Polytope of Type {8,52}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,52}*1664a
if this polytope has a name.
Group : SmallGroup(1664,3429)
Rank : 3
Schlafli Type : {8,52}
Number of vertices, edges, etc : 16, 416, 104
Order of s0s1s2 : 104
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 : {4,52}*832, {8,52}*832a, {8,52}*832b
4-fold quotients : {4,52}*416, {8,26}*416
8-fold quotients : {2,52}*208, {4,26}*208
13-fold quotients : {8,4}*128a
16-fold quotients : {2,26}*104
26-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64
32-fold quotients : {2,13}*52
52-fold quotients : {4,4}*32, {8,2}*32
104-fold quotients : {2,4}*16, {4,2}*16
208-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,417)( 2,418)( 3,419)( 4,420)( 5,421)( 6,422)( 7,423)( 8,424)
( 9,425)( 10,426)( 11,427)( 12,428)( 13,429)( 14,430)( 15,431)( 16,432)
( 17,433)( 18,434)( 19,435)( 20,436)( 21,437)( 22,438)( 23,439)( 24,440)
( 25,441)( 26,442)( 27,443)( 28,444)( 29,445)( 30,446)( 31,447)( 32,448)
( 33,449)( 34,450)( 35,451)( 36,452)( 37,453)( 38,454)( 39,455)( 40,456)
( 41,457)( 42,458)( 43,459)( 44,460)( 45,461)( 46,462)( 47,463)( 48,464)
( 49,465)( 50,466)( 51,467)( 52,468)( 53,482)( 54,483)( 55,484)( 56,485)
( 57,486)( 58,487)( 59,488)( 60,489)( 61,490)( 62,491)( 63,492)( 64,493)
( 65,494)( 66,469)( 67,470)( 68,471)( 69,472)( 70,473)( 71,474)( 72,475)
( 73,476)( 74,477)( 75,478)( 76,479)( 77,480)( 78,481)( 79,508)( 80,509)
( 81,510)( 82,511)( 83,512)( 84,513)( 85,514)( 86,515)( 87,516)( 88,517)
( 89,518)( 90,519)( 91,520)( 92,495)( 93,496)( 94,497)( 95,498)( 96,499)
( 97,500)( 98,501)( 99,502)(100,503)(101,504)(102,505)(103,506)(104,507)
(105,547)(106,548)(107,549)(108,550)(109,551)(110,552)(111,553)(112,554)
(113,555)(114,556)(115,557)(116,558)(117,559)(118,560)(119,561)(120,562)
(121,563)(122,564)(123,565)(124,566)(125,567)(126,568)(127,569)(128,570)
(129,571)(130,572)(131,521)(132,522)(133,523)(134,524)(135,525)(136,526)
(137,527)(138,528)(139,529)(140,530)(141,531)(142,532)(143,533)(144,534)
(145,535)(146,536)(147,537)(148,538)(149,539)(150,540)(151,541)(152,542)
(153,543)(154,544)(155,545)(156,546)(157,612)(158,613)(159,614)(160,615)
(161,616)(162,617)(163,618)(164,619)(165,620)(166,621)(167,622)(168,623)
(169,624)(170,599)(171,600)(172,601)(173,602)(174,603)(175,604)(176,605)
(177,606)(178,607)(179,608)(180,609)(181,610)(182,611)(183,586)(184,587)
(185,588)(186,589)(187,590)(188,591)(189,592)(190,593)(191,594)(192,595)
(193,596)(194,597)(195,598)(196,573)(197,574)(198,575)(199,576)(200,577)
(201,578)(202,579)(203,580)(204,581)(205,582)(206,583)(207,584)(208,585)
(209,625)(210,626)(211,627)(212,628)(213,629)(214,630)(215,631)(216,632)
(217,633)(218,634)(219,635)(220,636)(221,637)(222,638)(223,639)(224,640)
(225,641)(226,642)(227,643)(228,644)(229,645)(230,646)(231,647)(232,648)
(233,649)(234,650)(235,651)(236,652)(237,653)(238,654)(239,655)(240,656)
(241,657)(242,658)(243,659)(244,660)(245,661)(246,662)(247,663)(248,664)
