Polytope of Type {8,60}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,60}*1920b
if this polytope has a name.
Group : SmallGroup(1920,42340)
Rank : 3
Schlafli Type : {8,60}
Number of vertices, edges, etc : 16, 480, 120
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 : {8,20}*640b
   4-fold quotients : {4,60}*480a
   5-fold quotients : {8,12}*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 : {8,4}*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 := (  1,121)(  2,122)(  3,123)(  4,124)(  5,125)(  6,126)(  7,127)(  8,128)
(  9,129)( 10,130)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,136)
( 17,137)( 18,138)( 19,139)( 20,140)( 21,141)( 22,142)( 23,143)( 24,144)
( 25,145)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,151)( 32,152)
( 33,153)( 34,154)( 35,155)( 36,156)( 37,157)( 38,158)( 39,159)( 40,160)
( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,166)( 47,167)( 48,168)
( 49,169)( 50,170)( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)( 56,176)
( 57,177)( 58,178)( 59,179)( 60,180)( 61,226)( 62,227)( 63,228)( 64,229)
( 65,230)( 66,231)( 67,232)( 68,233)( 69,234)( 70,235)( 71,236)( 72,237)
( 73,238)( 74,239)( 75,240)( 76,211)( 77,212)( 78,213)( 79,214)( 80,215)
( 81,216)( 82,217)( 83,218)( 84,219)( 85,220)( 86,221)( 87,222)( 88,223)
( 89,224)( 90,225)( 91,196)( 92,197)( 93,198)( 94,199)( 95,200)( 96,201)
( 97,202)( 98,203)( 99,204)(100,205)(101,206)(102,207)(103,208)(104,209)
(105,210)(106,181)(107,182)(108,183)(109,184)(110,185)(111,186)(112,187)
(113,188)(114,189)(115,190)(116,191)(117,192)(118,193)(119,194)(120,195);;
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,  7)(  2,  6)(  3, 10)(  4,  9)(  5,  8)( 11, 12)( 13, 15)( 16, 22)
( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 37)( 32, 36)
( 33, 40)( 34, 39)( 35, 38)( 41, 42)( 43, 45)( 46, 52)( 47, 51)( 48, 55)
( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61,112)( 62,111)( 63,115)( 64,114)
( 65,113)( 66,107)( 67,106)( 68,110)( 69,109)( 70,108)( 71,117)( 72,116)
( 73,120)( 74,119)( 75,118)( 76, 97)( 77, 96)( 78,100)( 79, 99)( 80, 98)
( 81, 92)( 82, 91)( 83, 95)( 84, 94)( 85, 93)( 86,102)( 87,101)( 88,105)
( 89,104)( 90,103)(121,127)(122,126)(123,130)(124,129)(125,128)(131,132)
(133,135)(136,142)(137,141)(138,145)(139,144)(140,143)(146,147)(148,150)
(151,157)(152,156)(153,160)(154,159)(155,158)(161,162)(163,165)(166,172)
(167,171)(168,175)(169,174)(170,173)(176,177)(178,180)(181,232)(182,231)
(183,235)(184,234)(185,233)(186,227)(187,226)(188,230)(189,229)(190,228)
(191,237)(192,236)(193,240)(194,239)(195,238)(196,217)(197,216)(198,220)
(199,219)(200,218)(201,212)(202,211)(203,215)(204,214)(205,213)(206,222)
(207,221)(208,225)(209,224)(210,223);;
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, s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
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(240)!(  1,121)(  2,122)(  3,123)(  4,124)(  5,125)(  6,126)(  7,127)
(  8,128)(  9,129)( 10,130)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)
( 16,136)( 17,137)( 18,138)( 19,139)( 20,140)( 21,141)( 22,142)( 23,143)
( 24,144)( 25,145)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,151)
( 32,152)( 33,153)( 34,154)( 35,155)( 36,156)( 37,157)( 38,158)( 39,159)
( 40,160)( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,166)( 47,167)
( 48,168)( 49,169)( 50,170)( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)
( 56,176)( 57,177)( 58,178)( 59,179)( 60,180)( 61,226)( 62,227)( 63,228)
( 64,229)( 65,230)( 66,231)( 67,232)( 68,233)( 69,234)( 70,235)( 71,236)
( 72,237)( 73,238)( 74,239)( 75,240)( 76,211)( 77,212)( 78,213)( 79,214)
( 80,215)( 81,216)( 82,217)( 83,218)( 84,219)( 85,220)( 86,221)( 87,222)
( 88,223)( 89,224)( 90,225)( 91,196)( 92,197)( 93,198)( 94,199)( 95,200)
( 96,201)( 97,202)( 98,203)( 99,204)(100,205)(101,206)(102,207)(103,208)
(104,209)(105,210)(106,181)(107,182)(108,183)(109,184)(110,185)(111,186)
(112,187)(113,188)(114,189)(115,190)(116,191)(117,192)(118,193)(119,194)
(120,195);
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,  7)(  2,  6)(  3, 10)(  4,  9)(  5,  8)( 11, 12)( 13, 15)
( 16, 22)( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 37)
( 32, 36)( 33, 40)( 34, 39)( 35, 38)( 41, 42)( 43, 45)( 46, 52)( 47, 51)
( 48, 55)( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61,112)( 62,111)( 63,115)
( 64,114)( 65,113)( 66,107)( 67,106)( 68,110)( 69,109)( 70,108)( 71,117)
( 72,116)( 73,120)( 74,119)( 75,118)( 76, 97)( 77, 96)( 78,100)( 79, 99)
( 80, 98)( 81, 92)( 82, 91)( 83, 95)( 84, 94)( 85, 93)( 86,102)( 87,101)
( 88,105)( 89,104)( 90,103)(121,127)(122,126)(123,130)(124,129)(125,128)
(131,132)(133,135)(136,142)(137,141)(138,145)(139,144)(140,143)(146,147)
(148,150)(151,157)(152,156)(153,160)(154,159)(155,158)(161,162)(163,165)
(166,172)(167,171)(168,175)(169,174)(170,173)(176,177)(178,180)(181,232)
(182,231)(183,235)(184,234)(185,233)(186,227)(187,226)(188,230)(189,229)
(190,228)(191,237)(192,236)(193,240)(194,239)(195,238)(196,217)(197,216)
(198,220)(199,219)(200,218)(201,212)(202,211)(203,215)(204,214)(205,213)
(206,222)(207,221)(208,225)(209,224)(210,223);
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, s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
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 >;

References : None.
to this polytope