Polytope of Type {2,120,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,120,4}*1920b
if this polytope has a name.
Group : SmallGroup(1920,150669)
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
   3-fold quotients : {2,40,4}*640b
   4-fold quotients : {2,60,2}*480, {2,30,4}*480a
   5-fold quotients : {2,24,4}*384b
   6-fold quotients : {2,20,4}*320
   8-fold quotients : {2,30,2}*240
   10-fold quotients : {2,12,4}*192a
   12-fold quotients : {2,20,2}*160, {2,10,4}*160
   15-fold quotients : {2,8,4}*128b
   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
   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)( 33, 48)( 34, 52)
( 35, 51)( 36, 50)( 37, 49)( 38, 58)( 39, 62)( 40, 61)( 41, 60)( 42, 59)
( 43, 53)( 44, 57)( 45, 56)( 46, 55)( 47, 54)( 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)( 94, 97)( 95, 96)( 98,103)( 99,107)
(100,106)(101,105)(102,104)(109,112)(110,111)(113,118)(114,122)(115,121)
(116,120)(117,119)(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)
(153,228)(154,232)(155,231)(156,230)(157,229)(158,238)(159,242)(160,241)
(161,240)(162,239)(163,233)(164,237)(165,236)(166,235)(167,234)(168,213)
(169,217)(170,216)(171,215)(172,214)(173,223)(174,227)(175,226)(176,225)
(177,224)(178,218)(179,222)(180,221)(181,220)(182,219);;
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 := ( 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)( 76, 91)( 77, 92)( 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)(106,121)(107,122)(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)(183,228)(184,229)(185,230)(186,231)
(187,232)(188,233)(189,234)(190,235)(191,236)(192,237)(193,238)(194,239)
(195,240)(196,241)(197,242)(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)
(211,226)(212,227);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)( 33, 48)
( 34, 52)( 35, 51)( 36, 50)( 37, 49)( 38, 58)( 39, 62)( 40, 61)( 41, 60)
( 42, 59)( 43, 53)( 44, 57)( 45, 56)( 46, 55)( 47, 54)( 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)( 94, 97)( 95, 96)( 98,103)
( 99,107)(100,106)(101,105)(102,104)(109,112)(110,111)(113,118)(114,122)
(115,121)(116,120)(117,119)(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)(153,228)(154,232)(155,231)(156,230)(157,229)(158,238)(159,242)
(160,241)(161,240)(162,239)(163,233)(164,237)(165,236)(166,235)(167,234)
(168,213)(169,217)(170,216)(171,215)(172,214)(173,223)(174,227)(175,226)
(176,225)(177,224)(178,218)(179,222)(180,221)(181,220)(182,219);
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)!( 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)( 76, 91)( 77, 92)
( 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)(106,121)(107,122)(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)(183,228)(184,229)(185,230)
(186,231)(187,232)(188,233)(189,234)(190,235)(191,236)(192,237)(193,238)
(194,239)(195,240)(196,241)(197,242)(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)(211,226)(212,227);
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, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope