Questions?
See the FAQ
or other info.

Polytope of Type {120,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {120,4}*960a
Also Known As : {120,4|2}. if this polytope has another name.
Group : SmallGroup(960,5028)
Rank : 3
Schlafli Type : {120,4}
Number of vertices, edges, etc : 120, 240, 4
Order of s0s1s2 : 120
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {120,4,2} of size 1920
Vertex Figure Of :
   {2,120,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {60,4}*480a, {120,2}*480
   3-fold quotients : {40,4}*320a
   4-fold quotients : {60,2}*240, {30,4}*240a
   5-fold quotients : {24,4}*192a
   6-fold quotients : {20,4}*160, {40,2}*160
   8-fold quotients : {30,2}*120
   10-fold quotients : {12,4}*96a, {24,2}*96
   12-fold quotients : {20,2}*80, {10,4}*80
   15-fold quotients : {8,4}*64a
   16-fold quotients : {15,2}*60
   20-fold quotients : {12,2}*48, {6,4}*48a
   24-fold quotients : {10,2}*40
   30-fold quotients : {4,4}*32, {8,2}*32
   40-fold quotients : {6,2}*24
   48-fold quotients : {5,2}*20
   60-fold quotients : {2,4}*16, {4,2}*16
   80-fold quotients : {3,2}*12
   120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {120,4}*1920a, {120,8}*1920b, {120,8}*1920c, {240,4}*1920a, {240,4}*1920b
Permutation Representation (GAP) :
s0 := (  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)( 32, 35)( 33, 34)
( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 47, 50)( 48, 49)( 51, 56)
( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 76)( 62, 80)( 63, 79)( 64, 78)
( 65, 77)( 66, 86)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 81)( 72, 85)
( 73, 84)( 74, 83)( 75, 82)( 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)
(151,211)(152,215)(153,214)(154,213)(155,212)(156,221)(157,225)(158,224)
(159,223)(160,222)(161,216)(162,220)(163,219)(164,218)(165,217)(166,226)
(167,230)(168,229)(169,228)(170,227)(171,236)(172,240)(173,239)(174,238)
(175,237)(176,231)(177,235)(178,234)(179,233)(180,232);;
s1 := (  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)( 61,202)( 62,201)( 63,205)( 64,204)
( 65,203)( 66,197)( 67,196)( 68,200)( 69,199)( 70,198)( 71,207)( 72,206)
( 73,210)( 74,209)( 75,208)( 76,187)( 77,186)( 78,190)( 79,189)( 80,188)
( 81,182)( 82,181)( 83,185)( 84,184)( 85,183)( 86,192)( 87,191)( 88,195)
( 89,194)( 90,193)( 91,232)( 92,231)( 93,235)( 94,234)( 95,233)( 96,227)
( 97,226)( 98,230)( 99,229)(100,228)(101,237)(102,236)(103,240)(104,239)
(105,238)(106,217)(107,216)(108,220)(109,219)(110,218)(111,212)(112,211)
(113,215)(114,214)(115,213)(116,222)(117,221)(118,225)(119,224)(120,223);;
s2 := (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);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := 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)( 32, 35)
( 33, 34)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 47, 50)( 48, 49)
( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 76)( 62, 80)( 63, 79)
( 64, 78)( 65, 77)( 66, 86)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 81)
( 72, 85)( 73, 84)( 74, 83)( 75, 82)( 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)(151,211)(152,215)(153,214)(154,213)(155,212)(156,221)(157,225)
(158,224)(159,223)(160,222)(161,216)(162,220)(163,219)(164,218)(165,217)
(166,226)(167,230)(168,229)(169,228)(170,227)(171,236)(172,240)(173,239)
(174,238)(175,237)(176,231)(177,235)(178,234)(179,233)(180,232);
s1 := 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)( 61,202)( 62,201)( 63,205)
( 64,204)( 65,203)( 66,197)( 67,196)( 68,200)( 69,199)( 70,198)( 71,207)
( 72,206)( 73,210)( 74,209)( 75,208)( 76,187)( 77,186)( 78,190)( 79,189)
( 80,188)( 81,182)( 82,181)( 83,185)( 84,184)( 85,183)( 86,192)( 87,191)
( 88,195)( 89,194)( 90,193)( 91,232)( 92,231)( 93,235)( 94,234)( 95,233)
( 96,227)( 97,226)( 98,230)( 99,229)(100,228)(101,237)(102,236)(103,240)
(104,239)(105,238)(106,217)(107,216)(108,220)(109,219)(110,218)(111,212)
(112,211)(113,215)(114,214)(115,213)(116,222)(117,221)(118,225)(119,224)
(120,223);
s2 := 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);
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope