  4,102)(  5,105)(  6,108)(  7,107)(  8,106)
(  9,109)( 10,112)( 11,111)( 12,110)( 13,113)( 14,116)( 15,115)( 16,114)
( 17,117)( 18,120)( 19,119)( 20,118)( 21, 81)( 22, 84)( 23, 83)( 24, 82)
( 25, 85)( 26, 88)( 27, 87)( 28, 86)( 29, 89)( 30, 92)( 31, 91)( 32, 90)
( 33, 93)( 34, 96)( 35, 95)( 36, 94)( 37, 97)( 38,100)( 39, 99)( 40, 98)
( 41, 61)( 42, 64)( 43, 63)( 44, 62)( 45, 65)( 46, 68)( 47, 67)( 48, 66)
( 49, 69)( 50, 72)( 51, 71)( 52, 70)( 53, 73)( 54, 76)( 55, 75)( 56, 74)
( 57, 77)( 58, 80)( 59, 79)( 60, 78);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(120)!(  1,  3)(  2,  4)(  5, 19)(  6, 20)(  7, 17)(  8, 18)(  9, 15)
( 10, 16)( 11, 13)( 12, 14)( 21, 23)( 22, 24)( 25, 39)( 26, 40)( 27, 37)
( 28, 38)( 29, 35)( 30, 36)( 31, 33)( 32, 34)( 41, 43)( 42, 44)( 45, 59)
( 46, 60)( 47, 57)( 48, 58)( 49, 55)( 50, 56)( 51, 53)( 52, 54)( 61, 63)
( 62, 64)( 65, 79)( 66, 80)( 67, 77)( 68, 78)( 69, 75)( 70, 76)( 71, 73)
( 72, 74)( 81, 83)( 82, 84)( 85, 99)( 86,100)( 87, 97)( 88, 98)( 89, 95)
( 90, 96)( 91, 93)( 92, 94)(101,103)(102,104)(105,119)(106,120)(107,117)
(108,118)(109,115)(110,116)(111,113)(112,114);
s1 := Sym(120)!(  1,  5)(  2,  7)(  3,  6)(  4,  8)(  9, 17)( 10, 19)( 11, 18)
( 12, 20)( 14, 15)( 21, 45)( 22, 47)( 23, 46)( 24, 48)( 25, 41)( 26, 43)
( 27, 42)( 28, 44)( 29, 57)( 30, 59)( 31, 58)( 32, 60)( 33, 53)( 34, 55)
( 35, 54)( 36, 56)( 37, 49)( 38, 51)( 39, 50)( 40, 52)( 61, 65)( 62, 67)
( 63, 66)( 64, 68)( 69, 77)( 70, 79)( 71, 78)( 72, 80)( 74, 75)( 81,105)
( 82,107)( 83,106)( 84,108)( 85,101)( 86,103)( 87,102)( 88,104)( 89,117)
( 90,119)( 91,118)( 92,120)( 93,113)( 94,115)( 95,114)( 96,116)( 97,109)
( 98,111)( 99,110)(100,112);
s2 := Sym(120)!(  1,101)(  2,104)(  3,103)(  4,102)(  5,105)(  6,108)(  7,107)
(  8,106)(  9,109)( 10,112)( 11,111)( 12,110)( 13,113)( 14,116)( 15,115)
( 16,114)( 17,117)( 18,120)( 19,119)( 20,118)( 21, 81)( 22, 84)( 23, 83)
( 24, 82)( 25, 85)( 26, 88)( 27, 87)( 28, 86)( 29, 89)( 30, 92)( 31, 91)
( 32, 90)( 33, 93)( 34, 96)( 35, 95)( 36, 94)( 37, 97)( 38,100)( 39, 99)
( 40, 98)( 41, 61)( 42, 64)( 43, 63)( 44, 62)( 45, 65)( 46, 68)( 47, 67)
( 48, 66)( 49, 69)( 50, 72)( 51, 71)( 52, 70)( 53, 73)( 54, 76)( 55, 75)
( 56, 74)( 57, 77)( 58, 80)( 59, 79)( 60, 78);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1 >;

```
References : None.
to this polytope