Polytope of Type {4,120}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,120}*1920b
if this polytope has a name.
Group : SmallGroup(1920,42337)
Rank : 3
Schlafli Type : {4,120}
Number of vertices, edges, etc : 8, 480, 240
Order of s₀s₁s₂ : 60
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {4,60}*960a
   3-fold quotients : {4,40}*640b
   4-fold quotients : {4,60}*480a
   5-fold quotients : {4,24}*384b
   6-fold quotients : {4,20}*320
   8-fold quotients : {2,60}*240, {4,30}*240a
   10-fold quotients : {4,12}*192a
   12-fold quotients : {4,20}*160
   15-fold quotients : {4,8}*128b
   16-fold quotients : {2,30}*120
   20-fold quotients : {4,12}*96a
   24-fold quotients : {2,20}*80, {4,10}*80
   30-fold quotients : {4,4}*64
   32-fold quotients : {2,15}*60
   40-fold quotients : {2,12}*48, {4,6}*48a
   48-fold quotients : {2,10}*40
   60-fold quotients : {4,4}*32
   80-fold quotients : {2,6}*24
   96-fold quotients : {2,5}*20
   120-fold quotients : {2,4}*16, {4,2}*16
   160-fold quotients : {2,3}*12
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 61,106)( 62,107)( 63,108)( 64,109)( 65,110)( 66,111)( 67,112)( 68,113)
( 69,114)( 70,115)( 71,116)( 72,117)( 73,118)( 74,119)( 75,120)( 76, 91)
( 77, 92)( 78, 93)( 79, 94)( 80, 95)( 81, 96)( 82, 97)( 83, 98)( 84, 99)
( 85,100)( 86,101)( 87,102)( 88,103)( 89,104)( 90,105)(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);;
s1 := (  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)( 62, 65)( 63, 64)( 66, 71)
( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 77, 80)( 78, 79)( 81, 86)( 82, 90)
( 83, 89)( 84, 88)( 85, 87)( 91,106)( 92,110)( 93,109)( 94,108)( 95,107)
( 96,116)( 97,120)( 98,119)( 99,118)(100,117)(101,111)(102,115)(103,114)
(104,113)(105,112)(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);;
s2 := (  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)( 61,232)( 62,231)( 63,235)( 64,234)
( 65,233)( 66,227)( 67,226)( 68,230)( 69,229)( 70,228)( 71,237)( 72,236)
( 73,240)( 74,239)( 75,238)( 76,217)( 77,216)( 78,220)( 79,219)( 80,218)
( 81,212)( 82,211)( 83,215)( 84,214)( 85,213)( 86,222)( 87,221)( 88,225)
( 89,224)( 90,223)( 91,202)( 92,201)( 93,205)( 94,204)( 95,203)( 96,197)
( 97,196)( 98,200)( 99,199)(100,198)(101,207)(102,206)(103,210)(104,209)
(105,208)(106,187)(107,186)(108,190)(109,189)(110,188)(111,182)(112,181)
(113,185)(114,184)(115,183)(116,192)(117,191)(118,195)(119,194)(120,193);;
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*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(240)!( 61,106)( 62,107)( 63,108)( 64,109)( 65,110)( 66,111)( 67,112)
( 68,113)( 69,114)( 70,115)( 71,116)( 72,117)( 73,118)( 74,119)( 75,120)
( 76, 91)( 77, 92)( 78, 93)( 79, 94)( 80, 95)( 81, 96)( 82, 97)( 83, 98)
( 84, 99)( 85,100)( 86,101)( 87,102)( 88,103)( 89,104)( 90,105)(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);
s1 := 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)( 62, 65)( 63, 64)
( 66, 71)( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 77, 80)( 78, 79)( 81, 86)
( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 91,106)( 92,110)( 93,109)( 94,108)
( 95,107)( 96,116)( 97,120)( 98,119)( 99,118)(100,117)(101,111)(102,115)
(103,114)(104,113)(105,112)(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);
s2 := 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)( 61,232)( 62,231)( 63,235)
( 64,234)( 65,233)( 66,227)( 67,226)( 68,230)( 69,229)( 70,228)( 71,237)
( 72,236)( 73,240)( 74,239)( 75,238)( 76,217)( 77,216)( 78,220)( 79,219)
( 80,218)( 81,212)( 82,211)( 83,215)( 84,214)( 85,213)( 86,222)( 87,221)
( 88,225)( 89,224)( 90,223)( 91,202)( 92,201)( 93,205)( 94,204)( 95,203)
( 96,197)( 97,196)( 98,200)( 99,199)(100,198)(101,207)(102,206)(103,210)
(104,209)(105,208)(106,187)(107,186)(108,190)(109,189)(110,188)(111,182)
(112,181)(113,185)(114,184)(115,183)(116,192)(117,191)(118,195)(119,194)
(120,193);
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*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References : None.
to this polytope