Polytope of Type {8,15} with group SmallGroup(1920,240269)

Overview

Group: SmallGroup(1920,240269)
Rank: 3
Schläfli Type: {8,15}
Vertices, edges, …: 64, 480, 120
Order of s₀s₁s₂: 30
Order of s₀s₁s₂s₁: 8
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

3-fold

{8,5}*640a

4-fold

{4,15}*480

6-fold

12-fold

{4,5}*160

32-fold

{2,15}*60

96-fold

{2,5}*20

160-fold

{2,3}*12

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s1*s0*s1*(s2*s1*s0)^3*(s1*s2)^3> of order 2

60 facets

60 of {8}*16

32 vertex figures

32 of {15}*30

P/N, where N=<(s0*s2*s1)^2*s0*(s2*s1)^3*s2> of order 4

30 facets

30 of {8}*16

16 vertex figures

16 of {15}*30

Representations

Permutation Representation (GAP)

s0 := (  1,483)(  2,484)(  3,481)(  4,482)(  5,487)(  6,488)(  7,485)(  8,486)(  9,491)( 10,492)( 11,489)( 12,490)( 13,495)( 14,496)( 15,493)( 16,494)( 17,499)( 18,500)( 19,497)( 20,498)
( 21,503)( 22,504)( 23,501)( 24,502)( 25,507)( 26,508)( 27,505)( 28,506)( 29,511)( 30,512)( 31,509)( 32,510)( 33,515)( 34,516)( 35,513)( 36,514)( 37,519)( 38,520)( 39,517)( 40,518)( 41,523)( 42,524)( 43,521)( 44,522)( 45,527)( 46,528)( 47,525)( 48,526)( 49,531)( 50,532)( 51,529)( 52,530)( 53,535)( 54,536)( 55,533)( 56,534)( 57,539)( 58,540)( 59,537)( 60,538)( 61,543)( 62,544)( 63,541)( 64,542)( 65,547)( 66,548)( 67,545)( 68,546)( 69,551)( 70,552)( 71,549)( 72,550)( 73,555)( 74,556)( 75,553)( 76,554)( 77,559)( 78,560)( 79,557)( 80,558)( 81,563)( 82,564)( 83,561)( 84,562)( 85,567)( 86,568)( 87,565)( 88,566)( 89,571)( 90,572)( 91,569)( 92,570)( 93,575)( 94,576)( 95,573)( 96,574)( 97,579)( 98,580)( 99,577)(100,578)(101,583)(102,584)(103,581)(104,582)(105,587)(106,588)(107,585)(108,586)(109,591)(110,592)(111,589)(112,590)(113,595)(114,596)(115,593)(116,594)(117,599)(118,600)(119,597)(120,598)(121,603)(122,604)(123,601)(124,602)(125,607)(126,608)(127,605)(128,606)(129,611)(130,612)(131,609)(132,610)(133,615)(134,616)(135,613)(136,614)(137,619)(138,620)(139,617)(140,618)(141,623)(142,624)(143,621)(144,622)(145,627)(146,628)(147,625)(148,626)(149,631)(150,632)(151,629)(152,630)(153,635)(154,636)(155,633)(156,634)(157,639)(158,640)(159,637)(160,638)(161,643)(162,644)(163,641)(164,642)(165,647)(166,648)(167,645)(168,646)(169,651)(170,652)(171,649)(172,650)(173,655)(174,656)(175,653)(176,654)(177,659)(178,660)(179,657)(180,658)(181,663)(182,664)(183,661)(184,662)(185,667)(186,668)(187,665)(188,666)(189,671)(190,672)(191,669)(192,670)(193,675)(194,676)(195,673)(196,674)(197,679)(198,680)(199,677)(200,678)(201,683)(202,684)(203,681)(204,682)(205,687)(206,688)(207,685)(208,686)(209,691)(210,692)(211,689)(212,690)(213,695)(214,696)(215,693)(216,694)(217,699)(218,700)(219,697)(220,698)(221,703)(222,704)(223,701)(224,702)(225,707)(226,708)(227,705)(228,706)(229,711)(230,712)(231,709)(232,710)(233,715)(234,716)(235,713)(236,714)(237,719)(238,720)(239,717)(240,718)(241,723)(242,724)(243,721)(244,722)(245,727)(246,728)(247,725)(248,726)(249,731)(250,732)(251,729)(252,730)(253,735)(254,736)(255,733)(256,734)(257,739)(258,740)(259,737)(260,738)(261,743)(262,744)(263,741)(264,742)(265,747)(266,748)(267,745)(268,746)(269,751)(270,752)(271,749)(272,750)(273,755)(274,756)(275,753)(276,754)(277,759)(278,760)(279,757)(280,758)(281,763)(282,764)(283,761)(284,762)(285,767)(286,768)(287,765)(288,766)(289,771)(290,772)(291,769)(292,770)(293,775)(294,776)(295,773)(296,774)(297,779)(298,780)(299,777)(300,778)(301,783)(302,784)(303,781)(304,782)(305,787)(306,788)(307,785)(308,786)(309,791)(310,792)(311,789)(312,790)(313,795)(314,796)(315,793)(316,794)(317,799)(318,800)(319,797)(320,798)(321,803)(322,804)(323,801)(324,802)(325,807)(326,808)(327,805)(328,806)(329,811)(330,812)(331,809)(332,810)(333,815)(334,816)(335,813)(336,814)(337,819)(338,820)(339,817)(340,818)(341,823)(342,824)(343,821)(344,822)(345,827)(346,828)(347,825)(348,826)(349,831)(350,832)(351,829)(352,830)(353,835)(354,836)(355,833)(356,834)(357,839)(358,840)(359,837)(360,838)(361,843)(362,844)(363,841)(364,842)(365,847)(366,848)(367,845)(368,846)(369,851)(370,852)(371,849)(372,850)(373,855)(374,856)(375,853)(376,854)(377,859)(378,860)(379,857)(380,858)(381,863)(382,864)(383,861)(384,862)(385,867)(386,868)(387,865)(388,866)(389,871)(390,872)(391,869)(392,870)(393,875)(394,876)(395,873)(396,874)(397,879)(398,880)(399,877)(400,878)(401,883)(402,884)(403,881)(404,882)(405,887)(406,888)(407,885)(408,886)(409,891)(410,892)(411,889)(412,890)(413,895)(414,896)(415,893)(416,894)(417,899)(418,900)(419,897)(420,898)(421,903)(422,904)(423,901)(424,902)(425,907)(426,908)(427,905)(428,906)(429,911)(430,912)(431,909)(432,910)(433,915)(434,916)(435,913)(436,914)(437,919)(438,920)(439,917)(440,918)(441,923)(442,924)(443,921)(444,922)(445,927)(446,928)(447,925)(448,926)(449,931)(450,932)(451,929)(452,930)(453,935)(454,936)(455,933)(456,934)(457,939)(458,940)(459,937)(460,938)(461,943)(462,944)(463,941)(464,942)(465,947)(466,948)(467,945)(468,946)(469,951)(470,952)(471,949)(472,950)(473,955)(474,956)
(475,953)(476,954)(477,959)(478,960)(479,957)(480,958);;
s1 := (  1, 33)(  2, 34)(  3, 64)(  4, 63)(  5, 44)(  6, 43)(  7, 53)(  8, 54)(  9, 60)( 10, 59)( 11, 38)( 12, 37)( 13, 50)( 14, 49)( 15, 48)( 16, 47)( 17, 46)( 18, 45)( 19, 51)( 20, 52)
( 21, 39)( 22, 40)( 23, 58)( 24, 57)( 25, 56)( 26, 55)( 27, 42)( 28, 41)( 29, 62)( 30, 61)( 31, 36)( 32, 35)( 65,129)( 66,130)( 67,160)( 68,159)( 69,140)( 70,139)( 71,149)( 72,150)( 73,156)( 74,155)( 75,134)( 76,133)( 77,146)( 78,145)( 79,144)( 80,143)( 81,142)( 82,141)( 83,147)( 84,148)( 85,135)( 86,136)( 87,154)( 88,153)( 89,152)( 90,151)( 91,138)( 92,137)( 93,158)( 94,157)( 95,132)( 96,131)( 99,128)(100,127)(101,108)(102,107)(103,117)(104,118)(105,124)(106,123)(109,114)(110,113)(111,112)(119,122)(120,121)(125,126)(161,353)(162,354)(163,384)(164,383)(165,364)(166,363)(167,373)(168,374)(169,380)(170,379)(171,358)(172,357)(173,370)(174,369)(175,368)(176,367)(177,366)(178,365)(179,371)(180,372)(181,359)(182,360)(183,378)(184,377)(185,376)(186,375)(187,362)(188,361)(189,382)(190,381)(191,356)(192,355)(193,321)(194,322)(195,352)(196,351)(197,332)(198,331)(199,341)(200,342)(201,348)(202,347)(203,326)(204,325)(205,338)(206,337)(207,336)(208,335)(209,334)(210,333)(211,339)(212,340)(213,327)(214,328)(215,346)(216,345)(217,344)(218,343)(219,330)(220,329)(221,350)(222,349)(223,324)(224,323)(225,449)(226,450)(227,480)(228,479)(229,460)(230,459)(231,469)(232,470)(233,476)(234,475)(235,454)(236,453)(237,466)(238,465)(239,464)(240,463)(241,462)(242,461)(243,467)(244,468)(245,455)(246,456)(247,474)(248,473)(249,472)(250,471)(251,458)(252,457)(253,478)(254,477)(255,452)(256,451)(257,417)(258,418)(259,448)(260,447)(261,428)(262,427)(263,437)(264,438)(265,444)(266,443)(267,422)(268,421)(269,434)(270,433)(271,432)(272,431)(273,430)(274,429)(275,435