(249,665)(250,666)(251,667)(252,668)(253,669)(254,670)(255,671)(256,672)
(257,673)(258,674)(259,675)(260,676)(261,690)(262,691)(263,692)(264,693)
(265,694)(266,695)(267,696)(268,697)(269,698)(270,699)(271,700)(272,701)
(273,702)(274,677)(275,678)(276,679)(277,680)(278,681)(279,682)(280,683)
(281,684)(282,685)(283,686)(284,687)(285,688)(286,689)(287,716)(288,717)
(289,718)(290,719)(291,720)(292,721)(293,722)(294,723)(295,724)(296,725)
(297,726)(298,727)(299,728)(300,703)(301,704)(302,705)(303,706)(304,707)
(305,708)(306,709)(307,710)(308,711)(309,712)(310,713)(311,714)(312,715)
(313,755)(314,756)(315,757)(316,758)(317,759)(318,760)(319,761)(320,762)
(321,763)(322,764)(323,765)(324,766)(325,767)(326,768)(327,769)(328,770)
(329,771)(330,772)(331,773)(332,774)(333,775)(334,776)(335,777)(336,778)
(337,779)(338,780)(339,729)(340,730)(341,731)(342,732)(343,733)(344,734)
(345,735)(346,736)(347,737)(348,738)(349,739)(350,740)(351,741)(352,742)
(353,743)(354,744)(355,745)(356,746)(357,747)(358,748)(359,749)(360,750)
(361,751)(362,752)(363,753)(364,754)(365,820)(366,821)(367,822)(368,823)
(369,824)(370,825)(371,826)(372,827)(373,828)(374,829)(375,830)(376,831)
(377,832)(378,807)(379,808)(380,809)(381,810)(382,811)(383,812)(384,813)
(385,814)(386,815)(387,816)(388,817)(389,818)(390,819)(391,794)(392,795)
(393,796)(394,797)(395,798)(396,799)(397,800)(398,801)(399,802)(400,803)
(401,804)(402,805)(403,806)(404,781)(405,782)(406,783)(407,784)(408,785)
(409,786)(410,787)(411,788)(412,789)(413,790)(414,791)(415,792)(416,793);;
s1 := ( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 15, 26)( 16, 25)
( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 28, 39)( 29, 38)( 30, 37)( 31, 36)
( 32, 35)( 33, 34)( 41, 52)( 42, 51)( 43, 50)( 44, 49)( 45, 48)( 46, 47)
( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 67, 78)( 68, 77)
( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 80, 91)( 81, 90)( 82, 89)( 83, 88)
( 84, 87)( 85, 86)( 93,104)( 94,103)( 95,102)( 96,101)( 97,100)( 98, 99)
(105,131)(106,143)(107,142)(108,141)(109,140)(110,139)(111,138)(112,137)
(113,136)(114,135)(115,134)(116,133)(117,132)(118,144)(119,156)(120,155)
(121,154)(122,153)(123,152)(124,151)(125,150)(126,149)(127,148)(128,147)
(129,146)(130,145)(157,183)(158,195)(159,194)(160,193)(161,192)(162,191)
(163,190)(164,189)(165,188)(166,187)(167,186)(168,185)(169,184)(170,196)
(171,208)(172,207)(173,206)(174,205)(175,204)(176,203)(177,202)(178,201)
(179,200)(180,199)(181,198)(182,197)(209,261)(210,273)(211,272)(212,271)
(213,270)(214,269)(215,268)(216,267)(217,266)(218,265)(219,264)(220,263)
(221,262)(222,274)(223,286)(224,285)(225,284)(226,283)(227,282)(228,281)
(229,280)(230,279)(231,278)(232,277)(233,276)(234,275)(235,287)(236,299)
(237,298)(238,297)(239,296)(240,295)(241,294)(242,293)(243,292)(244,291)
(245,290)(246,289)(247,288)(248,300)(249,312)(250,311)(251,310)(252,309)
(253,308)(254,307)(255,306)(256,305)(257,304)(258,303)(259,302)(260,301)
(313,391)(314,403)(315,402)(316,401)(317,400)(318,399)(319,398)(320,397)
(321,396)(322,395)(323,394)(324,393)(325,392)(326,404)(327,416)(328,415)
(329,414)(330,413)(331,412)(332,411)(333,410)(334,409)(335,408)(336,407)
(337,406)(338,405)(339,365)(340,377)(341,376)(342,375)(343,374)(344,373)
(345,372)(346,371)(347,370)(348,369)(349,368)(350,367)(351,366)(352,378)
(353,390)(354,389)(355,388)(356,387)(357,386)(358,385)(359,384)(360,383)
(361,382)(362,381)(363,380)(364,379)(417,521)(418,533)(419,532)(420,531)
(421,530)(422,529)(423,528)(424,527)(425,526)(426,525)(427,524)(428,523)
(429,522)(430,534)(431,546)(432,545)(433,544)(434,543)(435,542)(436,541)
(437,540)(438,539)(439,538)(440,537)(441,536)(442,535)(443,547)(444,559)
(445,558)(446,557)(447,556)(448,555)(449,554)(450,553)(451,552)(452,551)
(453,550)(454,549)(455,548)(456,560)(457,572)(458,571)(459,570)(460,569)
(461,568)(462,567)(463,566)(464,565)(465,564)(466,563)(467,562)(468,561)
(469,573)(470,585)(471,584)(472,583)(473,582)(474,581)(475,580)(476,579)
(477,578)(478,577)(479,576)(480,575)(481,574)(482,586)(483,598)(484,597)
(485,596)(486,595)(487,594)(488,593)(489,592)(490,591)(491,590)(492,589)
(493,588)(494,587)(495,599)(496,611)(497,610)(498,609)(499,608)(500,607)
(501,606)(502,605)(503,604)(504,603)(505,602)(506,601)(507,600)(508,612)
(509,624)(510,623)(511,622)(512,621)(513,620)(514,619)(515,618)(516,617)
(517,616)(518,615)(519,614)(520,613)(625,794)(626,806)(627,805)(628,804)
(629,803)(630,802)(631,801)(632,800)(633,799)(634,798)(635,797)(636,796)
(637,795)(638,781)(639,793)(640,792)(641,791)(642,790)(643,789)(644,788)
(645,787)(646,786)(647,785)(648,784)(649,783)(650,782)(651,820)(652,832)
(653,831)(654,830)(655,829)(656,828)(657,827)(658,826)(659,825)(660,824)
(661,823)(662,822)(663,821)(664,807)(665,819)(666,818)(667,817)(668,816)
(669,815)(670,814)(671,813)(672,812)(673,811)(674,810)(675,809)(676,808)
(677,742)(678,754)(679,753)(680,752)(681,751)(682,750)(683,749)(684,748)
(685,747)(686,746)(687,745)(688,744)(689,743)(690,729)(691,741)(692,740)
(693,739)(694,738)(695,737)(696,736)(697,735)(698,734)(699,733)(700,732)
(701,731)(702,730)(703,768)(704,780)(705,779)(706,778)(707,777)(708,776)
(709,775)(710,774)(711,773)(712,772)(713,771)(714,770)(715,769)(716,755)
(717,767)(718,766)(719,765)(720,764)(721,763)(722,762)(723,761)(724,760)
(725,759)(726,758)(727,757)(728,756);;
s2 := ( 1,210)( 2,209)( 3,221)( 4,220)( 5,219)( 6,218)( 7,217)( 8,216)
( 9,215)( 10,214)( 11,213)( 12,212)( 13,211)( 14,223)( 15,222)( 16,234)
( 17,233)( 18,232)( 19,231)( 20,230)( 21,229)( 22,228)( 23,227)( 24,226)
( 25,225)( 26,224)( 27,236)( 28,235)( 29,247)( 30,246)( 31,245)( 32,244)
( 33,243)( 34,242)( 35,241)( 36,240)( 37,239)( 38,238)( 39,237)( 40,249)
( 41,248)( 42,260)( 43,259)( 44,258)( 45,257)( 46,256)( 47,255)( 48,254)
( 49,253)( 50,252)( 51,251)( 52,250)( 53,262)( 54,261)( 55,273)( 56,272)
( 57,271)( 58,270)( 59,269)( 60,268)( 61,267)( 62,266)( 63,265)( 64,264)
( 65,263)( 66,275)( 67,274)( 68,286)( 69,285)( 70,284)( 71,283)( 72,282)
( 73,281)( 74,280)( 75,279)( 76,278)( 77,277)( 78,276)( 79,288)( 80,287)
( 81,299)( 82,298)( 83,297)( 84,296)( 85,295)( 86,294)( 87,293)( 88,292)
( 89,291)( 90,290)( 91,289)( 92,301)( 93,300)( 94,312)( 95,311)( 96,310)
( 97,309)( 98,308)( 99,307)(100,306)(101,305)(102,304)(103,303)(104,302)
(105,327)(106,326)(107,338)(108,337)(109,336)(110,335)(111,334)(112,333)
(113,332)(114,331)(115,330)(116,329)(117,328)(118,314)(119,313)(120,325)
(121,324)(122,323)(123,322)(124,321)(125,320)(126,319)(127,318)(128,317)
(129,316)(130,315)(131,353)(132,352)(133,364)(134,363)(135,362)(136,361)
(137,360)(138,359)(139,358)(140,357)(141,356)(142,355)(143,354)(144,340)
(145,339)(146,351)(147,350)(148,349)(149,348)(150,347)(151,346)(152,345)
(153,344)(154,343)(155,342)(156,341)(157,379)(158,378)(159,390)(160,389)
(161,388)(162,387)(163,386)(164,385)(165,384)(166,383)(167,382)(168,381)
(169,380)(170,366)(171,365)(172,377)(173,376)(174,375)(175,374)(176,373)
(177,372)(178,371)(179,370)(180,369)(181,368)(182,367)(183,405)(184,404)
(185,416)(186,415)(187,414)(188,413)(189,412)(190,411)(191,410)(192,409)
(193,408)(194,407)(195,406)(196,392)(197,391)(198,403)(199,402)(200,401)
(201,400)(202,399)(203,398)(204,397)(205,396)(206,395)(207,394)(208,393)
(417,626)(418,625)(419,637)(420,636)(421,635)(422,634)(423,633)(424,632)
(425,631)(426,630)(427,629)(428,628)(429,627)(430,639)(431,638)(432,650)
(433,649)(434,648)(435,647)(436,646)(437,645)(438,644)(439,643)(440,642)
(441,641)(442,640)(443,652)(444,651)(445,663)(446,662)(447,661)(448,660)
(449,659)(450,658)(451,657)(452,656)(453,655)(454,654)(455,653)(456,665)
(457,664)(458,676)(459,675)(460,674)(461,673)(462,672)(463,671)(464,670)
(465,669)(466,668)(467,667)(468,666)(469,678)(470,677)(471,689)(472,688)
(473,687)(474,686)(475,685)(476,684)(477,683)(478,682)(479,681)(480,680)
(481,679)(482,691)(483,690)(484,702)(485,701)(486,700)(487,699)(488,698)
(489,697)(490,696)(491,695)(492,694)(493,693)(494,692)(495,704)(496,703)
(497,715)(498,714)(499,713)(500,712)(501,711)(502,710)(503,709)(504,708)
(505,707)(506,706)(507,705)(508,717)(509,716)(510,728)(511,727)(512,726)
(513,725)(514,724)(515,723)(516,722)(517,721)(518,720)(519,719)(520,718)
(521,743)(522,742)(523,754)(524,753)(525,752)(526,751)(527,750)(528,749)
(529,748)(530,747)(531,746)(532,745)(533,744)(534,730)(535,729)(536,741)
(537,740)(538,739)(539,738)(540,737)(541,736)(542,735)(543,734)(544,733)
(545,732)(546,731)(547,769)(548,768)(549,780)(550,779)(551,778)(552,777)
(553,776)(554,775)(555,774)(556,773)(557,772)(558,771)(559,770)(560,756)
(561,755)(562,767)(563,766)(564,765)(565,764)(566,763)(567,762)(568,761)
(569,760)(570,759)(571,758)(572,757)(573,795)(574,794)(575,806)(576,805)
(577,804)(578,803)(579,802)(580,801)(581,800)(582,799)(583,798)(584,797)
(585,796)(586,782)(587,781)(588,793)(589,792)(590,791)(591,790)(592,789)
(593,788)(594,787)(595,786)(596,785)(597,784)(598,783)(599,821)(600,820)
(601,832)(602,831)(603,830)(604,829)(605,828)(606,827)(607,826)(608,825)
(609,824)(610,823)(611,822)(612,808)(613,807)(614,819)(615,818)(616,817)
(617,816)(618,815)(619,814)(620,813)(621,812)(622,811)(623,810)(624,809);;
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*s0*s1*s2*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(832)!( 1,417)( 2,418)( 3,419)( 4,420)( 5,421)( 6,422)( 7,423)
( 8,424)( 9,425)( 10,426)( 11,427)( 12,428)( 13,429)( 14,430)( 15,431)
( 16,432)( 17,433)( 18,434)( 19,435)( 20,436)( 21,437)( 22,438)( 23,439)
( 24,440)( 25,441)( 26,442)( 27,443)( 28,444)( 29,445)( 30,446)( 31,447)
( 32,448)( 33,449)( 34,450)( 35,451)( 36,452)( 37,453)( 38,454)( 39,455)
( 40,456)( 41,457)( 42,458)( 43,459)( 44,460)( 45,461)( 46,462)( 47,463)
( 48,464)( 49,465)( 50,466)( 51,467)( 52,468)( 53,482)( 54,483)( 55,484)
( 56,485)( 57,486)( 58,487)( 59,488)( 60,489)( 61,490)( 62,491)( 63,492)
( 64,493)( 65,494)( 66,469)( 67,470)( 68,471)( 69,472)( 70,473)( 71,474)
( 72,475)( 73,476)( 74,477)( 75,478)( 76,479)( 77,480)( 78,481)( 79,508)
( 80,509)( 81,510)( 82,511)( 83,512)( 84,513)( 85,514)( 86,515)( 87,516)
( 88,517)( 89,518)( 90,519)( 91,520)( 92,495)( 93,496)( 94,497)( 95,498)
( 96,499)( 97,500)( 98,501)( 99,502)(100,503)(101,504)(102,505)(103,506)
(104,507)(105,547)(106,548)(107,549)(108,550)(109,551)(110,552)(111,553)
(112,554)(113,555)(114,556)(115,557)(116,558)(117,559)(118,560)(119,561)
(120,562)(121,563)(122,564)(123,565)(124,566)(125,567)(126,568)(127,569)
(128,570)(129,571)(130,572)(131,521)(132,522)(133,523)(134,524)(135,525)
(136,526)(137,527)(138,528)(139,529)(140,530)(141,531)(142,532)(143,533)
(144,534)(145,535)(146,536)(147,537)(148,538)(149,539)(150,540)(151,541)
(152,542)(153,543)(154,544)(155,545)(156,546)(157,612)(158,613)(159,614)
(160,615)(161,616)(162,617)(163,618)(164,619)(165,620)(166,621)(167,622)
(168,623)(169,624)(170,599)(171,600)(172,601)(173,602)(174,603)(175,604)
(176,605)(177,606)(178,607)(179,608)(180,609)(181,610)(182,611)(183,586)
(184,587)(185,588)(186,589)(187,590)(188,591)(189,592)(190,593)(191,594)
(192,595)(193,596)(194,597)(195,598)(196,573)(197,574)(198,575)(199,576)
(200,577)(201,578)(202,579)(203,580)(204,581)(205,582)(206,583)(207,584)
(208,585)(209,625)(210,626)(211,627)(212,628)(213,629)(214,630)(215,631)
(216,632)(217,633)(218,634)(219,635)(220,636)(221,637)(222,638)(223,639)
(224,640)(225,641)(226,642)(227,643)(228,644)(229,645)(230,646)(231,647)
(232,648)(233,649)(234,650)(235,651)(236,652)(237,653)(238,654)(239,655)
(240,656)(241,657)(242,658)(243,659)(244,660)(245,661)(246,662)(247,663)
(248,664)(249,665)(250,666)(251,667)(252,668)(253,669)(254,670)(255,671)
(256,672)(257,673)(258,674)(259,675)(260,676)(261,690)(262,691)(263,692)
(264,693)(265,694)(266,695)(267,696)(268,697)(269,698)(270,699)(271,700)
(272,701)(273,702)(274,677)(275,678)(276,679)(277,680)(278,681)(279,682)
(280,683)(281,684)(282,685)(283,686)(284,687)(285,688)(286,689)(287,716)
(288,717)(289,718)(290,719)(291,720)(292,721)(293,722)(294,723)(295,724)
(296,725)(297,726)(298,727)(299,728)(300,703)(301,704)(302,705)(303,706)
(304,707)(305,708)(306,709)(307,710)(308,711)(309,712)(310,713)(311,714)
(312,715)(313,755)(314,756)(315,757)(316,758)(317,759)(318,760)(319,761)
(320,762)(321,763)(322,764)(323,765)(324,766)(325,767)(326,768)(327,769)
(328,770)(329,771)(330,772)(331,773)(332,774)(333,775)(334,776)(335,777)
(336,778)(337,779)(338,780)(339,729)(340,730)(341,731)(342,732)(343,733)
(344,734)(345,735)(346,736)(347,737)(348,738)(349,739)(350,740)(351,741)
(352,742)(353,743)(354,744)(355,745)(356,746)(357,747)(358,748)(359,749)
(360,750)(361,751)(362,752)(363,753)(364,754)(365,820)(366,821)(367,822)
(368,823)(369,824)(370,825)(371,826)(372,827)(373,828)(374,829)(375,830)
(376,831)(377,832)(378,807)(379,808)(380,809)(381,810)(382,811)(383,812)
(384,813)(385,814)(386,815)(387,816)(388,817)(389,818)(390,819)(391,794)
(392,795)(393,796)(394,797)(395,798)(396,799)(397,800)(398,801)(399,802)
(400,803)(401,804)(402,805)(403,806)(404,781)(405,782)(406,783)(407,784)
(408,785)(409,786)(410,787)(411,788)(412,789)(413,790)(414,791)(415,792)
(416,793);
s1 := Sym(832)!( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 15, 26)
( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 28, 39)( 29, 38)( 30, 37)
( 31, 36)( 32, 35)( 33, 34)( 41, 52)( 42, 51)( 43, 50)( 44, 49)( 45, 48)
( 46, 47)( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 67, 78)
( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 80, 91)( 81, 90)( 82, 89)
( 83, 88)( 84, 87)( 85, 86)( 93,104)( 94,103)( 95,102)( 96,101)( 97,100)
( 98, 99)(105,131)(106,143)(107,142)(108,141)(109,140)(110,139)(111,138)
(112,137)(113,136)(114,135)(115,134)(116,133)(117,132)(118,144)(119,156)
(120,155)(121,154)(122,153)(123,152)(124,151)(125,150)(126,149)(127,148)
(128,147)(129,146)(130,145)(157,183)(158,195)(159,194)(160,193)(161,192)
(162,191)(163,190)(164,189)(165,188)(166,187)(167,186)(168,185)(169,184)
(170,196)(171,208)(172,207)(173,206)(174,205)(175,204)(176,203)(177,202)
(178,201)(179,200)(180,199)(181,198)(182,197)(209,261)(210,273)(211,272)
(212,271)(213,270)(214,269)(215,268)(216,267)(217,266)(218,265)(219,264)
(220,263)(221,262)(222,274)(223,286)(224,285)(225,284)(226,283)(227,282)
(228,281)(229,280)(230,279)(231,278)(232,277)(233,276)(234,275)(235,287)
(236,299)(237,298)(238,297)(239,296)(240,295)(241,294)(242,293)(243,292)
(244,291)(245,290)(246,289)(247,288)(248,300)(249,312)(250,311)(251,310)
(252,309)(253,308)(254,307)(255,306)(256,305)(257,304)(258,303)(259,302)
(260,301)(313,391)(314,403)(315,402)(316,401)(317,400)(318,399)(319,398)
(320,397)(321,396)(322,395)(323,394)(324,393)(325,392)(326,404)(327,416)
(328,415)(329,414)(330,413)(331,412)(332,411)(333,410)(334,409)(335,408)
(336,407)(337,406)(338,405)(339,365)(340,377)(341,376)(342,375)(343,374)
(344,373)(345,372)(346,371)(347,370)(348,369)(349,368)(350,367)(351,366)
(352,378)(353,390)(354,389)(355,388)(356,387)(357,386)(358,385)(359,384)
(360,383)(361,382)(362,381)(363,380)(364,379)(417,521)(418,533)(419,532)
(420,531)(421,530)(422,529)(423,528)(424,527)(425,526)(426,525)(427,524)
(428,523)(429,522)(430,534)(431,546)(432,545)(433,544)(434,543)(435,542)
(436,541)(437,540)(438,539)(439,538)(440,537)(441,536)(442,535)(443,547)
(444,559)(445,558)(446,557)(447,556)(448,555)(449,554)(450,553)(451,552)
(452,551)(453,550)(454,549)(455,548)(456,560)(457,572)(458,571)(459,570)
(460,569)(461,568)(462,567)(463,566)(464,565)(465,564)(466,563)(467,562)
(468,561)(469,573)(470,585)(471,584)(472,583)(473,582)(474,581)(475,580)
(476,579)(477,578)(478,577)(479,576)(480,575)(481,574)(482,586)(483,598)
(484,597)(485,596)(486,595)(487,594)(488,593)(489,592)(490,591)(491,590)
(492,589)(493,588)(494,587)(495,599)(496,611)(497,610)(498,609)(499,608)
(500,607)(501,606)(502,605)(503,604)(504,603)(505,602)(506,601)(507,600)
(508,612)(509,624)(510,623)(511,622)(512,621)(513,620)(514,619)(515,618)
(516,617)(517,616)(518,615)(519,614)(520,613)(625,794)(626,806)(627,805)
(628,804)(629,803)(630,802)(631,801)(632,800)(633,799)(634,798)(635,797)
(636,796)(637,795)(638,781)(639,793)(640,792)(641,791)(642,790)(643,789)
(644,788)(645,787)(646,786)(647,785)(648,784)(649,783)(650,782)(651,820)
(652,832)(653,831)(654,830)(655,829)(656,828)(657,827)(658,826)(659,825)
(660,824)(661,823)(662,822)(663,821)(664,807)(665,819)(666,818)(667,817)
(668,816)(669,815)(670,814)(671,813)(672,812)(673,811)(674,810)(675,809)
(676,808)(677,742)(678,754)(679,753)(680,752)(681,751)(682,750)(683,749)
(684,748)(685,747)(686,746)(687,745)(688,744)(689,743)(690,729)(691,741)
(692,740)(693,739)(694,738)(695,737)(696,736)(697,735)(698,734)(699,733)
(700,732)(701,731)(702,730)(703,768)(704,780)(705,779)(706,778)(707,777)
(708,776)(709,775)(710,774)(711,773)(712,772)(713,771)(714,770)(715,769)
(716,755)(717,767)(718,766)(719,765)(720,764)(721,763)(722,762)(723,761)
(724,760)(725,759)(726,758)(727,757)(728,756);
s2 := Sym(832)!( 1,210)( 2,209)( 3,221)( 4,220)( 5,219)( 6,218)( 7,217)
( 8,216)( 9,215)( 10,214)( 11,213)( 12,212)( 13,211)( 14,223)( 15,222)
( 16,234)( 17,233)( 18,232)( 19,231)( 20,230)( 21,229)( 22,228)( 23,227)
( 24,226)( 25,225)( 26,224)( 27,236)( 28,235)( 29,247)( 30,246)( 31,245)
( 32,244)( 33,243)( 34,242)( 35,241)( 36,240)( 37,239)( 38,238)( 39,237)
( 40,249)( 41,248)( 42,260)( 43,259)( 44,258)( 45,257)( 46,256)( 47,255)
( 48,254)( 49,253)( 50,252)( 51,251)( 52,250)( 53,262)( 54,261)( 55,273)
( 56,272)( 57,271)( 58,270)( 59,269)( 60,268)( 61,267)( 62,266)( 63,265)
( 64,264)( 65,263)( 66,275)( 67,274)( 68,286)( 69,285)( 70,284)( 71,283)
( 72,282)( 73,281)( 74,280)( 75,279)( 76,278)( 77,277)( 78,276)( 79,288)
( 80,287)( 81,299)( 82,298)( 83,297)( 84,296)( 85,295)( 86,294)( 87,293)
( 88,292)( 89,291)( 90,290)( 91,289)( 92,301)( 93,300)( 94,312)( 95,311)
( 96,310)( 97,309)( 98,308)( 99,307)(100,306)(101,305)(102,304)(103,303)
(104,302)(105,327)(106,326)(107,338)(108,337)(109,336)(110,335)(111,334)
(112,333)(113,332)(114,331)(115,330)(116,329)(117,328)(118,314)(119,313)
(120,325)(121,324)(122,323)(123,322)(124,321)(125,320)(126,319)(127,318)
(128,317)(129,316)(130,315)(131,353)(132,352)(133,364)(134,363)(135,362)
(136,361)(137,360)(138,359)(139,358)(140,357)(141,356)(142,355)(143,354)
(144,340)(145,339)(146,351)(147,350)(148,349)(149,348)(150,347)(151,346)
(152,345)(153,344)(154,343)(155,342)(156,341)(157,379)(158,378)(159,390)
(160,389)(161,388)(162,387)(163,386)(164,385)(165,384)(166,383)(167,382)
(168,381)(169,380)(170,366)(171,365)(172,377)(173,376)(174,375)(175,374)
(176,373)(177,372)(178,371)(179,370)(180,369)(181,368)(182,367)(183,405)
(184,404)(185,416)(186,415)(187,414)(188,413)(189,412)(190,411)(191,410)
(192,409)(193,408)(194,407)(195,406)(196,392)(197,391)(198,403)(199,402)
(200,401)(201,400)(202,399)(203,398)(204,397)(205,396)(206,395)(207,394)
(208,393)(417,626)(418,625)(419,637)(420,636)(421,635)(422,634)(423,633)
(424,632)(425,631)(426,630)(427,629)(428,628)(429,627)(430,639)(431,638)
(432,650)(433,649)(434,648)(435,647)(436,646)(437,645)(438,644)(439,643)
(440,642)(441,641)(442,640)(443,652)(444,651)(445,663)(446,662)(447,661)
(448,660)(449,659)(450,658)(451,657)(452,656)(453,655)(454,654)(455,653)
(456,665)(457,664)(458,676)(459,675)(460,674)(461,673)(462,672)(463,671)
(464,670)(465,669)(466,668)(467,667)(468,666)(469,678)(470,677)(471,689)
(472,688)(473,687)(474,686)(475,685)(476,684)(477,683)(478,682)(479,681)
(480,680)(481,679)(482,691)(483,690)(484,702)(485,701)(486,700)(487,699)
(488,698)(489,697)(490,696)(491,695)(492,694)(493,693)(494,692)(495,704)
(496,703)(497,715)(498,714)(499,713)(500,712)(501,711)(502,710)(503,709)
(504,708)(505,707)(506,706)(507,705)(508,717)(509,716)(510,728)(511,727)
(512,726)(513,725)(514,724)(515,723)(516,722)(517,721)(518,720)(519,719)
(520,718)(521,743)(522,742)(523,754)(524,753)(525,752)(526,751)(527,750)
(528,749)(529,748)(530,747)(531,746)(532,745)(533,744)(534,730)(535,729)
(536,741)(537,740)(538,739)(539,738)(540,737)(541,736)(542,735)(543,734)
(544,733)(545,732)(546,731)(547,769)(548,768)(549,780)(550,779)(551,778)
(552,777)(553,776)(554,775)(555,774)(556,773)(557,772)(558,771)(559,770)
(560,756)(561,755)(562,767)(563,766)(564,765)(565,764)(566,763)(567,762)
(568,761)(569,760)(570,759)(571,758)(572,757)(573,795)(574,794)(575,806)
(576,805)(577,804)(578,803)(579,802)(580,801)(581,800)(582,799)(583,798)
(584,797)(585,796)(586,782)(587,781)(588,793)(589,792)(590,791)(591,790)
(592,789)(593,788)(594,787)(595,786)(596,785)(597,784)(598,783)(599,821)
(600,820)(601,832)(602,831)(603,830)(604,829)(605,828)(606,827)(607,826)
(608,825)(609,824)(610,823)(611,822)(612,808)(613,807)(614,819)(615,818)
(616,817)(617,816)(618,815)(619,814)(620,813)(621,812)(622,811)(623,810)
(624,809);
poly := sub<Sym(832)|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*s0*s1*s2*s0*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 >;
References : None.
to this polytope