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# Polytope of Type {60,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,4}*480b
if this polytope has a name.
Group : SmallGroup(480,1026)
Rank : 3
Schlafli Type : {60,4}
Number of vertices, edges, etc : 60, 120, 4
Order of s0s1s2 : 60
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
{60,4,2} of size 960
Vertex Figure Of :
{2,60,4} of size 960
{4,60,4} of size 1920
{4,60,4} of size 1920
{4,60,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {30,4}*240b
4-fold quotients : {15,4}*120
5-fold quotients : {12,4}*96b
10-fold quotients : {6,4}*48c
20-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {120,4}*960c, {120,4}*960d, {60,4}*960b
3-fold covers : {180,4}*1440b
4-fold covers : {60,4}*1920b, {240,4}*1920c, {240,4}*1920d, {60,4}*1920d, {60,8}*1920e, {60,8}*1920f, {120,4}*1920c, {120,4}*1920d
Permutation Representation (GAP) :
```s0 := (  2,  3)(  5, 17)(  6, 19)(  7, 18)(  8, 20)(  9, 13)( 10, 15)( 11, 14)
( 12, 16)( 21, 41)( 22, 43)( 23, 42)( 24, 44)( 25, 57)( 26, 59)( 27, 58)
( 28, 60)( 29, 53)( 30, 55)( 31, 54)( 32, 56)( 33, 49)( 34, 51)( 35, 50)
( 36, 52)( 37, 45)( 38, 47)( 39, 46)( 40, 48)( 62, 63)( 65, 77)( 66, 79)
( 67, 78)( 68, 80)( 69, 73)( 70, 75)( 71, 74)( 72, 76)( 81,101)( 82,103)
( 83,102)( 84,104)( 85,117)( 86,119)( 87,118)( 88,120)( 89,113)( 90,115)
( 91,114)( 92,116)( 93,109)( 94,111)( 95,110)( 96,112)( 97,105)( 98,107)
( 99,106)(100,108)(121,181)(122,183)(123,182)(124,184)(125,197)(126,199)
(127,198)(128,200)(129,193)(130,195)(131,194)(132,196)(133,189)(134,191)
(135,190)(136,192)(137,185)(138,187)(139,186)(140,188)(141,221)(142,223)
(143,222)(144,224)(145,237)(146,239)(147,238)(148,240)(149,233)(150,235)
(151,234)(152,236)(153,229)(154,231)(155,230)(156,232)(157,225)(158,227)
(159,226)(160,228)(161,201)(162,203)(163,202)(164,204)(165,217)(166,219)
(167,218)(168,220)(169,213)(170,215)(171,214)(172,216)(173,209)(174,211)
(175,210)(176,212)(177,205)(178,207)(179,206)(180,208);;
s1 := (  1,145)(  2,146)(  3,148)(  4,147)(  5,141)(  6,142)(  7,144)(  8,143)
(  9,157)( 10,158)( 11,160)( 12,159)( 13,153)( 14,154)( 15,156)( 16,155)
( 17,149)( 18,150)( 19,152)( 20,151)( 21,125)( 22,126)( 23,128)( 24,127)
( 25,121)( 26,122)( 27,124)( 28,123)( 29,137)( 30,138)( 31,140)( 32,139)
( 33,133)( 34,134)( 35,136)( 36,135)( 37,129)( 38,130)( 39,132)( 40,131)
( 41,165)( 42,166)( 43,168)( 44,167)( 45,161)( 46,162)( 47,164)( 48,163)
( 49,177)( 50,178)( 51,180)( 52,179)( 53,173)( 54,174)( 55,176)( 56,175)
( 57,169)( 58,170)( 59,172)( 60,171)( 61,205)( 62,206)( 63,208)( 64,207)
( 65,201)( 66,202)( 67,204)( 68,203)( 69,217)( 70,218)( 71,220)( 72,219)
( 73,213)( 74,214)( 75,216)( 76,215)( 77,209)( 78,210)( 79,212)( 80,211)
( 81,185)( 82,186)( 83,188)( 84,187)( 85,181)( 86,182)( 87,184)( 88,183)
( 89,197)( 90,198)( 91,200)( 92,199)( 93,193)( 94,194)( 95,196)( 96,195)
( 97,189)( 98,190)( 99,192)(100,191)(101,225)(102,226)(103,228)(104,227)
(105,221)(106,222)(107,224)(108,223)(109,237)(110,238)(111,240)(112,239)
(113,233)(114,234)(115,236)(116,235)(117,229)(118,230)(119,232)(120,231);;
s2 := (  1,  4)(  2,  3)(  5,  8)(  6,  7)(  9, 12)( 10, 11)( 13, 16)( 14, 15)
( 17, 20)( 18, 19)( 21, 24)( 22, 23)( 25, 28)( 26, 27)( 29, 32)( 30, 31)
( 33, 36)( 34, 35)( 37, 40)( 38, 39)( 41, 44)( 42, 43)( 45, 48)( 46, 47)
( 49, 52)( 50, 51)( 53, 56)( 54, 55)( 57, 60)( 58, 59)( 61, 64)( 62, 63)
( 65, 68)( 66, 67)( 69, 72)( 70, 71)( 73, 76)( 74, 75)( 77, 80)( 78, 79)
( 81, 84)( 82, 83)( 85, 88)( 86, 87)( 89, 92)( 90, 91)( 93, 96)( 94, 95)
( 97,100)( 98, 99)(101,104)(102,103)(105,108)(106,107)(109,112)(110,111)
(113,116)(114,115)(117,120)(118,119)(121,124)(122,123)(125,128)(126,127)
(129,132)(130,131)(133,136)(134,135)(137,140)(138,139)(141,144)(142,143)
(145,148)(146,147)(149,152)(150,151)(153,156)(154,155)(157,160)(158,159)
(161,164)(162,163)(165,168)(166,167)(169,172)(170,171)(173,176)(174,175)
(177,180)(178,179)(181,184)(182,183)(185,188)(186,187)(189,192)(190,191)
(193,196)(194,195)(197,200)(198,199)(201,204)(202,203)(205,208)(206,207)
(209,212)(210,211)(213,216)(214,215)(217,220)(218,219)(221,224)(222,223)
(225,228)(226,227)(229,232)(230,231)(233,236)(234,235)(237,240)(238,239);;
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,
s2*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope