Polytope of Type {2,60,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,60,8}*1920a
if this polytope has a name.
Group : SmallGroup(1920,148884)
Rank : 4
Schlafli Type : {2,60,8}
Number of vertices, edges, etc : 2, 60, 240, 8
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, {2,30,8}*960
   3-fold quotients : {2,20,8}*640a
   4-fold quotients : {2,60,2}*480, {2,30,4}*480a
   5-fold quotients : {2,12,8}*384a
   6-fold quotients : {2,20,4}*320, {2,10,8}*320
   8-fold quotients : {2,30,2}*240
   10-fold quotients : {2,12,4}*192a, {2,6,8}*192
   12-fold quotients : {2,20,2}*160, {2,10,4}*160
   15-fold quotients : {2,4,8}*128a
   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, {2,2,8}*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)( 34, 37)( 35, 36)
( 38, 43)( 39, 47)( 40, 46)( 41, 45)( 42, 44)( 49, 52)( 50, 51)( 53, 58)
( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 64, 67)( 65, 66)( 68, 73)( 69, 77)
( 70, 76)( 71, 75)( 72, 74)( 79, 82)( 80, 81)( 83, 88)( 84, 92)( 85, 91)
( 86, 90)( 87, 89)( 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)(153,213)(154,217)
(155,216)(156,215)(157,214)(158,223)(159,227)(160,226)(161,225)(162,224)
(163,218)(164,222)(165,221)(166,220)(167,219)(168,228)(169,232)(170,231)
(171,230)(172,229)(173,238)(174,242)(175,241)(176,240)(177,239)(178,233)
(179,237)(180,236)(181,235)(182,234);;
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)( 33,174)( 34,173)
( 35,177)( 36,176)( 37,175)( 38,169)( 39,168)( 40,172)( 41,171)( 42,170)
( 43,179)( 44,178)( 45,182)( 46,181)( 47,180)( 48,159)( 49,158)( 50,162)
( 51,161)( 52,160)( 53,154)( 54,153)( 55,157)( 56,156)( 57,155)( 58,164)
( 59,163)( 60,167)( 61,166)( 62,165)( 63,189)( 64,188)( 65,192)( 66,191)
( 67,190)( 68,184)( 69,183)( 70,187)( 71,186)( 72,185)( 73,194)( 74,193)
( 75,197)( 76,196)( 77,195)( 78,204)( 79,203)( 80,207)( 81,206)( 82,205)
( 83,199)( 84,198)( 85,202)( 86,201)( 87,200)( 88,209)( 89,208)( 90,212)
( 91,211)( 92,210)( 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 := ( 33, 48)( 34, 49)( 35, 50)( 36, 51)( 37, 52)( 38, 53)( 39, 54)( 40, 55)
( 41, 56)( 42, 57)( 43, 58)( 44, 59)( 45, 60)( 46, 61)( 47, 62)( 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)(183,213)(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)
(211,241)(212,242);;
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*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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*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)( 34, 37)
( 35, 36)( 38, 43)( 39, 47)( 40, 46)( 41, 45)( 42, 44)( 49, 52)( 50, 51)
( 53, 58)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 64, 67)( 65, 66)( 68, 73)
( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 79, 82)( 80, 81)( 83, 88)( 84, 92)
( 85, 91)( 86, 90)( 87, 89)( 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)(153,213)
(154,217)(155,216)(156,215)(157,214)(158,223)(159,227)(160,226)(161,225)
(162,224)(163,218)(164,222)(165,221)(166,220)(167,219)(168,228)(169,232)
(170,231)(171,230)(172,229)(173,238)(174,242)(175,241)(176,240)(177,239)
(178,233)(179,237)(180,236)(181,235)(182,234);
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)( 33,174)
( 34,173)( 35,177)( 36,176)( 37,175)( 38,169)( 39,168)( 40,172)( 41,171)
( 42,170)( 43,179)( 44,178)( 45,182)( 46,181)( 47,180)( 48,159)( 49,158)
( 50,162)( 51,161)( 52,160)( 53,154)( 54,153)( 55,157)( 56,156)( 57,155)
( 58,164)( 59,163)( 60,167)( 61,166)( 62,165)( 63,189)( 64,188)( 65,192)
( 66,191)( 67,190)( 68,184)( 69,183)( 70,187)( 71,186)( 72,185)( 73,194)
( 74,193)( 75,197)( 76,196)( 77,195)( 78,204)( 79,203)( 80,207)( 81,206)
( 82,205)( 83,199)( 84,198)( 85,202)( 86,201)( 87,200)( 88,209)( 89,208)
( 90,212)( 91,211)( 92,210)( 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)!( 33, 48)( 34, 49)( 35, 50)( 36, 51)( 37, 52)( 38, 53)( 39, 54)
( 40, 55)( 41, 56)( 42, 57)( 43, 58)( 44, 59)( 45, 60)( 46, 61)( 47, 62)
( 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)(183,213)(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)(211,241)(212,242);
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*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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*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