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# Polytope of Type {120,4}

Atlas Canonical Name : {120,4}*960b
if this polytope has a name.
Group : SmallGroup(960,5043)
Rank : 3
Schlafli Type : {120,4}
Number of vertices, edges, etc : 120, 240, 4
Order of s0s1s2 : 120
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{120,4,2} of size 1920
Vertex Figure Of :
{2,120,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {60,4}*480a
3-fold quotients : {40,4}*320b
4-fold quotients : {60,2}*240, {30,4}*240a
5-fold quotients : {24,4}*192b
6-fold quotients : {20,4}*160
8-fold quotients : {30,2}*120
10-fold quotients : {12,4}*96a
12-fold quotients : {20,2}*80, {10,4}*80
15-fold quotients : {8,4}*64b
16-fold quotients : {15,2}*60
20-fold quotients : {12,2}*48, {6,4}*48a
24-fold quotients : {10,2}*40
30-fold quotients : {4,4}*32
40-fold quotients : {6,2}*24
48-fold quotients : {5,2}*20
60-fold quotients : {2,4}*16, {4,2}*16
80-fold quotients : {3,2}*12
120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {120,4}*1920a, {120,8}*1920a, {120,8}*1920d
Permutation Representation (GAP) :
```s0 := (  2,  5)(  3,  4)(  6, 11)(  7, 15)(  8, 14)(  9, 13)( 10, 12)( 17, 20)
( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 31, 46)( 32, 50)
( 33, 49)( 34, 48)( 35, 47)( 36, 56)( 37, 60)( 38, 59)( 39, 58)( 40, 57)
( 41, 51)( 42, 55)( 43, 54)( 44, 53)( 45, 52)( 61, 76)( 62, 80)( 63, 79)
( 64, 78)( 65, 77)( 66, 86)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 81)
( 72, 85)( 73, 84)( 74, 83)( 75, 82)( 92, 95)( 93, 94)( 96,101)( 97,105)
( 98,104)( 99,103)(100,102)(107,110)(108,109)(111,116)(112,120)(113,119)
(114,118)(115,117)(121,181)(122,185)(123,184)(124,183)(125,182)(126,191)
(127,195)(128,194)(129,193)(130,192)(131,186)(132,190)(133,189)(134,188)
(135,187)(136,196)(137,200)(138,199)(139,198)(140,197)(141,206)(142,210)
(143,209)(144,208)(145,207)(146,201)(147,205)(148,204)(149,203)(150,202)
(151,226)(152,230)(153,229)(154,228)(155,227)(156,236)(157,240)(158,239)
(159,238)(160,237)(161,231)(162,235)(163,234)(164,233)(165,232)(166,211)
(167,215)(168,214)(169,213)(170,212)(171,221)(172,225)(173,224)(174,223)
(175,222)(176,216)(177,220)(178,219)(179,218)(180,217);;
s1 := (  1,127)(  2,126)(  3,130)(  4,129)(  5,128)(  6,122)(  7,121)(  8,125)
(  9,124)( 10,123)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)( 16,142)
( 17,141)( 18,145)( 19,144)( 20,143)( 21,137)( 22,136)( 23,140)( 24,139)
( 25,138)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,157)( 32,156)
( 33,160)( 34,159)( 35,158)( 36,152)( 37,151)( 38,155)( 39,154)( 40,153)
( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,172)( 47,171)( 48,175)
( 49,174)( 50,173)( 51,167)( 52,166)( 53,170)( 54,169)( 55,168)( 56,177)
( 57,176)( 58,180)( 59,179)( 60,178)( 61,202)( 62,201)( 63,205)( 64,204)
( 65,203)( 66,197)( 67,196)( 68,200)( 69,199)( 70,198)( 71,207)( 72,206)
( 73,210)( 74,209)( 75,208)( 76,187)( 77,186)( 78,190)( 79,189)( 80,188)
( 81,182)( 82,181)( 83,185)( 84,184)( 85,183)( 86,192)( 87,191)( 88,195)
( 89,194)( 90,193)( 91,232)( 92,231)( 93,235)( 94,234)( 95,233)( 96,227)
( 97,226)( 98,230)( 99,229)(100,228)(101,237)(102,236)(103,240)(104,239)
(105,238)(106,217)(107,216)(108,220)(109,219)(110,218)(111,212)(112,211)
(113,215)(114,214)(115,213)(116,222)(117,221)(118,225)(119,224)(120,223);;
s2 := ( 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)(121,151)(122,152)
(123,153)(124,154)(125,155)(126,156)(127,157)(128,158)(129,159)(130,160)
(131,161)(132,162)(133,163)(134,164)(135,165)(136,166)(137,167)(138,168)
(139,169)(140,170)(141,171)(142,172)(143,173)(144,174)(145,175)(146,176)
(147,177)(148,178)(149,179)(150,180)(181,226)(182,227)(183,228)(184,229)
(185,230)(186,231)(187,232)(188,233)(189,234)(190,235)(191,236)(192,237)
(193,238)(194,239)(195,240)(196,211)(197,212)(198,213)(199,214)(200,215)
(201,216)(202,217)(203,218)(204,219)(205,220)(206,221)(207,222)(208,223)
(209,224)(210,225);;
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,
s0*s2*s1*s2*s1*s0*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*s2*s1*s0*s1*s0*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 ];;
poly := F / rels;;

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

```
References : None.
to this polytope