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Polytope of Type {4,8,26}

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