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Polytope of Type {4,26,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,26,8}*1664
Also Known As : {{4,26|2},{26,8|2}}. if this polytope has another name.
Group : SmallGroup(1664,16180)
Rank : 4
Schlafli Type : {4,26,8}
Number of vertices, edges, etc : 4, 52, 104, 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 : {4,26,4}*832, {2,26,8}*832
   4-fold quotients : {2,26,4}*416, {4,26,2}*416
   8-fold quotients : {2,26,2}*208
   13-fold quotients : {4,2,8}*128
   16-fold quotients : {2,13,2}*104
   26-fold quotients : {4,2,4}*64, {2,2,8}*64
   52-fold quotients : {2,2,4}*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 := (  1,157)(  2,169)(  3,168)(  4,167)(  5,166)(  6,165)(  7,164)(  8,163)
(  9,162)( 10,161)( 11,160)( 12,159)( 13,158)( 14,170)( 15,182)( 16,181)
( 17,180)( 18,179)( 19,178)( 20,177)( 21,176)( 22,175)( 23,174)( 24,173)
( 25,172)( 26,171)( 27,183)( 28,195)( 29,194)( 30,193)( 31,192)( 32,191)
( 33,190)( 34,189)( 35,188)( 36,187)( 37,186)( 38,185)( 39,184)( 40,196)
( 41,208)( 42,207)( 43,206)( 44,205)( 45,204)( 46,203)( 47,202)( 48,201)
( 49,200)( 50,199)( 51,198)( 52,197)( 53,118)( 54,130)( 55,129)( 56,128)
( 57,127)( 58,126)( 59,125)( 60,124)( 61,123)( 62,122)( 63,121)( 64,120)
( 65,119)( 66,105)( 67,117)( 68,116)( 69,115)( 70,114)( 71,113)( 72,112)
( 73,111)( 74,110)( 75,109)( 76,108)( 77,107)( 78,106)( 79,144)( 80,156)
( 81,155)( 82,154)( 83,153)( 84,152)( 85,151)( 86,150)( 87,149)( 88,148)
( 89,147)( 90,146)( 91,145)( 92,131)( 93,143)( 94,142)( 95,141)( 96,140)
( 97,139)( 98,138)( 99,137)(100,136)(101,135)(102,134)(103,133)(104,132)
(209,391)(210,403)(211,402)(212,401)(213,400)(214,399)(215,398)(216,397)
(217,396)(218,395)(219,394)(220,393)(221,392)(222,404)(223,416)(224,415)
(225,414)(226,413)(227,412)(228,411)(229,410)(230,409)(231,408)(232,407)
(233,406)(234,405)(235,365)(236,377)(237,376)(238,375)(239,374)(240,373)
(241,372)(242,371)(243,370)(244,369)(245,368)(246,367)(247,366)(248,378)
(249,390)(250,389)(251,388)(252,387)(253,386)(254,385)(255,384)(256,383)
(257,382)(258,381)(259,380)(260,379)(261,352)(262,364)(263,363)(264,362)
(265,361)(266,360)(267,359)(268,358)(269,357)(270,356)(271,355)(272,354)
(273,353)(274,339)(275,351)(276,350)(277,349)(278,348)(279,347)(280,346)
(281,345)(282,344)(283,343)(284,342)(285,341)(286,340)(287,326)(288,338)
(289,337)(290,336)(291,335)(292,334)(293,333)(294,332)(295,331)(296,330)
(297,329)(298,328)(299,327)(300,313)(301,325)(302,324)(303,323)(304,322)
(305,321)(306,320)(307,319)(308,318)(309,317)(310,316)(311,315)(312,314)
(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)
(625,755)(626,767)(627,766)(628,765)(629,764)(630,763)(631,762)(632,761)
(633,760)(634,759)(635,758)(636,757)(637,756)(638,768)(639,780)(640,779)
(641,778)(642,777)(643,776)(644,775)(645,774)(646,773)(647,772)(648,771)
(649,770)(650,769)(651,729)(652,741)(653,740)(654,739)(655,738)(656,737)
(657,736)(658,735)(659,734)(660,733)(661,732)(662,731)(663,730)(664,742)
(665,754)(666,753)(667,752)(668,751)(669,750)(670,749)(671,748)(672,747)
(673,746)(674,745)(675,744)(676,743)(677,807)(678,819)(679,818)(680,817)
(681,816)(682,815)(683,814)(684,813)(685,812)(686,811)(687,810)(688,809)
(689,808)(690,820)(691,832)(692,831)(693,830)(694,829)(695,828)(696,827)
(697,826)(698,825)(699,824)(700,823)(701,822)(702,821)(703,781)(704,793)
(705,792)(706,791)(707,790)(708,789)(709,788)(710,787)(711,786)(712,785)
(713,784)(714,783)(715,782)(716,794)(717,806)(718,805)(719,804)(720,803)
(721,802)(722,801)(723,800)(724,799)(725,798)(726,797)(727,796)(728,795);;
s2 := (  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)( 53,171)( 54,170)( 55,182)( 56,181)
( 57,180)( 58,179)( 59,178)( 60,177)( 61,176)( 62,175)( 63,174)( 64,173)
( 65,172)( 66,158)( 67,157)( 68,169)( 69,168)( 70,167)( 71,166)( 72,165)
( 73,164)( 74,163)( 75,162)( 76,161)( 77,160)( 78,159)( 79,197)( 80,196)
( 81,208)( 82,207)( 83,206)( 84,205)( 85,204)( 86,203)( 87,202)( 88,201)
( 89,200)( 90,199)( 91,198)( 92,184)( 93,183)( 94,195)( 95,194)( 96,193)
( 97,192)( 98,191)( 99,190)(100,189)(101,188)(102,187)(103,186)(104,185)
(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)(261,379)(262,378)(263,390)(264,389)
(265,388)(266,387)(267,386)(268,385)(269,384)(270,383)(271,382)(272,381)
(273,380)(274,366)(275,365)(276,377)(277,376)(278,375)(279,374)(280,373)
(281,372)(282,371)(283,370)(284,369)(285,368)(286,367)(287,405)(288,404)
(289,416)(290,415)(291,414)(292,413)(293,412)(294,411)(295,410)(296,409)
(297,408)(298,407)(299,406)(300,392)(301,391)(302,403)(303,402)(304,401)
(305,400)(306,399)(307,398)(308,397)(309,396)(310,395)(311,394)(312,393)
(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)(469,587)(470,586)(471,598)(472,597)
(473,596)(474,595)(475,594)(476,593)(477,592)(478,591)(479,590)(480,589)
(481,588)(482,574)(483,573)(484,585)(485,584)(486,583)(487,582)(488,581)
(489,580)(490,579)(491,578)(492,577)(493,576)(494,575)(495,613)(496,612)
(497,624)(498,623)(499,622)(500,621)(501,620)(502,619)(503,618)(504,617)
(505,616)(506,615)(507,614)(508,600)(509,599)(510,611)(511,610)(512,609)
(513,608)(514,607)(515,606)(516,605)(517,604)(518,603)(519,602)(520,601)
(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)(677,795)(678,794)(679,806)(680,805)
(681,804)(682,803)(683,802)(684,801)(685,800)(686,799)(687,798)(688,797)
(689,796)(690,782)(691,781)(692,793)(693,792)(694,791)(695,790)(696,789)
(697,788)(698,787)(699,786)(700,785)(701,784)(702,783)(703,821)(704,820)
(705,832)(706,831)(707,830)(708,829)(709,828)(710,827)(711,826)(712,825)
(713,824)(714,823)(715,822)(716,808)(717,807)(718,819)(719,818)(720,817)
(721,816)(722,815)(723,814)(724,813)(725,812)(726,811)(727,810)(728,809);;
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)
(105,573)(106,574)(107,575)(108,576)(109,577)(110,578)(111,579)(112,580)
(113,581)(114,582)(115,583)(116,584)(117,585)(118,586)(119,587)(120,588)
(121,589)(122,590)(123,591)(124,592)(125,593)(126,594)(127,595)(128,596)
