Polytope of Type {2,120,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,120,4}*1920a
if this polytope has a name.
Group : SmallGroup(1920,148887)
Rank : 4
Schlafli Type : {2,120,4}
Number of vertices, edges, etc : 2, 120, 240, 4
Order of s₀s₁s₂s₃ : 120
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,60,4}*960a, {2,120,2}*960
   3-fold quotients : {2,40,4}*640a
   4-fold quotients : {2,60,2}*480, {2,30,4}*480a
   5-fold quotients : {2,24,4}*384a
   6-fold quotients : {2,20,4}*320, {2,40,2}*320
   8-fold quotients : {2,30,2}*240
   10-fold quotients : {2,12,4}*192a, {2,24,2}*192
   12-fold quotients : {2,20,2}*160, {2,10,4}*160
   15-fold quotients : {2,8,4}*128a
   16-fold quotients : {2,15,2}*120
   20-fold quotients : {2,12,2}*96, {2,6,4}*96a
   24-fold quotients : {2,10,2}*80
   30-fold quotients : {2,4,4}*64, {2,8,2}*64
   40-fold quotients : {2,6,2}*48
   48-fold quotients : {2,5,2}*40
   60-fold quotients : {2,2,4}*32, {2,4,2}*32
   80-fold quotients : {2,3,2}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  7)(  5,  6)(  8, 13)(  9, 17)( 10, 16)( 11, 15)( 12, 14)( 19, 22)
( 20, 21)( 23, 28)( 24, 32)( 25, 31)( 26, 30)( 27, 29)( 34, 37)( 35, 36)
( 38, 43)( 39, 47)( 40, 46)( 41, 45)( 42, 44)( 49, 52)( 50, 51)( 53, 58)
( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 63, 78)( 64, 82)( 65, 81)( 66, 80)
( 67, 79)( 68, 88)( 69, 92)( 70, 91)( 71, 90)( 72, 89)( 73, 83)( 74, 87)
( 75, 86)( 76, 85)( 77, 84)( 93,108)( 94,112)( 95,111)( 96,110)( 97,109)
( 98,118)( 99,122)(100,121)(101,120)(102,119)(103,113)(104,117)(105,116)
(106,115)(107,114)(123,183)(124,187)(125,186)(126,185)(127,184)(128,193)
(129,197)(130,196)(131,195)(132,194)(133,188)(134,192)(135,191)(136,190)
(137,189)(138,198)(139,202)(140,201)(141,200)(142,199)(143,208)(144,212)
(145,211)(146,210)(147,209)(148,203)(149,207)(150,206)(151,205)(152,204)
(153,213)(154,217)(155,216)(156,215)(157,214)(158,223)(159,227)(160,226)
(161,225)(162,224)(163,218)(164,222)(165,221)(166,220)(167,219)(168,228)
(169,232)(170,231)(171,230)(172,229)(173,238)(174,242)(175,241)(176,240)
(177,239)(178,233)(179,237)(180,236)(181,235)(182,234);;
s2 := (  3,129)(  4,128)(  5,132)(  6,131)(  7,130)(  8,124)(  9,123)( 10,127)
( 11,126)( 12,125)( 13,134)( 14,133)( 15,137)( 16,136)( 17,135)( 18,144)
( 19,143)( 20,147)( 21,146)( 22,145)( 23,139)( 24,138)( 25,142)( 26,141)
( 27,140)( 28,149)( 29,148)( 30,152)( 31,151)( 32,150)( 33,159)( 34,158)
( 35,162)( 36,161)( 37,160)( 38,154)( 39,153)( 40,157)( 41,156)( 42,155)
( 43,164)( 44,163)( 45,167)( 46,166)( 47,165)( 48,174)( 49,173)( 50,177)
( 51,176)( 52,175)( 53,169)( 54,168)( 55,172)( 56,171)( 57,170)( 58,179)
( 59,178)( 60,182)( 61,181)( 62,180)( 63,204)( 64,203)( 65,207)( 66,206)
( 67,205)( 68,199)( 69,198)( 70,202)( 71,201)( 72,200)( 73,209)( 74,208)
( 75,212)( 76,211)( 77,210)( 78,189)( 79,188)( 80,192)( 81,191)( 82,190)
( 83,184)( 84,183)( 85,187)( 86,186)( 87,185)( 88,194)( 89,193)( 90,197)
( 91,196)( 92,195)( 93,234)( 94,233)( 95,237)( 96,236)( 97,235)( 98,229)
( 99,228)(100,232)(101,231)(102,230)(103,239)(104,238)(105,242)(106,241)
(107,240)(108,219)(109,218)(110,222)(111,221)(112,220)(113,214)(114,213)
(115,217)(116,216)(117,215)(118,224)(119,223)(120,227)(121,226)(122,225);;
s3 := (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)(151,181)(152,182)(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)(211,241)(212,242);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
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(242)!(1,2);
s1 := Sym(242)!(  4,  7)(  5,  6)(  8, 13)(  9, 17)( 10, 16)( 11, 15)( 12, 14)
( 19, 22)( 20, 21)( 23, 28)( 24, 32)( 25, 31)( 26, 30)( 27, 29)( 34, 37)
( 35, 36)( 38, 43)( 39, 47)( 40, 46)( 41, 45)( 42, 44)( 49, 52)( 50, 51)
( 53, 58)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 63, 78)( 64, 82)( 65, 81)
( 66, 80)( 67, 79)( 68, 88)( 69, 92)( 70, 91)( 71, 90)( 72, 89)( 73, 83)
( 74, 87)( 75, 86)( 76, 85)( 77, 84)( 93,108)( 94,112)( 95,111)( 96,110)
( 97,109)( 98,118)( 99,122)(100,121)(101,120)(102,119)(103,113)(104,117)
(105,116)(106,115)(107,114)(123,183)(124,187)(125,186)(126,185)(127,184)
(128,193)(129,197)(130,196)(131,195)(132,194)(133,188)(134,192)(135,191)
(136,190)(137,189)(138,198)(139,202)(140,201)(141,200)(142,199)(143,208)
(144,212)(145,211)(146,210)(147,209)(148,203)(149,207)(150,206)(151,205)
(152,204)(153,213)(154,217)(155,216)(156,215)(157,214)(158,223)(159,227)
(160,226)(161,225)(162,224)(163,218)(164,222)(165,221)(166,220)(167,219)
(168,228)(169,232)(170,231)(171,230)(172,229)(173,238)(174,242)(175,241)
(176,240)(177,239)(178,233)(179,237)(180,236)(181,235)(182,234);
s2 := Sym(242)!(  3,129)(  4,128)(  5,132)(  6,131)(  7,130)(  8,124)(  9,123)
( 10,127)( 11,126)( 12,125)( 13,134)( 14,133)( 15,137)( 16,136)( 17,135)
( 18,144)( 19,143)( 20,147)( 21,146)( 22,145)( 23,139)( 24,138)( 25,142)
( 26,141)( 27,140)( 28,149)( 29,148)( 30,152)( 31,151)( 32,150)( 33,159)
( 34,158)( 35,162)( 36,161)( 37,160)( 38,154)( 39,153)( 40,157)( 41,156)
( 42,155)( 43,164)( 44,163)( 45,167)( 46,166)( 47,165)( 48,174)( 49,173)
( 50,177)( 51,176)( 52,175)( 53,169)( 54,168)( 55,172)( 56,171)( 57,170)
( 58,179)( 59,178)( 60,182)( 61,181)( 62,180)( 63,204)( 64,203)( 65,207)
( 66,206)( 67,205)( 68,199)( 69,198)( 70,202)( 71,201)( 72,200)( 73,209)
( 74,208)( 75,212)( 76,211)( 77,210)( 78,189)( 79,188)( 80,192)( 81,191)
( 82,190)( 83,184)( 84,183)( 85,187)( 86,186)( 87,185)( 88,194)( 89,193)
( 90,197)( 91,196)( 92,195)( 93,234)( 94,233)( 95,237)( 96,236)( 97,235)
( 98,229)( 99,228)(100,232)(101,231)(102,230)(103,239)(104,238)(105,242)
(106,241)(107,240)(108,219)(109,218)(110,222)(111,221)(112,220)(113,214)
(114,213)(115,217)(116,216)(117,215)(118,224)(119,223)(120,227)(121,226)
(122,225);
s3 := Sym(242)!(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)(151,181)(152,182)(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)(211,241)(212,242);
poly := sub<Sym(242)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, 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 >;

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