# Polytope of Type {60,6}

Atlas Canonical Name : {60,6}*960b
if this polytope has a name.
Group : SmallGroup(960,10979)
Rank : 3
Schlafli Type : {60,6}
Number of vertices, edges, etc : 80, 240, 8
Order of s0s1s2 : 40
Order of s0s1s2s1 : 12
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{60,6,2} of size 1920
Vertex Figure Of :
{2,60,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {30,6}*480
4-fold quotients : {15,6}*240
5-fold quotients : {12,6}*192b
10-fold quotients : {12,3}*96, {6,6}*96
20-fold quotients : {3,6}*48, {6,3}*48
24-fold quotients : {10,2}*40
40-fold quotients : {3,3}*24
48-fold quotients : {5,2}*20
120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {60,12}*1920a, {60,6}*1920, {60,12}*1920d
Permutation Representation (GAP) :
```s0 := (  3,  6)(  4,  5)(  7,  8)(  9, 33)( 10, 34)( 11, 38)( 12, 37)( 13, 36)
( 14, 35)( 15, 40)( 16, 39)( 17, 25)( 18, 26)( 19, 30)( 20, 29)( 21, 28)
( 22, 27)( 23, 32)( 24, 31)( 41, 81)( 42, 82)( 43, 86)( 44, 85)( 45, 84)
( 46, 83)( 47, 88)( 48, 87)( 49,113)( 50,114)( 51,118)( 52,117)( 53,116)
( 54,115)( 55,120)( 56,119)( 57,105)( 58,106)( 59,110)( 60,109)( 61,108)
( 62,107)( 63,112)( 64,111)( 65, 97)( 66, 98)( 67,102)( 68,101)( 69,100)
( 70, 99)( 71,104)( 72,103)( 73, 89)( 74, 90)( 75, 94)( 76, 93)( 77, 92)
( 78, 91)( 79, 96)( 80, 95)(121,122)(123,125)(124,126)(129,154)(130,153)
(131,157)(132,158)(133,155)(134,156)(135,159)(136,160)(137,146)(138,145)
(139,149)(140,150)(141,147)(142,148)(143,151)(144,152)(161,202)(162,201)
(163,205)(164,206)(165,203)(166,204)(167,207)(168,208)(169,234)(170,233)
(171,237)(172,238)(173,235)(174,236)(175,239)(176,240)(177,226)(178,225)
(179,229)(180,230)(181,227)(182,228)(183,231)(184,232)(185,218)(186,217)
(187,221)(188,222)(189,219)(190,220)(191,223)(192,224)(193,210)(194,209)
(195,213)(196,214)(197,211)(198,212)(199,215)(200,216);;
s1 := (  1,169)(  2,170)(  3,172)(  4,171)(  5,175)(  6,176)(  7,173)(  8,174)
(  9,161)( 10,162)( 11,164)( 12,163)( 13,167)( 14,168)( 15,165)( 16,166)
( 17,193)( 18,194)( 19,196)( 20,195)( 21,199)( 22,200)( 23,197)( 24,198)
( 25,185)( 26,186)( 27,188)( 28,187)( 29,191)( 30,192)( 31,189)( 32,190)
( 33,177)( 34,178)( 35,180)( 36,179)( 37,183)( 38,184)( 39,181)( 40,182)
( 41,129)( 42,130)( 43,132)( 44,131)( 45,135)( 46,136)( 47,133)( 48,134)
( 49,121)( 50,122)( 51,124)( 52,123)( 53,127)( 54,128)( 55,125)( 56,126)
( 57,153)( 58,154)( 59,156)( 60,155)( 61,159)( 62,160)( 63,157)( 64,158)
( 65,145)( 66,146)( 67,148)( 68,147)( 69,151)( 70,152)( 71,149)( 72,150)
( 73,137)( 74,138)( 75,140)( 76,139)( 77,143)( 78,144)( 79,141)( 80,142)
( 81,209)( 82,210)( 83,212)( 84,211)( 85,215)( 86,216)( 87,213)( 88,214)
( 89,201)( 90,202)( 91,204)( 92,203)( 93,207)( 94,208)( 95,205)( 96,206)
( 97,233)( 98,234)( 99,236)(100,235)(101,239)(102,240)(103,237)(104,238)
(105,225)(106,226)(107,228)(108,227)(109,231)(110,232)(111,229)(112,230)
(113,217)(114,218)(115,220)(116,219)(117,223)(118,224)(119,221)(120,222);;
s2 := (  1,127)(  2,128)(  3,123)(  4,124)(  5,126)(  6,125)(  7,121)(  8,122)
(  9,135)( 10,136)( 11,131)( 12,132)( 13,134)( 14,133)( 15,129)( 16,130)
( 17,143)( 18,144)( 19,139)( 20,140)( 21,142)( 22,141)( 23,137)( 24,138)
( 25,151)( 26,152)( 27,147)( 28,148)( 29,150)( 30,149)( 31,145)( 32,146)
( 33,159)( 34,160)( 35,155)( 36,156)( 37,158)( 38,157)( 39,153)( 40,154)
( 41,207)( 42,208)( 43,203)( 44,204)( 45,206)( 46,205)( 47,201)( 48,202)
( 49,215)( 50,216)( 51,211)( 52,212)( 53,214)( 54,213)( 55,209)( 56,210)
( 57,223)( 58,224)( 59,219)( 60,220)( 61,222)( 62,221)( 63,217)( 64,218)
( 65,231)( 66,232)( 67,227)( 68,228)( 69,230)( 70,229)( 71,225)( 72,226)
( 73,239)( 74,240)( 75,235)( 76,236)( 77,238)( 78,237)( 79,233)( 80,234)
( 81,167)( 82,168)( 83,163)( 84,164)( 85,166)( 86,165)( 87,161)( 88,162)
( 89,175)( 90,176)( 91,171)( 92,172)( 93,174)( 94,173)( 95,169)( 96,170)
( 97,183)( 98,184)( 99,179)(100,180)(101,182)(102,181)(103,177)(104,178)
(105,191)(106,192)(107,187)(108,188)(109,190)(110,189)(111,185)(112,186)
(113,199)(114,200)(115,195)(116,196)(117,198)(118,197)(119,193)(120,194);;
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*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(240)!(  3,  6)(  4,  5)(  7,  8)(  9, 33)( 10, 34)( 11, 38)( 12, 37)
( 13, 36)( 14, 35)( 15, 40)( 16, 39)( 17, 25)( 18, 26)( 19, 30)( 20, 29)
( 21, 28)( 22, 27)( 23, 32)( 24, 31)( 41, 81)( 42, 82)( 43, 86)( 44, 85)
( 45, 84)( 46, 83)( 47, 88)( 48, 87)( 49,113)( 50,114)( 51,118)( 52,117)
( 53,116)( 54,115)( 55,120)( 56,119)( 57,105)( 58,106)( 59,110)( 60,109)
( 61,108)( 62,107)( 63,112)( 64,111)( 65, 97)( 66, 98)( 67,102)( 68,101)
( 69,100)( 70, 99)( 71,104)( 72,103)( 73, 89)( 74, 90)( 75, 94)( 76, 93)
( 77, 92)( 78, 91)( 79, 96)( 80, 95)(121,122)(123,125)(124,126)(129,154)
(130,153)(131,157)(132,158)(133,155)(134,156)(135,159)(136,160)(137,146)
(138,145)(139,149)(140,150)(141,147)(142,148)(143,151)(144,152)(161,202)
(162,201)(163,205)(164,206)(165,203)(166,204)(167,207)(168,208)(169,234)
(170,233)(171,237)(172,238)(173,235)(174,236)(175,239)(176,240)(177,226)
(178,225)(179,229)(180,230)(181,227)(182,228)(183,231)(184,232)(185,218)
(186,217)(187,221)(188,222)(189,219)(190,220)(191,223)(192,224)(193,210)
(194,209)(195,213)(196,214)(197,211)(198,212)(199,215)(200,216);
s1 := Sym(240)!(  1,169)(  2,170)(  3,172)(  4,171)(  5,175)(  6,176)(  7,173)
(  8,174)(  9,161)( 10,162)( 11,164)( 12,163)( 13,167)( 14,168)( 15,165)
( 16,166)( 17,193)( 18,194)( 19,196)( 20,195)( 21,199)( 22,200)( 23,197)
( 24,198)( 25,185)( 26,186)( 27,188)( 28,187)( 29,191)( 30,192)( 31,189)
( 32,190)( 33,177)( 34,178)( 35,180)( 36,179)( 37,183)( 38,184)( 39,181)
( 40,182)( 41,129)( 42,130)( 43,132)( 44,131)( 45,135)( 46,136)( 47,133)
( 48,134)( 49,121)( 50,122)( 51,124)( 52,123)( 53,127)( 54,128)( 55,125)
( 56,126)( 57,153)( 58,154)( 59,156)( 60,155)( 61,159)( 62,160)( 63,157)
( 64,158)( 65,145)( 66,146)( 67,148)( 68,147)( 69,151)( 70,152)( 71,149)
( 72,150)( 73,137)( 74,138)( 75,140)( 76,139)( 77,143)( 78,144)( 79,141)
( 80,142)( 81,209)( 82,210)( 83,212)( 84,211)( 85,215)( 86,216)( 87,213)
( 88,214)( 89,201)( 90,202)( 91,204)( 92,203)( 93,207)( 94,208)( 95,205)
( 96,206)( 97,233)( 98,234)( 99,236)(100,235)(101,239)(102,240)(103,237)
(104,238)(105,225)(106,226)(107,228)(108,227)(109,231)(110,232)(111,229)
(112,230)(113,217)(114,218)(115,220)(116,219)(117,223)(118,224)(119,221)
(120,222);
s2 := Sym(240)!(  1,127)(  2,128)(  3,123)(  4,124)(  5,126)(  6,125)(  7,121)
(  8,122)(  9,135)( 10,136)( 11,131)( 12,132)( 13,134)( 14,133)( 15,129)
( 16,130)( 17,143)( 18,144)( 19,139)( 20,140)( 21,142)( 22,141)( 23,137)
( 24,138)( 25,151)( 26,152)( 27,147)( 28,148)( 29,150)( 30,149)( 31,145)
( 32,146)( 33,159)( 34,160)( 35,155)( 36,156)( 37,158)( 38,157)( 39,153)
( 40,154)( 41,207)( 42,208)( 43,203)( 44,204)( 45,206)( 46,205)( 47,201)
( 48,202)( 49,215)( 50,216)( 51,211)( 52,212)( 53,214)( 54,213)( 55,209)
( 56,210)( 57,223)( 58,224)( 59,219)( 60,220)( 61,222)( 62,221)( 63,217)
( 64,218)( 65,231)( 66,232)( 67,227)( 68,228)( 69,230)( 70,229)( 71,225)
( 72,226)( 73,239)( 74,240)( 75,235)( 76,236)( 77,238)( 78,237)( 79,233)
( 80,234)( 81,167)( 82,168)( 83,163)( 84,164)( 85,166)( 86,165)( 87,161)
( 88,162)( 89,175)( 90,176)( 91,171)( 92,172)( 93,174)( 94,173)( 95,169)
( 96,170)( 97,183)( 98,184)( 99,179)(100,180)(101,182)(102,181)(103,177)
(104,178)(105,191)(106,192)(107,187)(108,188)(109,190)(110,189)(111,185)
(112,186)(113,199)(114,200)(115,195)(116,196)(117,198)(118,197)(119,193)
(120,194);
poly := sub<Sym(240)|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*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1 >;

```
References : None.
to this polytope