(129,597)(130,598)(131,599)(132,600)(133,601)(134,602)(135,603)(136,604)
(137,605)(138,606)(139,607)(140,608)(141,609)(142,610)(143,611)(144,612)
(145,613)(146,614)(147,615)(148,616)(149,617)(150,618)(151,619)(152,620)
(153,621)(154,622)(155,623)(156,624)(157,521)(158,522)(159,523)(160,524)
(161,525)(162,526)(163,527)(164,528)(165,529)(166,530)(167,531)(168,532)
(169,533)(170,534)(171,535)(172,536)(173,537)(174,538)(175,539)(176,540)
(177,541)(178,542)(179,543)(180,544)(181,545)(182,546)(183,547)(184,548)
(185,549)(186,550)(187,551)(188,552)(189,553)(190,554)(191,555)(192,556)
(193,557)(194,558)(195,559)(196,560)(197,561)(198,562)(199,563)(200,564)
(201,565)(202,566)(203,567)(204,568)(205,569)(206,570)(207,571)(208,572)
(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)
(313,781)(314,782)(315,783)(316,784)(317,785)(318,786)(319,787)(320,788)
(321,789)(322,790)(323,791)(324,792)(325,793)(326,794)(327,795)(328,796)
(329,797)(330,798)(331,799)(332,800)(333,801)(334,802)(335,803)(336,804)
(337,805)(338,806)(339,807)(340,808)(341,809)(342,810)(343,811)(344,812)
(345,813)(346,814)(347,815)(348,816)(349,817)(350,818)(351,819)(352,820)
(353,821)(354,822)(355,823)(356,824)(357,825)(358,826)(359,827)(360,828)
(361,829)(362,830)(363,831)(364,832)(365,729)(366,730)(367,731)(368,732)
(369,733)(370,734)(371,735)(372,736)(373,737)(374,738)(375,739)(376,740)
(377,741)(378,742)(379,743)(380,744)(381,745)(382,746)(383,747)(384,748)
(385,749)(386,750)(387,751)(388,752)(389,753)(390,754)(391,755)(392,756)
(393,757)(394,758)(395,759)(396,760)(397,761)(398,762)(399,763)(400,764)
(401,765)(402,766)(403,767)(404,768)(405,769)(406,770)(407,771)(408,772)
(409,773)(410,774)(411,775)(412,776)(413,777)(414,778)(415,779)(416,780);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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)!(  1,209)(  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)!(  1,157)(  2,169)(  3,168)(  4,167)(  5,166)(  6,165)(  7,164)
(  8,163)(  9,162)( 10,161)( 11,160)( 12,159)( 13,158)( 14,170)( 15,182)
( 16,181)( 17,180)( 18,179)( 19,178)( 20,177)( 21,176)( 22,175)( 23,174)
( 24,173)( 25,172)( 26,171)( 27,183)( 28,195)( 29,194)( 30,193)( 31,192)
( 32,191)( 33,190)( 34,189)( 35,188)( 36,187)( 37,186)( 38,185)( 39,184)
( 40,196)( 41,208)( 42,207)( 43,206)( 44,205)( 45,204)( 46,203)( 47,202)
( 48,201)( 49,200)( 50,199)( 51,198)( 52,197)( 53,118)( 54,130)( 55,129)
( 56,128)( 57,127)( 58,126)( 59,125)( 60,124)( 61,123)( 62,122)( 63,121)
( 64,120)( 65,119)( 66,105)( 67,117)( 68,116)( 69,115)( 70,114)( 71,113)
( 72,112)( 73,111)( 74,110)( 75,109)( 76,108)( 77,107)( 78,106)( 79,144)
( 80,156)( 81,155)( 82,154)( 83,153)( 84,152)( 85,151)( 86,150)( 87,149)
( 88,148)( 89,147)( 90,146)( 91,145)( 92,131)( 93,143)( 94,142)( 95,141)
( 96,140)( 97,139)( 98,138)( 99,137)(100,136)(101,135)(102,134)(103,133)
(104,132)(209,391)(210,403)(211,402)(212,401)(213,400)(214,399)(215,398)
(216,397)(217,396)(218,395)(219,394)(220,393)(221,392)(222,404)(223,416)
(224,415)(225,414)(226,413)(227,412)(228,411)(229,410)(230,409)(231,408)
(232,407)(233,406)(234,405)(235,365)(236,377)(237,376)(238,375)(239,374)
(240,373)(241,372)(242,371)(243,370)(244,369)(245,368)(246,367)(247,366)
(248,378)(249,390)(250,389)(251,388)(252,387)(253,386)(254,385)(255,384)
(256,383)(257,382)(258,381)(259,380)(260,379)(261,352)(262,364)(263,363)
(264,362)(265,361)(266,360)(267,359)(268,358)(269,357)(270,356)(271,355)
(272,354)(273,353)(274,339)(275,351)(276,350)(277,349)(278,348)(279,347)
(280,346)(281,345)(282,344)(283,343)(284,342)(285,341)(286,340)(287,326)
(288,338)(289,337)(290,336)(291,335)(292,334)(293,333)(294,332)(295,331)
(296,330)(297,329)(298,328)(299,327)(300,313)(301,325)(302,324)(303,323)
(304,322)(305,321)(306,320)(307,319)(308,318)(309,317)(310,316)(311,315)
(312,314)(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)(625,755)(626,767)(627,766)(628,765)(629,764)(630,763)(631,762)
(632,761)(633,760)(634,759)(635,758)(636,757)(637,756)(638,768)(639,780)
(640,779)(641,778)(642,777)(643,776)(644,775)(645,774)(646,773)(647,772)
(648,771)(649,770)(650,769)(651,729)(652,741)(653,740)(654,739)(655,738)
(656,737)(657,736)(658,735)(659,734)(660,733)(661,732)(662,731)(663,730)
(664,742)(665,754)(666,753)(667,752)(668,751)(669,750)(670,749)(671,748)
(672,747)(673,746)(674,745)(675,744)(676,743)(677,807)(678,819)(679,818)
(680,817)(681,816)(682,815)(683,814)(684,813)(685,812)(686,811)(687,810)
(688,809)(689,808)(690,820)(691,832)(692,831)(693,830)(694,829)(695,828)
(696,827)(697,826)(698,825)(699,824)(700,823)(701,822)(702,821)(703,781)
(704,793)(705,792)(706,791)(707,790)(708,789)(709,788)(710,787)(711,786)
(712,785)(713,784)(714,783)(715,782)(716,794)(717,806)(718,805)(719,804)
(720,803)(721,802)(722,801)(723,800)(724,799)(725,798)(726,797)(727,796)
(728,795);
s2 := 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)( 53,171)( 54,170)( 55,182)
( 56,181)( 57,180)( 58,179)( 59,178)( 60,177)( 61,176)( 62,175)( 63,174)
( 64,173)( 65,172)( 66,158)( 67,157)( 68,169)( 69,168)( 70,167)( 71,166)
( 72,165)( 73,164)( 74,163)( 75,162)( 76,161)( 77,160)( 78,159)( 79,197)
( 80,196)( 81,208)( 82,207)( 83,206)( 84,205)( 85,204)( 86,203)( 87,202)
( 88,201)( 89,200)( 90,199)( 91,198)( 92,184)( 93,183)( 94,195)( 95,194)
( 96,193)( 97,192)( 98,191)( 99,190)(100,189)(101,188)(102,187)(103,186)
(104,185)(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)(261,379)(262,378)(263,390)
(264,389)(265,388)(266,387)(267,386)(268,385)(269,384)(270,383)(271,382)
(272,381)(273,380)(274,366)(275,365)(276,377)(277,376)(278,375)(279,374)
(280,373)(281,372)(282,371)(283,370)(284,369)(285,368)(286,367)(287,405)
(288,404)(289,416)(290,415)(291,414)(292,413)(293,412)(294,411)(295,410)
(296,409)(297,408)(298,407)(299,406)(300,392)(301,391)(302,403)(303,402)
(304,401)(305,400)(306,399)(307,398)(308,397)(309,396)(310,395)(311,394)
(312,393)(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)(469,587)(470,586)(471,598)
(472,597)(473,596)(474,595)(475,594)(476,593)(477,592)(478,591)(479,590)
(480,589)(481,588)(482,574)(483,573)(484,585)(485,584)(486,583)(487,582)
(488,581)(489,580)(490,579)(491,578)(492,577)(493,576)(494,575)(495,613)
(496,612)(497,624)(498,623)(499,622)(500,621)(501,620)(502,619)(503,618)
(504,617)(505,616)(506,615)(507,614)(508,600)(509,599)(510,611)(511,610)
(512,609)(513,608)(514,607)(515,606)(516,605)(517,604)(518,603)(519,602)
(520,601)(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)(677,795)(678,794)(679,806)
(680,805)(681,804)(682,803)(683,802)(684,801)(685,800)(686,799)(687,798)
(688,797)(689,796)(690,782)(691,781)(692,793)(693,792)(694,791)(695,790)
(696,789)(697,788)(698,787)(699,786)(700,785)(701,784)(702,783)(703,821)
(704,820)(705,832)(706,831)(707,830)(708,829)(709,828)(710,827)(711,826)
(712,825)(713,824)(714,823)(715,822)(716,808)(717,807)(718,819)(719,818)
(720,817)(721,816)(722,815)(723,814)(724,813)(725,812)(726,811)(727,810)
(728,809);
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)(105,573)(106,574)(107,575)(108,576)(109,577)(110,578)(111,579)
(112,580)(113,581)(114,582)(115,583)(116,584)(117,585)(118,586)(119,587)
(120,588)(121,589)(122,590)(123,591)(124,592)(125,593)(126,594)(127,595)
(128,596)(129,597)(130,598)(131,599)(132,600)(133,601)(134,602)(135,603)
(136,604)(137,605)(138,606)(139,607)(140,608)(141,609)(142,610)(143,611)
(144,612)(145,613)(146,614)(147,615)(148,616)(149,617)(150,618)(151,619)
(152,620)(153,621)(154,622)(155,623)(156,624)(157,521)(158,522)(159,523)
(160,524)(161,525)(162,526)(163,527)(164,528)(165,529)(166,530)(167,531)
(168,532)(169,533)(170,534)(171,535)(172,536)(173,537)(174,538)(175,539)
(176,540)(177,541)(178,542)(179,543)(180,544)(181,545)(182,546)(183,547)
(184,548)(185,549)(186,550)(187,551)(188,552)(189,553)(190,554)(191,555)
(192,556)(193,557)(194,558)(195,559)(196,560)(197,561)(198,562)(199,563)
(200,564)(201,565)(202,566)(203,567)(204,568)(205,569)(206,570)(207,571)
(208,572)(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)(313,781)(314,782)(315,783)(316,784)(317,785)(318,786)(319,787)
(320,788)(321,789)(322,790)(323,791)(324,792)(325,793)(326,794)(327,795)
(328,796)(329,797)(330,798)(331,799)(332,800)(333,801)(334,802)(335,803)
(336,804)(337,805)(338,806)(339,807)(340,808)(341,809)(342,810)(343,811)
(344,812)(345,813)(346,814)(347,815)(348,816)(349,817)(350,818)(351,819)
(352,820)(353,821)(354,822)(355,823)(356,824)(357,825)(358,826)(359,827)
(360,828)(361,829)(362,830)(363,831)(364,832)(365,729)(366,730)(367,731)
(368,732)(369,733)(370,734)(371,735)(372,736)(373,737)(374,738)(375,739)
(376,740)(377,741)(378,742)(379,743)(380,744)(381,745)(382,746)(383,747)
(384,748)(385,749)(386,750)(387,751)(388,752)(389,753)(390,754)(391,755)
(392,756)(393,757)(394,758)(395,759)(396,760)(397,761)(398,762)(399,763)
(400,764)(401,765)(402,766)(403,767)(404,768)(405,769)(406,770)(407,771)
(408,772)(409,773)(410,774)(411,775)(412,776)(413,777)(414,778)(415,779)
(416,780);
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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