Polytope of Type {4,120}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,120}*960a
Also Known As : {4,120|2}. if this polytope has another name.
Group : SmallGroup(960,5028)
Rank : 3
Schlafli Type : {4,120}
Number of vertices, edges, etc : 4, 240, 120
Order of s₀s₁s₂ : 120
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,120,2} of size 1920
Vertex Figure Of :
   {2,4,120} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,60}*480a, {2,120}*480
   3-fold quotients : {4,40}*320a
   4-fold quotients : {2,60}*240, {4,30}*240a
   5-fold quotients : {4,24}*192a
   6-fold quotients : {4,20}*160, {2,40}*160
   8-fold quotients : {2,30}*120
   10-fold quotients : {4,12}*96a, {2,24}*96
   12-fold quotients : {2,20}*80, {4,10}*80
   15-fold quotients : {4,8}*64a
   16-fold quotients : {2,15}*60
   20-fold quotients : {2,12}*48, {4,6}*48a
   24-fold quotients : {2,10}*40
   30-fold quotients : {4,4}*32, {2,8}*32
   40-fold quotients : {2,6}*24
   48-fold quotients : {2,5}*20
   60-fold quotients : {2,4}*16, {4,2}*16
   80-fold quotients : {2,3}*12
   120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,120}*1920a, {8,120}*1920b, {8,120}*1920c, {4,240}*1920a, {4,240}*1920b
Permutation Representation (GAP) :

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