Polytope of Type {60,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,8}*960b
if this polytope has a name.
Group : SmallGroup(960,5118)
Rank : 3
Schlafli Type : {60,8}
Number of vertices, edges, etc : 60, 240, 8
Order of s₀s₁s₂ : 120
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {60,8,2} of size 1920
Vertex Figure Of :
   {2,60,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {60,4}*480a
   3-fold quotients : {20,8}*320b
   4-fold quotients : {60,2}*240, {30,4}*240a
   5-fold quotients : {12,8}*192b
   6-fold quotients : {20,4}*160
   8-fold quotients : {30,2}*120
   10-fold quotients : {12,4}*96a
   12-fold quotients : {20,2}*80, {10,4}*80
   15-fold quotients : {4,8}*64b
   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
   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 : {60,8}*1920a, {120,8}*1920b, {120,8}*1920d
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)( 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);;
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)( 31,172)( 32,171)
( 33,175)( 34,174)( 35,173)( 36,167)( 37,166)( 38,170)( 39,169)( 40,168)
( 41,177)( 42,176)( 43,180)( 44,179)( 45,178)( 46,157)( 47,156)( 48,160)
( 49,159)( 50,158)( 51,152)( 52,151)( 53,155)( 54,154)( 55,153)( 56,162)
( 57,161)( 58,165)( 59,164)( 60,163)( 61,187)( 62,186)( 63,190)( 64,189)
( 65,188)( 66,182)( 67,181)( 68,185)( 69,184)( 70,183)( 71,192)( 72,191)
( 73,195)( 74,194)( 75,193)( 76,202)( 77,201)( 78,205)( 79,204)( 80,203)
( 81,197)( 82,196)( 83,200)( 84,199)( 85,198)( 86,207)( 87,206)( 88,210)
( 89,209)( 90,208)( 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 := ( 31, 46)( 32, 47)( 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)( 61, 76)
( 62, 77)( 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)(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)(181,226)(182,227)(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)(196,211)(197,212)(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);;
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*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*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)( 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);
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)( 31,172)
( 32,171)( 33,175)( 34,174)( 35,173)( 36,167)( 37,166)( 38,170)( 39,169)
( 40,168)( 41,177)( 42,176)( 43,180)( 44,179)( 45,178)( 46,157)( 47,156)
( 48,160)( 49,159)( 50,158)( 51,152)( 52,151)( 53,155)( 54,154)( 55,153)
( 56,162)( 57,161)( 58,165)( 59,164)( 60,163)( 61,187)( 62,186)( 63,190)
( 64,189)( 65,188)( 66,182)( 67,181)( 68,185)( 69,184)( 70,183)( 71,192)
( 72,191)( 73,195)( 74,194)( 75,193)( 76,202)( 77,201)( 78,205)( 79,204)
( 80,203)( 81,197)( 82,196)( 83,200)( 84,199)( 85,198)( 86,207)( 87,206)
( 88,210)( 89,209)( 90,208)( 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)!( 31, 46)( 32, 47)( 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)
( 61, 76)( 62, 77)( 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)(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)(181,226)(182,227)(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)(196,211)(197,212)(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);
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*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*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