)(276,436)(277,423)(278,424)(279,442)(280,441)(281,440)(282,439)(283,426)(284,425)(285,446)(286,445)(287,420)(288,419)(289,385)(290,386)(291,416)(292,415)(293,396)(294,395)(295,405)(296,406)(297,412)(298,411)(299,390)(300,389)(301,402)(302,401)(303,400)(304,399)(305,398)(306,397)(307,403)(308,404)(309,391)(310,392)(311,410)(312,409)(313,408)(314,407)(315,394)(316,393)(317,414)(318,413)(319,388)(320,387)(481,513)(482,514)(483,544)(484,543)(485,524)(486,523)(487,533)(488,534)(489,540)(490,539)(491,518)(492,517)(493,530)(494,529)(495,528)(496,527)(497,526)(498,525)(499,531)(500,532)(501,519)(502,520)(503,538)(504,537)(505,536)(506,535)(507,522)(508,521)(509,542)(510,541)(511,516)(512,515)(545,609)(546,610)(547,640)(548,639)(549,620)(550,619)(551,629)(552,630)(553,636)(554,635)(555,614)(556,613)(557,626)(558,625)(559,624)(560,623)(561,622)(562,621)(563,627)(564,628)(565,615)(566,616)(567,634)(568,633)(569,632)(570,631)(571,618)(572,617)(573,638)(574,637)(575,612)(576,611)(579,608)(580,607)(581,588)(582,587)(583,597)(584,598)(585,604)(586,603)(589,594)(590,593)(591,592)(599,602)(600,601)(605,606)(641,833)(642,834)(643,864)(644,863)(645,844)(646,843)(647,853)(648,854)(649,860)(650,859)(651,838)(652,837)(653,850)(654,849)(655,848)(656,847)(657,846)(658,845)(659,851)(660,852)(661,839)(662,840)(663,858)(664,857)(665,856)(666,855)(667,842)(668,841)(669,862)(670,861)(671,836)(672,835)(673,801)(674,802)(675,832)(676,831)(677,812)(678,811)(679,821)(680,822)(681,828)(682,827)(683,806)(684,805)(685,818)(686,817)(687,816)(688,815)(689,814)(690,813)(691,819)(692,820)(693,807)(694,808)(695,826)(696,825)(697,824)(698,823)(699,810)(700,809)(701,830)(702,829)(703,804)(704,803)(705,929)(706,930)(707,960)(708,959)(709,940)(710,939)(711,949)(712,950)(713,956)(714,955)(715,934)(716,933)(717,946)(718,945)(719,944)(720,943)(721,942)(722,941)(723,947)(724,948)(725,935)(726,936)(727,954)(728,953)(729,952)(730,951)(731,938)(732,937)(733,958)(734,957)(735,932)(736,931)(737,897)(738,898)(739,928)(740,927)(741,908)(742,907)(743,917)(744,918)(745,924)(746,923)(747,902)(748,901)(749,914)(750,913)(751,912)(752,911)(753,910)(754,909)(755,915)(756,916)(757,903)(758,904)(759,922)(760,921)(761,920)(762,919)(763,906)(764,905)(765,926)(766,925)(767,900)(768,899)(769,865)(770,866)(771,896)(772,895)(773,876)(774,875)(775,885)(776,886)(777,892)(778,891)(779,870)(780,869)(781,882)(782,881)(783,880)(784,879)(785,878)(786,877)(787,883)(788,884)(789,871)(790,872)(791,890)(792,889)(793,888)(794,887)(795,874)(796,873)(797,894)(798,893)
(799,868)(800,867);;
s2 := (  1,161)(  2,162)(  3,163)(  4,164)(  5,168)(  6,167)(  7,166)(  8,165)(  9,170)( 10,169)( 11,172)( 12,171)( 13,175)( 14,176)( 15,173)( 16,174)( 17,188)( 18,187)( 19,186)( 20,185)
( 21,189)( 22,190)( 23,191)( 24,192)( 25,180)( 26,179)( 27,178)( 28,177)( 29,181)( 30,182)( 31,183)( 32,184)( 33,289)( 34,290)( 35,291)( 36,292)( 37,296)( 38,295)( 39,294)( 40,293)( 41,298)( 42,297)( 43,300)( 44,299)( 45,303)( 46,304)( 47,301)( 48,302)( 49,316)( 50,315)( 51,314)( 52,313)( 53,317)( 54,318)( 55,319)( 56,320)( 57,308)( 58,307)( 59,306)( 60,305)( 61,309)( 62,310)( 63,311)( 64,312)( 65,257)( 66,258)( 67,259)( 68,260)( 69,264)( 70,263)( 71,262)( 72,261)( 73,266)( 74,265)( 75,268)( 76,267)( 77,271)( 78,272)( 79,269)( 80,270)( 81,284)( 82,283)( 83,282)( 84,281)( 85,285)( 86,286)( 87,287)( 88,288)( 89,276)( 90,275)( 91,274)( 92,273)( 93,277)( 94,278)( 95,279)( 96,280)( 97,225)( 98,226)( 99,227)(100,228)(101,232)(102,231)(103,230)(104,229)(105,234)(106,233)(107,236)(108,235)(109,239)(110,240)(111,237)(112,238)(113,252)(114,251)(115,250)(116,249)(117,253)(118,254)(119,255)(120,256)(121,244)(122,243)(123,242)(124,241)(125,245)(126,246)(127,247)(128,248)(129,193)(130,194)(131,195)(132,196)(133,200)(134,199)(135,198)(136,197)(137,202)(138,201)(139,204)(140,203)(141,207)(142,208)(143,205)(144,206)(145,220)(146,219)(147,218)(148,217)(149,221)(150,222)(151,223)(152,224)(153,212)(154,211)(155,210)(156,209)(157,213)(158,214)(159,215)(160,216)(325,328)(326,327)(329,330)(331,332)(333,335)(334,336)(337,348)(338,347)(339,346)(340,345)(341,349)(342,350)(343,351)(344,352)(353,449)(354,450)(355,451)(356,452)(357,456)(358,455)(359,454)(360,453)(361,458)(362,457)(363,460)(364,459)(365,463)(366,464)(367,461)(368,462)(369,476)(370,475)(371,474)(372,473)(373,477)(374,478)(375,479)(376,480)(377,468)(378,467)(379,466)(380,465)(381,469)(382,470)(383,471)(384,472)(385,417)(386,418)(387,419)(388,420)(389,424)(390,423)(391,422)(392,421)(393,426)(394,425)(395,428)(396,427)(397,431)(398,432)(399,429)(400,430)(401,444)(402,443)(403,442)(404,441)(405,445)(406,446)(407,447)(408,448)(409,436)(410,435)(411,434)(412,433)(413,437)(414,438)(415,439)(416,440)(481,641)(482,642)(483,643)(484,644)(485,648)(486,647)(487,646)(488,645)(489,650)(490,649)(491,652)(492,651)(493,655)(494,656)(495,653)(496,654)(497,668)(498,667)(499,666)(500,665)(501,669)(502,670)(503,671)(504,672)(505,660)(506,659)(507,658)(508,657)(509,661)(510,662)(511,663)(512,664)(513,769)(514,770)(515,771)(516,772)(517,776)(518,775)(519,774)(520,773)(521,778)(522,777)(523,780)(524,779)(525,783)(526,784)(527,781)(528,782)(529,796)(530,795)(531,794)(532,793)(533,797)(534,798)(535,799)(536,800)(537,788)(538,787)(539,786)(540,785)(541,789)(542,790)(543,791)(544,792)(545,737)(546,738)(547,739)(548,740)(549,744)(550,743)(551,742)(552,741)(553,746)(554,745)(555,748)(556,747)(557,751)(558,752)(559,749)(560,750)(561,764)(562,763)(563,762)(564,761)(565,765)(566,766)(567,767)(568,768)(569,756)(570,755)(571,754)(572,753)(573,757)(574,758)(575,759)(576,760)(577,705)(578,706)(579,707)(580,708)(581,712)(582,711)(583,710)(584,709)(585,714)(586,713)(587,716)(588,715)(589,719)(590,720)(591,717)(592,718)(593,732)(594,731)(595,730)(596,729)(597,733)(598,734)(599,735)(600,736)(601,724)(602,723)(603,722)(604,721)(605,725)(606,726)(607,727)(608,728)(609,673)(610,674)(611,675)(612,676)(613,680)(614,679)(615,678)(616,677)(617,682)(618,681)(619,684)(620,683)(621,687)(622,688)(623,685)(624,686)(625,700)(626,699)(627,698)(628,697)(629,701)(630,702)(631,703)(632,704)(633,692)(634,691)(635,690)(636,689)(637,693)(638,694)(639,695)(640,696)(805,808)(806,807)(809,810)(811,812)(813,815)(814,816)(817,828)(818,827)(819,826)(820,825)(821,829)(822,830)(823,831)(824,832)(833,929)(834,930)(835,931)(836,932)(837,936)(838,935)(839,934)(840,933)(841,938)(842,937)(843,940)(844,939)(845,943)(846,944)(847,941)(848,942)(849,956)(850,955)(851,954)(852,953)(853,957)(854,958)(855,959)(856,960)(857,948)(858,947)(859,946)(860,945)(861,949)(862,950)(863,951)(864,952)(865,897)(866,898)(867,899)(868,900)(869,904)(870,903)(871,902)(872,901)(873,906)(874,905)(875,908)(876,907)(877,911)(878,912)(879,909)(880,910)(881,924)(882,923)(883,922)(884,921)(885,925)(886,926)(887,927)(888,928)(889,916)(890,915)(891,914)(892,913)(893,917)(894,918)
(895,919)(896,920);;
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, s0*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, 
s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*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 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(960)!(  1,483)(  2,484)(  3,481)(  4,482)(  5,487)(  6,488)(  7,485)(  8,486)(  9,491)( 10,492)( 11,489)( 12,490)( 13,495)( 14,496)( 15,493)( 16,494)( 17,499)( 18,500)( 19,497)
( 20,498)( 21,503)( 22,504)( 23,501)( 24,502)( 25,507)( 26,508)( 27,505)( 28,506)( 29,511)( 30,512)( 31,509)( 32,510)( 33,515)( 34,516)( 35,513)( 36,514)( 37,519)( 38,520)( 39,517)( 40,518)( 41,523)( 42,524)( 43,521)( 44,522)( 45,527)( 46,528)( 47,525)( 48,526)( 49,531)( 50,532)( 51,529)( 52,530)( 53,535)( 54,536)( 55,533)( 56,534)( 57,539)( 58,540)( 59,537)( 60,538)( 61,543)( 62,544)( 63,541)( 64,542)( 65,547)( 66,548)( 67,545)( 68,546)( 69,551)( 70,552)( 71,549)( 72,550)( 73,555)( 74,556)( 75,553)( 76,554)( 77,559)( 78,560)( 79,557)( 80,558)( 81,563)( 82,564)( 83,561)( 84,562)( 85,567)( 86,568)( 87,565)( 88,566)( 89,571)( 90,572)( 91,569)( 92,570)( 93,575)( 94,576)( 95,573)( 96,574)( 97,579)( 98,580)( 99,577)(100,578)(101,583)(102,584)(103,581)(104,582)(105,587)(106,588)(107,585)(108,586)(109,591)(110,592)(111,589)(112,590)(113,595)(114,596)(115,593)(116,594)(117,599)(118,600)(119,597)(120,598)(121,603)(122,604)(123,601)(124,602)(125,607)(126,608)(127,605)(128,606)(129,611)(130,612)(131,609)(132,610)(133,615)(134,616)(135,613)(136,614)(137,619)(138,620)(139,617)(140,618)(141,623)(142,624)(143,621)(144,622)(145,627)(146,628)(147,625)(148,626)(149,631)(150,632)(151,629)(152,630)(153,635)(154,636)(155,633)(156,634)(157,639)(158,640)(159,637)(160,638)(161,643)(162,644)(163,641)(164,642)(165,647)(166,648)(167,645)(168,646)(169,651)(170,652)(171,649)(172,650)(173,655)(174,656)(175,653)(176,654)(177,659)(178,660)(179,657)(180,658)(181,663)(182,664)(183,661)(184,662)(185,667)(186,668)(187,665)(188,666)(189,671)(190,672)(191,669)(192,670)(193,675)(194,676)(195,673)(196,674)(197,679)(198,680)(199,677)(200,678)(201,683)(202,684)(203,681)(204,682)(205,687)(206,688)(207,685)(208,686)(209,691)(210,692)(211,689)(212,690)(213,695)(214,696)(215,693)(216,694)(217,699)(218,700)(219,697)(220,698)(221,703)(222,704)(223,701)(224,702)(225,707)(226,708)(227,705)(228,706)(229,711)(230,712)(231,709)(232,710)(233,715)(234,716)(235,713)(236,714)(237,719)(238,720)(239,717)(240,718)(241,723)(242,724)(243,721)(244,722)(245,727)(246,728)(247,725)(248,726)(249,731)(250,732)(251,729)(252,730)(253,735)(254,736)(255,733)(256,734)(257,739)(258,740)(259,737)(260,738)(261,743)(262,744)(263,741)(264,742)(265,747)(266,748)(267,745)(268,746)(269,751)(270,752)(271,749)(272,750)(273,755)(274,756)(275,753)(276,754)(277,759)(278,760)(279,757)(280,758)(281,763)(282,764)(283,761)(284,762)(285,767)(286,768)(287,765)(288,766)(289,771)(290,772)(291,769)(292,770)(293,775)(294,776)(295,773)(296,774)(297,779)(298,780)(299,777)(300,778)(301,783)(302,784)(303,781)(304,782)(305,787)(306,788)(307,785)(308,786)(309,791)(310,792)(311,789)(312,790)(313,795)(314,796)(315,793)(316,794)(317,799)(318,800)(319,797)(320,798)(321,803)(322,804)(323,801)(324,802)(325,807)(326,808)(327,805)(328,806)(329,811)(330,812)(331,809)(332,810)(333,815)(334,816)(335,813)(336,814)(337,819)(338,820)(339,817)(340,818)(341,823)(342,824)(343,821)(344,822)(345,827)(346,828)(347,825)(348,826)(349,831)(350,832)(351,829)(352,830)(353,835)(354,836)(355,833)(356,834)(357,839)(358,840)(359,837)(360,838)(361,843)(362,844)(363,841)(364,842)(365,847)(366,848)(367,845)(368,846)(369,851)(370,852)(371,849)(372,850)(373,855)(374,856)(375,853)(376,854)(377,859)(378,860)(379,857)(380,858)(381,863)(382,864)(383,861)(384,862)(385,867)(386,868)(387,865)(388,866)(389,871)(390,872)(391,869)(392,870)(393,875)(394,876)(395,873)(396,874)(397,879)(398,880)(399,877)(400,878)(401,883)(402,884)(403,881)(404,882)(405,887)(406,888)(407,885)(408,886)(409,891)(410,892)(411,889)(412,890)(413,895)(414,896)(415,893)(416,894)(417,899)(418,900)(419,897)(420,898)(421,903)(422,904)(423,901)(424,902)(425,907)(426,908)(427,905)(428,906)(429,911)(430,912)(431,909)(432,910)(433,915)(434,916)(435,913)(436,914)(437,919)(438,920)(439,917)(440,918)(441,923)(442,924)(443,921)(444,922)(445,927)(446,928)(447,925)(448,926)(449,931)(450,932)(451,929)(452,930)(453,935)(454,936)(455,933)(456,934)(457,939)(458,940)(459,937)(460,938)(461,943)(462,944)(463,941)(464,942)(465,947)(466,948)(467,945)(468,946)(469,951)(470,952)(471,949)(472,950)(473,955)
(474,956)(475,953)(476,954)(477,959)(478,960)(479,957)(480,958);
s1 := Sym(960)!(  1, 33)(  2, 34)(  3, 64)(  4, 63)(  5, 44)(  6, 43)(  7, 53)(  8, 54)(  9, 60)( 10, 59)( 11, 38)( 12, 37)( 13, 50)( 14, 49)( 15, 48)( 16, 47)( 17, 46)( 18, 45)( 19, 51)
( 20, 52)( 21, 39)( 22, 40)( 23, 58)( 24, 57)( 25, 56)( 26, 55)( 27, 42)( 28, 41)( 29, 62)( 30, 61)( 31, 36)( 32, 35)( 65,129)( 66,130)( 67,160)( 68,159)( 69,140)( 70,139)( 71,149)( 72,150)( 73,156)( 74,155)( 75,134)( 76,133)( 77,146)( 78,145)( 79,144)( 80,143)( 81,142)( 82,141)( 83,147)( 84,148)( 85,135)( 86,136)( 87,154)( 88,153)( 89,152)( 90,151)( 91,138)( 92,137)( 93,158)( 94,157)( 95,132)( 96,131)( 99,128)(100,127)(101,108)(102,107)(103,117)(104,118)(105,124)(106,123)(109,114)(110,113)(111,112)(119,122)(120,121)(125,126)(161,353)(162,354)(163,384)(164,383)(165,364)(166,363)(167,373)(168,374)(169,380)(170,379)(171,358)(172,357)(173,370)(174,369)(175,368)(176,367)(177,366)(178,365)(179,371)(180,372)(181,359)(182,360)(183,378)(184,377)(185,376)(186,375)(187,362)(188,361)(189,382)(190,381)(191,356)(192,355)(193,321)(194,322)(195,352)(196,351)(197,332)(198,331)(199,341)(200,342)(201,348)(202,347)(203,326)(204,325)(205,338)(206,337)(207,336)(208,335)(209,334)(210,333)(211,339)(212,340)(213,327)(214,328)(215,346)(216,345)(217,344)(218,343)(219,330)(220,329)(221,350)(222,349)(223,324)(224,323)(225,449)(226,450)(227,480)(228,479)(229,460)(230,459)(231,469)(232,470)(233,476)(234,475)(235,454)(236,453)(237,466)(238,465)(239,464)(240,463)(241,462)(242,461)(243,467)(244,468)(245,455)(246,456)(247,474)(248,473)(249,472)(250,471)(251,458)(252,457)(253,478)(254,477)(255,452)(256,451)(257,417)(258,418)(259,448)(260,447)(261,428)(262,427)(263,437)(264,438)(265,444)(266,443)(267,422)(268,421)(269,434)(270,433)(271,432)(272,431)(273,430)(274,429)(275,435)(276,436)(277,423)(278,424)(279,442)(280,441)(281,440)(282,439)(283,426)(284,425)(285,446)(286,445)(287,420)(288,419)(289,385)(290,386)(291,416)(292,415)(293,396)(294,395)(295,405)(296,406)(297,412)(298,411)(299,390)(300,389)(301,402)(302,401)(303,400)(304,399)(305,398)(306,397)(307,403)(308,404)(309,391)(310,392)(311,410)(312,409)(313,408)(314,407)(315,394)(316,393)(317,414)(318,413)(319,388)(320,387)(481,513)(482,514)(483,544)(484,543)(485,524)(486,523)(487,533)(488,534)(489,540)(490,539)(491,518)(492,517)(493,530)(494,529)(495,528)(496,527)(497,526)(498,525)(499,531)(500,532)(501,519)(502,520)(503,538)(504,537)(505,536)(506,535)(507,522)(508,521)(509,542)(510,541)(511,516)(512,515)(545,609)(546,610)(547,640)(548,639)(549,620)(550,619)(551,629)(552,630)(553,636)(554,635)(555,614)(556,613)(557,626)(558,625)(559,624)(560,623)(561,622)(562,621)(563,627)(564,628)(565,615)(566,616)(567,634)(568,633)(569,632)(570,631)(571,618)(572,617)(573,638)(574,637)(575,612)(576,611)(579,608)(580,607)(581,588)(582,587)(583,597)(584,598)(585,604)(586,603)(589,594)(590,593)(591,592)(599,602)(600,601)(605,606)(641,833)(642,834)(643,864)(644,863)(645,844)(646,843)(647,853)(648,854)(649,860)(650,859)(651,838)(652,837)(653,850)(654,849)(655,848)(656,847)(657,846)(658,845)(659,851)(660,852)(661,839)(662,840)(663,858)(664,857)(665,856)(666,855)(667,842)(668,841)(669,862)(670,861)(671,836)(672,835)(673,801)(674,802)(675,832)(676,831)(677,812)(678,811)(679,821)(680,822)(681,828)(682,827)(683,806)(684,805)(685,818)(686,817)(687,816)(688,815)(689,814)(690,813)(691,819)(692,820)(693,807)(694,808)(695,826)(696,825)(697,824)(698,823)(699,810)(700,809)(701,830)(702,829)(703,804)(704,803)(705,929)(706,930)(707,960)(708,959)(709,940)(710,939)(711,949)(712,950)(713,956)(714,955)(715,934)(716,933)(717,946)(718,945)(719,944)(720,943)(721,942)(722,941)(723,947)(724,948)(725,935)(726,936)(727,954)(728,953)(729,952)(730,951)(731,938)(732,937)(733,958)(734,957)(735,932)(736,931)(737,897)(738,898)(739,928)(740,927)(741,908)(742,907)(743,917)(744,918)(745,924)(746,923)(747,902)(748,901)(749,914)(750,913)(751,912)(752,911)(753,910)(754,909)(755,915)(756,916)(757,903)(758,904)(759,922)(760,921)(761,920)(762,919)(763,906)(764,905)(765,926)(766,925)(767,900)(768,899)(769,865)(770,866)(771,896)(772,895)(773,876)(774,875)(775,885)(776,886)(777,892)(778,891)(779,870)(780,869)(781,882)(782,881)(783,880)(784,879)(785,878)(786,877)(787,883)(788,884)(789,871)(790,872)(791,890)(792,889)(793,888)(794,887)(795,874)(796,873)(797,894)
(798,893)(799,868)(800,867);
s2 := Sym(960)!(  1,161)(  2,162)(  3,163)(  4,164)(  5,168)(  6,167)(  7,166)(  8,165)(  9,170)( 10,169)( 11,172)( 12,171)( 13,175)( 14,176)( 15,173)( 16,174)( 17,188)( 18,187)( 19,186)
( 20,185)( 21,189)( 22,190)( 23,191)( 24,192)( 25,180)( 26,179)( 27,178)( 28,177)( 29,181)( 30,182)( 31,183)( 32,184)( 33,289)( 34,290)( 35,291)( 36,292)( 37,296)( 38,295)( 39,294)( 40,293)( 41,298)( 42,297)( 43,300)( 44,299)( 45,303)( 46,304)( 47,301)( 48,302)( 49,316)( 50,315)( 51,314)( 52,313)( 53,317)( 54,318)( 55,319)( 56,320)( 57,308)( 58,307)( 59,306)( 60,305)( 61,309)( 62,310)( 63,311)( 64,312)( 65,257)( 66,258)( 67,259)( 68,260)( 69,264)( 70,263)( 71,262)( 72,261)( 73,266)( 74,265)( 75,268)( 76,267)( 77,271)( 78,272)( 79,269)( 80,270)( 81,284)( 82,283)( 83,282)( 84,281)( 85,285)( 86,286)( 87,287)( 88,288)( 89,276)( 90,275)( 91,274)( 92,273)( 93,277)( 94,278)( 95,279)( 96,280)( 97,225)( 98,226)( 99,227)(100,228)(101,232)(102,231)(103,230)(104,229)(105,234)(106,233)(107,236)(108,235)(109,239)(110,240)(111,237)(112,238)(113,252)(114,251)(115,250)(116,249)(117,253)(118,254)(119,255)(120,256)(121,244)(122,243)(123,242)(124,241)(125,245)(126,246)(127,247)(128,248)(129,193)(130,194)(131,195)(132,196)(133,200)(134,199)(135,198)(136,197)(137,202)(138,201)(139,204)(140,203)(141,207)(142,208)(143,205)(144,206)(145,220)(146,219)(147,218)(148,217)(149,221)(150,222)(151,223)(152,224)(153,212)(154,211)(155,210)(156,209)(157,213)(158,214)(159,215)(160,216)(325,328)(326,327)(329,330)(331,332)(333,335)(334,336)(337,348)(338,347)(339,346)(340,345)(341,349)(342,350)(343,351)(344,352)(353,449)(354,450)(355,451)(356,452)(357,456)(358,455)(359,454)(360,453)(361,458)(362,457)(363,460)(364,459)(365,463)(366,464)(367,461)(368,462)(369,476)(370,475)(371,474)(372,473)(373,477)(374,478)(375,479)(376,480)(377,468)(378,467)(379,466)(380,465)(381,469)(382,470)(383,471)(384,472)(385,417)(386,418)(387,419)(388,420)(389,424)(390,423)(391,422)(392,421)(393,426)(394,425)(395,428)(396,427)(397,431)(398,432)(399,429)(400,430)(401,444)(402,443)(403,442)(404,441)(405,445)(406,446)(407,447)(408,448)(409,436)(410,435)(411,434)(412,433)(413,437)(414,438)(415,439)(416,440)(481,641)(482,642)(483,643)(484,644)(485,648)(486,647)(487,646)(488,645)(489,650)(490,649)(491,652)(492,651)(493,655)(494,656)(495,653)(496,654)(497,668)(498,667)(499,666)(500,665)(501,669)(502,670)(503,671)(504,672)(505,660)(506,659)(507,658)(508,657)(509,661)(510,662)(511,663)(512,664)(513,769)(514,770)(515,771)(516,772)(517,776)(518,775)(519,774)(520,773)(521,778)(522,777)(523,780)(524,779)(525,783)(526,784)(527,781)(528,782)(529,796)(530,795)(531,794)(532,793)(533,797)(534,798)(535,799)(536,800)(537,788)(538,787)(539,786)(540,785)(541,789)(542,790)(543,791)(544,792)(545,737)(546,738)(547,739)(548,740)(549,744)(550,743)(551,742)(552,741)(553,746)(554,745)(555,748)(556,747)(557,751)(558,752)(559,749)(560,750)(561,764)(562,763)(563,762)(564,761)(565,765)(566,766)(567,767)(568,768)(569,756)(570,755)(571,754)(572,753)(573,757)(574,758)(575,759)(576,760)(577,705)(578,706)(579,707)(580,708)(581,712)(582,711)(583,710)(584,709)(585,714)(586,713)(587,716)(588,715)(589,719)(590,720)(591,717)(592,718)(593,732)(594,731)(595,730)(596,729)(597,733)(598,734)(599,735)(600,736)(601,724)(602,723)(603,722)(604,721)(605,725)(606,726)(607,727)(608,728)(609,673)(610,674)(611,675)(612,676)(613,680)(614,679)(615,678)(616,677)(617,682)(618,681)(619,684)(620,683)(621,687)(622,688)(623,685)(624,686)(625,700)(626,699)(627,698)(628,697)(629,701)(630,702)(631,703)(632,704)(633,692)(634,691)(635,690)(636,689)(637,693)(638,694)(639,695)(640,696)(805,808)(806,807)(809,810)(811,812)(813,815)(814,816)(817,828)(818,827)(819,826)(820,825)(821,829)(822,830)(823,831)(824,832)(833,929)(834,930)(835,931)(836,932)(837,936)(838,935)(839,934)(840,933)(841,938)(842,937)(843,940)(844,939)(845,943)(846,944)(847,941)(848,942)(849,956)(850,955)(851,954)(852,953)(853,957)(854,958)(855,959)(856,960)(857,948)(858,947)(859,946)(860,945)(861,949)(862,950)(863,951)(864,952)(865,897)(866,898)(867,899)(868,900)(869,904)(870,903)(871,902)(872,901)(873,906)(874,905)(875,908)(876,907)(877,911)(878,912)(879,909)(880,910)(881,924)(882,923)(883,922)(884,921)(885,925)(886,926)(887,927)(888,928)(889,916)(890,915)(891,914)(892,913)(893,917)
(894,918)(895,919)(896,920);
poly := sub<Sym(960)|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, s0*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, 
s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*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 >;

References

None.

to this polytope.