Polytope of Type {2,60,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,60,6}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240142)
Rank : 4
Schlafli Type : {2,60,6}
Number of vertices, edges, etc : 2, 80, 240, 8
Order of s₀s₁s₂s₃ : 20
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 : {2,30,6}*960
   4-fold quotients : {2,15,6}*480
   5-fold quotients : {2,12,6}*384a
   10-fold quotients : {2,6,6}*192
   12-fold quotients : {2,20,2}*160
   20-fold quotients : {2,3,6}*96, {2,6,3}*96
   24-fold quotients : {2,10,2}*80
   40-fold quotients : {2,3,3}*48
   48-fold quotients : {2,5,2}*40
   60-fold quotients : {2,4,2}*32
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope