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Polytope of Type {26,4,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,4,8}*1664a
Also Known As : {{26,4|2},{4,8|2}}. if this polytope has another name.
Group : SmallGroup(1664,13683)
Rank : 4
Schlafli Type : {26,4,8}
Number of vertices, edges, etc : 26, 52, 16, 8
Order of s0s1s2s3 : 104
Order of s0s1s2s3s2s1 : 2
Special Properties :
   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 : {26,4,4}*832, {26,2,8}*832
   4-fold quotients : {13,2,8}*416, {26,2,4}*416, {26,4,2}*416
   8-fold quotients : {13,2,4}*208, {26,2,2}*208
   13-fold quotients : {2,4,8}*128a
   16-fold quotients : {13,2,2}*104
   26-fold quotients : {2,4,4}*64, {2,2,8}*64
   52-fold quotients : {2,2,4}*32, {2,4,2}*32
   104-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,105)(  2,117)(  3,116)(  4,115)(  5,114)(  6,113)(  7,112)(  8,111)
(  9,110)( 10,109)( 11,108)( 12,107)( 13,106)( 14,118)( 15,130)( 16,129)
( 17,128)( 18,127)( 19,126)( 20,125)( 21,124)( 22,123)( 23,122)( 24,121)
( 25,120)( 26,119)( 27,131)( 28,143)( 29,142)( 30,141)( 31,140)( 32,139)
( 33,138)( 34,137)( 35,136)( 36,135)( 37,134)( 38,133)( 39,132)( 40,144)
( 41,156)( 42,155)( 43,154)( 44,153)( 45,152)( 46,151)( 47,150)( 48,149)
( 49,148)( 50,147)( 51,146)( 52,145)( 53,157)( 54,169)( 55,168)( 56,167)
( 57,166)( 58,165)( 59,164)( 60,163)( 61,162)( 62,161)( 63,160)( 64,159)
( 65,158)( 66,170)( 67,182)( 68,181)( 69,180)( 70,179)( 71,178)( 72,177)
( 73,176)( 74,175)( 75,174)( 76,173)( 77,172)( 78,171)( 79,183)( 80,195)
( 81,194)( 82,193)( 83,192)( 84,191)( 85,190)( 86,189)( 87,188)( 88,187)
( 89,186)( 90,185)( 91,184)( 92,196)( 93,208)( 94,207)( 95,206)( 96,205)
( 97,204)( 98,203)( 99,202)(100,201)(101,200)(102,199)(103,198)(104,197)
(209,313)(210,325)(211,324)(212,323)(213,322)(214,321)(215,320)(216,319)
(217,318)(218,317)(219,316)(220,315)(221,314)(222,326)(223,338)(224,337)
(225,336)(226,335)(227,334)(228,333)(229,332)(230,331)(231,330)(232,329)
(233,328)(234,327)(235,339)(236,351)(237,350)(238,349)(239,348)(240,347)
(241,346)(242,345)(243,344)(244,343)(245,342)(246,341)(247,340)(248,352)
(249,364)(250,363)(251,362)(252,361)(253,360)(254,359)(255,358)(256,357)
(257,356)(258,355)(259,354)(260,353)(261,365)(262,377)(263,376)(264,375)
(265,374)(266,373)(267,372)(268,371)(269,370)(270,369)(271,368)(272,367)
(273,366)(274,378)(275,390)(276,389)(277,388)(278,387)(279,386)(280,385)
(281,384)(282,383)(283,382)(284,381)(285,380)(286,379)(287,391)(288,403)
(289,402)(290,401)(291,400)(292,399)(293,398)(294,397)(295,396)(296,395)
(297,394)(298,393)(299,392)(300,404)(301,416)(302,415)(303,414)(304,413)
(305,412)(306,411)(307,410)(308,409)(309,408)(310,407)(311,406)(312,405)
(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)
(625,729)(626,741)(627,740)(628,739)(629,738)(630,737)(631,736)(632,735)
(633,734)(634,733)(635,732)(636,731)(637,730)(638,742)(639,754)(640,753)
(641,752)(642,751)(643,750)(644,749)(645,748)(646,747)(647,746)(648,745)
(649,744)(650,743)(651,755)(652,767)(653,766)(654,765)(655,764)(656,763)
(657,762)(658,761)(659,760)(660,759)(661,758)(662,757)(663,756)(664,768)
(665,780)(666,779)(667,778)(668,777)(669,776)(670,775)(671,774)(672,773)
(673,772)(674,771)(675,770)(676,769)(677,781)(678,793)(679,792)(680,791)
(681,790)(682,789)(683,788)(684,787)(685,786)(686,785)(687,784)(688,783)
(689,782)(690,794)(691,806)(692,805)(693,804)(694,803)(695,802)(696,801)
(697,800)(698,799)(699,798)(700,797)(701,796)(702,795)(703,807)(704,819)
(705,818)(706,817)(707,816)(708,815)(709,814)(710,813)(711,812)(712,811)
(713,810)(714,809)(715,808)(716,820)(717,832)(718,831)(719,830)(720,829)
(721,828)(722,827)(723,826)(724,825)(725,824)(726,823)(727,822)(728,821);;
s1 := (  1,314)(  2,313)(  3,325)(  4,324)(  5,323)(  6,322)(  7,321)(  8,320)
(  9,319)( 10,318)( 11,317)( 12,316)( 13,315)( 14,327)( 15,326)( 16,338)
( 17,337)( 18,336)( 19,335)( 20,334)( 21,333)( 22,332)( 23,331)( 24,330)
( 25,329)( 26,328)( 27,340)( 28,339)( 29,351)( 30,350)( 31,349)( 32,348)
( 33,347)( 34,346)( 35,345)( 36,344)( 37,343)( 38,342)( 39,341)( 40,353)
( 41,352)( 42,364)( 43,363)( 44,362)( 45,361)( 46,360)( 47,359)( 48,358)
( 49,357)( 50,356)( 51,355)( 52,354)( 53,366)( 54,365)( 55,377)( 56,376)
( 57,375)( 58,374)( 59,373)( 60,372)( 61,371)( 62,370)( 63,369)( 64,368)
( 65,367)( 66,379)( 67,378)( 68,390)( 69,389)( 70,388)( 71,387)( 72,386)
( 73,385)( 74,384)( 75,383)( 76,382)( 77,381)( 78,380)( 79,392)( 80,391)
( 81,403)( 82,402)( 83,401)( 84,400)( 85,399)( 86,398)( 87,397)( 88,396)
( 89,395)( 90,394)( 91,393)( 92,405)( 93,404)( 94,416)( 95,415)( 96,414)
( 97,413)( 98,412)( 99,411)(100,410)(101,409)(102,408)(103,407)(104,406)
(105,210)(106,209)(107,221)(108,220)(109,219)(110,218)(111,217)(112,216)
(113,215)(114,214)(115,213)(116,212)(117,211)(118,223)(119,222)(120,234)
(121,233)(122,232)(123,231)(124,230)(125,229)(126,228)(127,227)(128,226)
(129,225)(130,224)(131,236)(132,235)(133,247)(134,246)(135,245)(136,244)
(137,243)(138,242)(139,241)(140,240)(141,239)(142,238)(143,237)(144,249)
(145,248)(146,260)(147,259)(148,258)(149,257)(150,256)(151,255)(152,254)
(153,253)(154,252)(155,251)(156,250)(157,262)(158,261)(159,273)(160,272)
(161,271)(162,270)(163,269)(164,268)(165,267)(166,266)(167,265)(168,264)
(169,263)(170,275)(171,274)(172,286)(173,285)(174,284)(175,283)(176,282)
(177,281)(178,280)(179,279)(180,278)(181,277)(182,276)(183,288)(184,287)
(185,299)(186,298)(187,297)(188,296)(189,295)(190,294)(191,293)(192,292)
(193,291)(194,290)(195,289)(196,301)(197,300)(198,312)(199,311)(200,310)
(201,309)(202,308)(203,307)(204,306)(205,305)(206,304)(207,303)(208,302)
(417,730)(418,729)(419,741)(420,740)(421,739)(422,738)(423,737)(424,736)
(425,735)(426,734)(427,733)(428,732)(429,731)(430,743)(431,742)(432,754)
(433,753)(434,752)(435,751)(436,750)(437,749)(438,748)(439,747)(440,746)
(441,745)(442,744)(443,756)(444,755)(445,767)(446,766)(447,765)(448,764)
(449,763)(450,762)(451,761)(452,760)(453,759)(454,758)(455,757)(456,769)
(457,768)(458,780)(459,779)(460,778)(461,777)(462,776)(463,775)(464,774)
(465,773)(466,772)(467,771)(468,770)(469,782)(470,781)(471,793)(472,792)
(473,791)(474,790)(475,789)(476,788)(477,787)(478,786)(479,785)(480,784)
(481,783)(482,795)(483,794)(484,806)(485,805)(486,804)(487,803)(488,802)
(489,801)(490,800)(491,799)(492,798)(493,797)(494,796)(495,808)(496,807)
(497,819)(498,818)(499,817)(500,816)(501,815)(502,814)(503,813)(504,812)
(505,811)(506,810)(507,809)(508,821)(509,820)(510,832)(511,831)(512,830)
(513,829)(514,828)(515,827)(516,826)(517,825)(518,824)(519,823)(520,822)
(521,626)(522,625)(523,637)(524,636)(525,635)(526,634)(527,633)(528,632)
(529,631)(530,630)(531,629)(532,628)(533,627)(534,639)(535,638)(536,650)
(537,649)(538,648)(539,647)(540,646)(541,645)(542,644)(543,643)(544,642)
(545,641)(546,640)(547,652)(548,651)(549,663)(550,662)(551,661)(552,660)
(553,659)(554,658)(555,657)(556,656)(557,655)(558,654)(559,653)(560,665)
(561,664)(562,676)(563,675)(564,674)(565,673)(566,672)(567,671)(568,670)
(569,669)(570,668)(571,667)(572,666)(573,678)(574,677)(575,689)(576,688)
(577,687)(578,686)(579,685)(580,684)(581,683)(582,682)(583,681)(584,680)
(585,679)(586,691)(587,690)(588,702)(589,701)(590,700)(591,699)(592,698)
(593,697)(594,696)(595,695)(596,694)(597,693)(598,692)(599,704)(600,703)
(601,715)(602,714)(603,713)(604,712)(605,711)(606,710)(607,709)(608,708)
(609,707)(610,706)(611,705)(612,717)(613,716)(614,728)(615,727)(616,726)
(617,725)(618,724)(619,723)(620,722)(621,721)(622,720)(623,719)(624,718);;
s2 := ( 53, 66)( 54, 67)( 55, 68)( 56, 69)( 57, 70)( 58, 71)( 59, 72)( 60, 73)
( 61, 74)( 62, 75)( 63, 76)( 64, 77)( 65, 78)( 79, 92)( 80, 93)( 81, 94)
( 82, 95)( 83, 96)( 84, 97)( 85, 98)( 86, 99)( 87,100)( 88,101)( 89,102)
( 90,103)( 91,104)(157,170)(158,171)(159,172)(160,173)(161,174)(162,175)
(163,176)(164,177)(165,178)(166,179)(167,180)(168,181)(169,182)(183,196)
(184,197)(185,198)(186,199)(187,200)(188,201)(189,202)(190,203)(191,204)
(192,205)(193,206)(194,207)(195,208)(209,235)(210,236)(211,237)(212,238)
(213,239)(214,240)(215,241)(216,242)(217,243)(218,244)(219,245)(220,246)
(221,247)(222,248)(223,249)(224,250)(225,251)(226,252)(227,253)(228,254)
(229,255)(230,256)(231,257)(232,258)(233,259)(234,260)(261,300)(262,301)
(263,302)(264,303)(265,304)(266,305)(267,306)(268,307)(269,308)(270,309)
(271,310)(272,311)(273,312)(274,287)(275,288)(276,289)(277,290)(278,291)
(279,292)(280,293)(281,294)(282,295)(283,296)(284,297)(285,298)(286,299)
(313,339)(314,340)(315,341)(316,342)(317,343)(318,344)(319,345)(320,346)
(321,347)(322,348)(323,349)(324,350)(325,351)(326,352)(327,353)(328,354)
(329,355)(330,356)(331,357)(332,358)(333,359)(334,360)(335,361)(336,362)
(337,363)(338,364)(365,404)(366,405)(367,406)(368,407)(369,408)(370,409)
(371,410)(372,411)(373,412)(374,413)(375,414)(376,415)(377,416)(378,391)
(379,392)(380,393)(381,394)(382,395)(383,396)(384,397)(385,398)(386,399)
(387,400)(388,401)(389,402)(390,403)(417,469)(418,470)(419,471)(420,472)
(421,473)(422,474)(423,475)(424,476)(425,477)(426,478)(427,479)(428,480)
(429,481)(430,482)(431,483)(432,484)(433,485)(434,486)(435,487)(436,488)
(437,489)(438,490)(439,491)(440,492)(441,493)(442,494)(443,495)(444,496)
(445,497)(446,498)(447,499)(448,500)(449,501)(450,502)(451,503)(452,504)
(453,505)(454,506)(455,507)(456,508)(457,509)(458,510)(459,511)(460,512)
(461,513)(462,514)(463,515)(464,516)(465,517)(466,518)(467,519)(468,520)
(521,573)(522,574)(523,575)(524,576)(525,577)(526,578)(527,579)(528,580)
(529,581)(530,582)(531,583)(532,584)(533,585)(534,586)(535,587)(536,588)
(537,589)(538,590)(539,591)(540,592)(541,593)(542,594)(543,595)(544,596)
(545,597)(546,598)(547,599)(548,600)(549,601)(550,602)(551,603)(552,604)
(553,605)(554,606)(555,607)(556,608)(557,609)(558,610)(559,611)(560,612)
(561,613)(562,614)(563,615)(564,616)(565,617)(566,618)(567,619)(568,620)
(569,621)(570,622)(571,623)(572,624)(625,703)(626,704)(627,705)(628,706)
(629,707)(630,708)(631,709)(632,710)(633,711)(634,712)(635,713)(636,714)
(637,715)(638,716)(639,717)(640,718)(641,719)(642,720)(643,721)(644,722)
(645,723)(646,724)(647,725)(648,726)(649,727)(650,728)(651,677)(652,678)
(653,679)(654,680)(655,681)(656,682)(657,683)(658,684)(659,685)(660,686)
(661,687)(662,688)(663,689)(664,690)(665,691)(666,692)(667,693)(668,694)
(669,695)(670,696)(671,697)(672,698)(673,699)(674,700)(675,701)(676,702)
(729,807)(730,808)(731,809)(732,810)(733,811)(734,812)(735,813)(736,814)
(737,815)(738,816)(739,817)(740,818)(741,819)(742,820)(743,821)(744,822)
(745,823)(746,824)(747,825)(748,826)(749,827)(750,828)(751,829)(752,830)
(753,831)(754,832)(755,781)(756,782)(757,783)(758,784)(759,785)(760,786)
(761,787)(762,788)(763,789)(764,790)(765,791)(766,792)(767,793)(768,794)
(769,795)(770,796)(771,797)(772,798)(773,799)(774,800)(775,801)(776,802)
(777,803)(778,804)(779,805)(780,806);;
s3 := (  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)
(105,521)(106,522)(107,523)(108,524)(109,525)(110,526)(111,527)(112,528)
(113,529)(114,530)(115,531)(116,532)(117,533)(118,534)(119,535)(120,536)
(121,537)(122,538)(123,539)(124,540)(125,541)(126,542)(127,543)(128,544)
(129,545)(130,546)(131,547)(132,548)(133,549)(134,550)(135,551)(136,552)
(137,553)(138,554)(139,555)(140,556)(141,557)(142,558)(143,559)(144,560)
(145,561)(146,562)(147,563)(148,564)(149,565)(150,566)(151,567)(152,568)
(153,569)(154,570)(155,571)(156,572)(157,586)(158,587)(159,588)(160,589)
(161,590)(162,591)(163,592)(164,593)(165,594)(166,595)(167,596)(168,597)
(169,598)(170,573)(171,574)(172,575)(173,576)(174,577)(175,578)(176,579)
(177,580)(178,581)(179,582)(180,583)(181,584)(182,585)(183,612)(184,613)
(185,614)(186,615)(187,616)(188,617)(189,618)(190,619)(191,620)(192,621)
(193,622)(194,623)(195,624)(196,599)(197,600)(198,601)(199,602)(200,603)
(201,604)(202,605)(203,606)(204,607)(205,608)(206,609)(207,610)(208,611)
(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)
(313,729)(314,730)(315,731)(316,732)(317,733)(318,734)(319,735)(320,736)
(321,737)(322,738)(323,739)(324,740)(325,741)(326,742)(327,743)(328,744)
(329,745)(330,746)(331,747)(332,748)(333,749)(334,750)(335,751)(336,752)
(337,753)(338,754)(339,755)(340,756)(341,757)(342,758)(343,759)(344,760)
(345,761)(346,762)(347,763)(348,764)(349,765)(350,766)(351,767)(352,768)
(353,769)(354,770)(355,771)(356,772)(357,773)(358,774)(359,775)(360,776)
(361,777)(362,778)(363,779)(364,780)(365,794)(366,795)(367,796)(368,797)
(369,798)(370,799)(371,800)(372,801)(373,802)(374,803)(375,804)(376,805)
(377,806)(378,781)(379,782)(380,783)(381,784)(382,785)(383,786)(384,787)
(385,788)(386,789)(387,790)(388,791)(389,792)(390,793)(391,820)(392,821)
(393,822)(394,823)(395,824)(396,825)(397,826)(398,827)(399,828)(400,829)
(401,830)(402,831)(403,832)(404,807)(405,808)(406,809)(407,810)(408,811)
(409,812)(410,813)(411,814)(412,815)(413,816)(414,817)(415,818)(416,819);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(832)!(  1,105)(  2,117)(  3,116)(  4,115)(  5,114)(  6,113)(  7,112)
(  8,111)(  9,110)( 10,109)( 11,108)( 12,107)( 13,106)( 14,118)( 15,130)
( 16,129)( 17,128)( 18,127)( 19,126)( 20,125)( 21,124)( 22,123)( 23,122)
( 24,121)( 25,120)( 26,119)( 27,131)( 28,143)( 29,142)( 30,141)( 31,140)
( 32,139)( 33,138)( 34,137)( 35,136)( 36,135)( 37,134)( 38,133)( 39,132)
( 40,144)( 41,156)( 42,155)( 43,154)( 44,153)( 45,152)( 46,151)( 47,150)
( 48,149)( 49,148)( 50,147)( 51,146)( 52,145)( 53,157)( 54,169)( 55,168)
( 56,167)( 57,166)( 58,165)( 59,164)( 60,163)( 61,162)( 62,161)( 63,160)
( 64,159)( 65,158)( 66,170)( 67,182)( 68,181)( 69,180)( 70,179)( 71,178)
( 72,177)( 73,176)( 74,175)( 75,174)( 76,173)( 77,172)( 78,171)( 79,183)
( 80,195)( 81,194)( 82,193)( 83,192)( 84,191)( 85,190)( 86,189)( 87,188)
( 88,187)( 89,186)( 90,185)( 91,184)( 92,196)( 93,208)( 94,207)( 95,206)
( 96,205)( 97,204)( 98,203)( 99,202)(100,201)(101,200)(102,199)(103,198)
(104,197)(209,313)(210,325)(211,324)(212,323)(213,322)(214,321)(215,320)
(216,319)(217,318)(218,317)(219,316)(220,315)(221,314)(222,326)(223,338)
(224,337)(225,336)(226,335)(227,334)(228,333)(229,332)(230,331)(231,330)
(232,329)(233,328)(234,327)(235,339)(236,351)(237,350)(238,349)(239,348)
(240,347)(241,346)(242,345)(243,344)(244,343)(245,342)(246,341)(247,340)
(248,352)(249,364)(250,363)(251,362)(252,361)(253,360)(254,359)(255,358)
(256,357)(257,356)(258,355)(259,354)(260,353)(261,365)(262,377)(263,376)
(264,375)(265,374)(266,373)(267,372)(268,371)(269,370)(270,369)(271,368)
(272,367)(273,366)(274,378)(275,390)(276,389)(277,388)(278,387)(279,386)
(280,385)(281,384)(282,383)(283,382)(284,381)(285,380)(286,379)(287,391)
(288,403)(289,402)(290,401)(291,400)(292,399)(293,398)(294,397)(295,396)
(296,395)(297,394)(298,393)(299,392)(300,404)(301,416)(302,415)(303,414)
(304,413)(305,412)(306,411)(307,410)(308,409)(309,408)(310,407)(311,406)
(312,405)(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)(625,729)(626,741)(627,740)(628,739)(629,738)(630,737)(631,736)
(632,735)(633,734)(634,733)(635,732)(636,731)(637,730)(638,742)(639,754)
(640,753)(641,752)(642,751)(643,750)(644,749)(645,748)(646,747)(647,746)
(648,745)(649,744)(650,743)(651,755)(652,767)(653,766)(654,765)(655,764)
(656,763)(657,762)(658,761)(659,760)(660,759)(661,758)(662,757)(663,756)
(664,768)(665,780)(666,779)(667,778)(668,777)(669,776)(670,775)(671,774)
(672,773)(673,772)(674,771)(675,770)(676,769)(677,781)(678,793)(679,792)
(680,791)(681,790)(682,789)(683,788)(684,787)(685,786)(686,785)(687,784)
(688,783)(689,782)(690,794)(691,806)(692,805)(693,804)(694,803)(695,802)
(696,801)(697,800)(698,799)(699,798)(700,797)(701,796)(702,795)(703,807)
(704,819)(705,818)(706,817)(707,816)(708,815)(709,814)(710,813)(711,812)
(712,811)(713,810)(714,809)(715,808)(716,820)(717,832)(718,831)(719,830)
(720,829)(721,828)(722,827)(723,826)(724,825)(725,824)(726,823)(727,822)
(728,821);
s1 := Sym(832)!(  1,314)(  2,313)(  3,325)(  4,324)(  5,323)(  6,322)(  7,321)
(  8,320)(  9,319)( 10,318)( 11,317)( 12,316)( 13,315)( 14,327)( 15,326)
( 16,338)( 17,337)( 18,336)( 19,335)( 20,334)( 21,333)( 22,332)( 23,331)
( 24,330)( 25,329)( 26,328)( 27,340)( 28,339)( 29,351)( 30,350)( 31,349)
( 32,348)( 33,347)( 34,346)( 35,345)( 36,344)( 37,343)( 38,342)( 39,341)
( 40,353)( 41,352)( 42,364)( 43,363)( 44,362)( 45,361)( 46,360)( 47,359)
( 48,358)( 49,357)( 50,356)( 51,355)( 52,354)( 53,366)( 54,365)( 55,377)
( 56,376)( 57,375)( 58,374)( 59,373)( 60,372)( 61,371)( 62,370)( 63,369)
( 64,368)( 65,367)( 66,379)( 67,378)( 68,390)( 69,389)( 70,388)( 71,387)
( 72,386)( 73,385)( 74,384)( 75,383)( 76,382)( 77,381)( 78,380)( 79,392)
( 80,391)( 81,403)( 82,402)( 83,401)( 84,400)( 85,399)( 86,398)( 87,397)
( 88,396)( 89,395)( 90,394)( 91,393)( 92,405)( 93,404)( 94,416)( 95,415)
( 96,414)( 97,413)( 98,412)( 99,411)(100,410)(101,409)(102,408)(103,407)
(104,406)(105,210)(106,209)(107,221)(108,220)(109,219)(110,218)(111,217)
(112,216)(113,215)(114,214)(115,213)(116,212)(117,211)(118,223)(119,222)
(120,234)(121,233)(122,232)(123,231)(124,230)(125,229)(126,228)(127,227)
(128,226)(129,225)(130,224)(131,236)(132,235)(133,247)(134,246)(135,245)
(136,244)(137,243)(138,242)(139,241)(140,240)(141,239)(142,238)(143,237)
(144,249)(145,248)(146,260)(147,259)(148,258)(149,257)(150,256)(151,255)
(152,254)(153,253)(154,252)(155,251)(156,250)(157,262)(158,261)(159,273)
(160,272)(161,271)(162,270)(163,269)(164,268)(165,267)(166,266)(167,265)
(168,264)(169,263)(170,275)(171,274)(172,286)(173,285)(174,284)(175,283)
(176,282)(177,281)(178,280)(179,279)(180,278)(181,277)(182,276)(183,288)
(184,287)(185,299)(186,298)(187,297)(188,296)(189,295)(190,294)(191,293)
(192,292)(193,291)(194,290)(195,289)(196,301)(197,300)(198,312)(199,311)
(200,310)(201,309)(202,308)(203,307)(204,306)(205,305)(206,304)(207,303)
(208,302)(417,730)(418,729)(419,741)(420,740)(421,739)(422,738)(423,737)
(424,736)(425,735)(426,734)(427,733)(428,732)(429,731)(430,743)(431,742)
(432,754)(433,753)(434,752)(435,751)(436,750)(437,749)(438,748)(439,747)
(440,746)(441,745)(442,744)(443,756)(444,755)(445,767)(446,766)(447,765)
(448,764)(449,763)(450,762)(451,761)(452,760)(453,759)(454,758)(455,757)
(456,769)(457,768)(458,780)(459,779)(460,778)(461,777)(462,776)(463,775)
(464,774)(465,773)(466,772)(467,771)(468,770)(469,782)(470,781)(471,793)
(472,792)(473,791)(474,790)(475,789)(476,788)(477,787)(478,786)(479,785)
(480,784)(481,783)(482,795)(483,794)(484,806)(485,805)(486,804)(487,803)
(488,802)(489,801)(490,800)(491,799)(492,798)(493,797)(494,796)(495,808)
(496,807)(497,819)(498,818)(499,817)(500,816)(501,815)(502,814)(503,813)
(504,812)(505,811)(506,810)(507,809)(508,821)(509,820)(510,832)(511,831)
(512,830)(513,829)(514,828)(515,827)(516,826)(517,825)(518,824)(519,823)
(520,822)(521,626)(522,625)(523,637)(524,636)(525,635)(526,634)(527,633)
(528,632)(529,631)(530,630)(531,629)(532,628)(533,627)(534,639)(535,638)
(536,650)(537,649)(538,648)(539,647)(540,646)(541,645)(542,644)(543,643)
(544,642)(545,641)(546,640)(547,652)(548,651)(549,663)(550,662)(551,661)
(552,660)(553,659)(554,658)(555,657)(556,656)(557,655)(558,654)(559,653)
(560,665)(561,664)(562,676)(563,675)(564,674)(565,673)(566,672)(567,671)
(568,670)(569,669)(570,668)(571,667)(572,666)(573,678)(574,677)(575,689)
(576,688)(577,687)(578,686)(579,685)(580,684)(581,683)(582,682)(583,681)
(584,680)(585,679)(586,691)(587,690)(588,702)(589,701)(590,700)(591,699)
(592,698)(593,697)(594,696)(595,695)(596,694)(597,693)(598,692)(599,704)
(600,703)(601,715)(602,714)(603,713)(604,712)(605,711)(606,710)(607,709)
(608,708)(609,707)(610,706)(611,705)(612,717)(613,716)(614,728)(615,727)
(616,726)(617,725)(618,724)(619,723)(620,722)(621,721)(622,720)(623,719)
(624,718);
s2 := Sym(832)!( 53, 66)( 54, 67)( 55, 68)( 56, 69)( 57, 70)( 58, 71)( 59, 72)
( 60, 73)( 61, 74)( 62, 75)( 63, 76)( 64, 77)( 65, 78)( 79, 92)( 80, 93)
( 81, 94)( 82, 95)( 83, 96)( 84, 97)( 85, 98)( 86, 99)( 87,100)( 88,101)
( 89,102)( 90,103)( 91,104)(157,170)(158,171)(159,172)(160,173)(161,174)
(162,175)(163,176)(164,177)(165,178)(166,179)(167,180)(168,181)(169,182)
(183,196)(184,197)(185,198)(186,199)(187,200)(188,201)(189,202)(190,203)
(191,204)(192,205)(193,206)(194,207)(195,208)(209,235)(210,236)(211,237)
(212,238)(213,239)(214,240)(215,241)(216,242)(217,243)(218,244)(219,245)
(220,246)(221,247)(222,248)(223,249)(224,250)(225,251)(226,252)(227,253)
(228,254)(229,255)(230,256)(231,257)(232,258)(233,259)(234,260)(261,300)
(262,301)(263,302)(264,303)(265,304)(266,305)(267,306)(268,307)(269,308)
(270,309)(271,310)(272,311)(273,312)(274,287)(275,288)(276,289)(277,290)
(278,291)(279,292)(280,293)(281,294)(282,295)(283,296)(284,297)(285,298)
(286,299)(313,339)(314,340)(315,341)(316,342)(317,343)(318,344)(319,345)
(320,346)(321,347)(322,348)(323,349)(324,350)(325,351)(326,352)(327,353)
(328,354)(329,355)(330,356)(331,357)(332,358)(333,359)(334,360)(335,361)
(336,362)(337,363)(338,364)(365,404)(366,405)(367,406)(368,407)(369,408)
(370,409)(371,410)(372,411)(373,412)(374,413)(375,414)(376,415)(377,416)
(378,391)(379,392)(380,393)(381,394)(382,395)(383,396)(384,397)(385,398)
(386,399)(387,400)(388,401)(389,402)(390,403)(417,469)(418,470)(419,471)
(420,472)(421,473)(422,474)(423,475)(424,476)(425,477)(426,478)(427,479)
(428,480)(429,481)(430,482)(431,483)(432,484)(433,485)(434,486)(435,487)
(436,488)(437,489)(438,490)(439,491)(440,492)(441,493)(442,494)(443,495)
(444,496)(445,497)(446,498)(447,499)(448,500)(449,501)(450,502)(451,503)
(452,504)(453,505)(454,506)(455,507)(456,508)(457,509)(458,510)(459,511)
(460,512)(461,513)(462,514)(463,515)(464,516)(465,517)(466,518)(467,519)
(468,520)(521,573)(522,574)(523,575)(524,576)(525,577)(526,578)(527,579)
(528,580)(529,581)(530,582)(531,583)(532,584)(533,585)(534,586)(535,587)
(536,588)(537,589)(538,590)(539,591)(540,592)(541,593)(542,594)(543,595)
(544,596)(545,597)(546,598)(547,599)(548,600)(549,601)(550,602)(551,603)
(552,604)(553,605)(554,606)(555,607)(556,608)(557,609)(558,610)(559,611)
(560,612)(561,613)(562,614)(563,615)(564,616)(565,617)(566,618)(567,619)
(568,620)(569,621)(570,622)(571,623)(572,624)(625,703)(626,704)(627,705)
(628,706)(629,707)(630,708)(631,709)(632,710)(633,711)(634,712)(635,713)
(636,714)(637,715)(638,716)(639,717)(640,718)(641,719)(642,720)(643,721)
(644,722)(645,723)(646,724)(647,725)(648,726)(649,727)(650,728)(651,677)
(652,678)(653,679)(654,680)(655,681)(656,682)(657,683)(658,684)(659,685)
(660,686)(661,687)(662,688)(663,689)(664,690)(665,691)(666,692)(667,693)
(668,694)(669,695)(670,696)(671,697)(672,698)(673,699)(674,700)(675,701)
(676,702)(729,807)(730,808)(731,809)(732,810)(733,811)(734,812)(735,813)
(736,814)(737,815)(738,816)(739,817)(740,818)(741,819)(742,820)(743,821)
(744,822)(745,823)(746,824)(747,825)(748,826)(749,827)(750,828)(751,829)
(752,830)(753,831)(754,832)(755,781)(756,782)(757,783)(758,784)(759,785)
(760,786)(761,787)(762,788)(763,789)(764,790)(765,791)(766,792)(767,793)
(768,794)(769,795)(770,796)(771,797)(772,798)(773,799)(774,800)(775,801)
(776,802)(777,803)(778,804)(779,805)(780,806);
s3 := 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)(105,521)(106,522)(107,523)(108,524)(109,525)(110,526)(111,527)
(112,528)(113,529)(114,530)(115,531)(116,532)(117,533)(118,534)(119,535)
(120,536)(121,537)(122,538)(123,539)(124,540)(125,541)(126,542)(127,543)
(128,544)(129,545)(130,546)(131,547)(132,548)(133,549)(134,550)(135,551)
(136,552)(137,553)(138,554)(139,555)(140,556)(141,557)(142,558)(143,559)
(144,560)(145,561)(146,562)(147,563)(148,564)(149,565)(150,566)(151,567)
(152,568)(153,569)(154,570)(155,571)(156,572)(157,586)(158,587)(159,588)
(160,589)(161,590)(162,591)(163,592)(164,593)(165,594)(166,595)(167,596)
(168,597)(169,598)(170,573)(171,574)(172,575)(173,576)(174,577)(175,578)
(176,579)(177,580)(178,581)(179,582)(180,583)(181,584)(182,585)(183,612)
(184,613)(185,614)(186,615)(187,616)(188,617)(189,618)(190,619)(191,620)
(192,621)(193,622)(194,623)(195,624)(196,599)(197,600)(198,601)(199,602)
(200,603)(201,604)(202,605)(203,606)(204,607)(205,608)(206,609)(207,610)
(208,611)(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)(313,729)(314,730)(315,731)(316,732)(317,733)(318,734)(319,735)
(320,736)(321,737)(322,738)(323,739)(324,740)(325,741)(326,742)(327,743)
(328,744)(329,745)(330,746)(331,747)(332,748)(333,749)(334,750)(335,751)
(336,752)(337,753)(338,754)(339,755)(340,756)(341,757)(342,758)(343,759)
(344,760)(345,761)(346,762)(347,763)(348,764)(349,765)(350,766)(351,767)
(352,768)(353,769)(354,770)(355,771)(356,772)(357,773)(358,774)(359,775)
(360,776)(361,777)(362,778)(363,779)(364,780)(365,794)(366,795)(367,796)
(368,797)(369,798)(370,799)(371,800)(372,801)(373,802)(374,803)(375,804)
(376,805)(377,806)(378,781)(379,782)(380,783)(381,784)(382,785)(383,786)
(384,787)(385,788)(386,789)(387,790)(388,791)(389,792)(390,793)(391,820)
(392,821)(393,822)(394,823)(395,824)(396,825)(397,826)(398,827)(399,828)
(400,829)(401,830)(402,831)(403,832)(404,807)(405,808)(406,809)(407,810)
(408,811)(409,812)(410,813)(411,814)(412,815)(413,816)(414,817)(415,818)
(416,819);
poly := sub<Sym(832)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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