Polytope of Type {2,4,120}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,120}*1920b
if this polytope has a name.
Group : SmallGroup(1920,150669)
Rank : 4
Schlafli Type : {2,4,120}
Number of vertices, edges, etc : 2, 4, 240, 120
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 : {2,4,60}*960a
   3-fold quotients : {2,4,40}*640b
   4-fold quotients : {2,2,60}*480, {2,4,30}*480a
   5-fold quotients : {2,4,24}*384b
   6-fold quotients : {2,4,20}*320
   8-fold quotients : {2,2,30}*240
   10-fold quotients : {2,4,12}*192a
   12-fold quotients : {2,2,20}*160, {2,4,10}*160
   15-fold quotients : {2,4,8}*128b
   16-fold quotients : {2,2,15}*120
   20-fold quotients : {2,2,12}*96, {2,4,6}*96a
   24-fold quotients : {2,2,10}*80
   30-fold quotients : {2,4,4}*64
   40-fold quotients : {2,2,6}*48
   48-fold quotients : {2,2,5}*40
   60-fold quotients : {2,2,4}*32, {2,4,2}*32
   80-fold quotients : {2,2,3}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope