Polytope of Type {2,4,60}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,60}*1920a
if this polytope has a name.
Group : SmallGroup(1920,151302)
Rank : 4
Schlafli Type : {2,4,60}
Number of vertices, edges, etc : 2, 8, 240, 120
Order of s₀s₁s₂s₃ : 60
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 : {2,4,20}*640
   4-fold quotients : {2,2,60}*480, {2,4,30}*480a
   5-fold quotients : {2,4,12}*384a
   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 : {2,4,4}*128
   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)( 63,183)( 64,187)( 65,186)( 66,185)
( 67,184)( 68,193)( 69,197)( 70,196)( 71,195)( 72,194)( 73,188)( 74,192)
( 75,191)( 76,190)( 77,189)( 78,198)( 79,202)( 80,201)( 81,200)( 82,199)
( 83,208)( 84,212)( 85,211)( 86,210)( 87,209)( 88,203)( 89,207)( 90,206)
( 91,205)( 92,204)( 93,213)( 94,217)( 95,216)( 96,215)( 97,214)( 98,223)
( 99,227)(100,226)(101,225)(102,224)(103,218)(104,222)(105,221)(106,220)
(107,219)(108,228)(109,232)(110,231)(111,230)(112,229)(113,238)(114,242)
(115,241)(116,240)(117,239)(118,233)(119,237)(120,236)(121,235)(122,234);;
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, 69)( 64, 68)( 65, 72)
( 66, 71)( 67, 70)( 73, 74)( 75, 77)( 78, 84)( 79, 83)( 80, 87)( 81, 86)
( 82, 85)( 88, 89)( 90, 92)( 93,114)( 94,113)( 95,117)( 96,116)( 97,115)
( 98,109)( 99,108)(100,112)(101,111)(102,110)(103,119)(104,118)(105,122)
(106,121)(107,120)(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, 
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*s2*s3*s2*s3 ];;
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)( 63,183)( 64,187)( 65,186)
( 66,185)( 67,184)( 68,193)( 69,197)( 70,196)( 71,195)( 72,194)( 73,188)
( 74,192)( 75,191)( 76,190)( 77,189)( 78,198)( 79,202)( 80,201)( 81,200)
( 82,199)( 83,208)( 84,212)( 85,211)( 86,210)( 87,209)( 88,203)( 89,207)
( 90,206)( 91,205)( 92,204)( 93,213)( 94,217)( 95,216)( 96,215)( 97,214)
( 98,223)( 99,227)(100,226)(101,225)(102,224)(103,218)(104,222)(105,221)
(106,220)(107,219)(108,228)(109,232)(110,231)(111,230)(112,229)(113,238)
(114,242)(115,241)(116,240)(117,239)(118,233)(119,237)(120,236)(121,235)
(122,234);
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, 69)( 64, 68)
( 65, 72)( 66, 71)( 67, 70)( 73, 74)( 75, 77)( 78, 84)( 79, 83)( 80, 87)
( 81, 86)( 82, 85)( 88, 89)( 90, 92)( 93,114)( 94,113)( 95,117)( 96,116)
( 97,115)( 98,109)( 99,108)(100,112)(101,111)(102,110)(103,119)(104,118)
(105,122)(106,121)(107,120)(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, 
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*s2*s3*s2*s3 >;

to this polytope