Polytope of Type {8,4,26}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,26}*1664a
Also Known As : {{8,4|2},{4,26|2}}. if this polytope has another name.
Group : SmallGroup(1664,13683)
Rank : 4
Schlafli Type : {8,4,26}
Number of vertices, edges, etc : 8, 16, 52, 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, {8,2,26}*832
4-fold quotients : {8,2,13}*416, {2,4,26}*416, {4,2,26}*416
8-fold quotients : {4,2,13}*208, {2,2,26}*208
13-fold quotients : {8,4,2}*128a
16-fold quotients : {2,2,13}*104
26-fold quotients : {4,4,2}*64, {8,2,2}*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 := ( 1,417)( 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);;
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 := ( 1,313)( 2,325)( 3,324)( 4,323)( 5,322)( 6,321)( 7,320)( 8,319)
( 9,318)( 10,317)( 11,316)( 12,315)( 13,314)( 14,326)( 15,338)( 16,337)
( 17,336)( 18,335)( 19,334)( 20,333)( 21,332)( 22,331)( 23,330)( 24,329)
( 25,328)( 26,327)( 27,339)( 28,351)( 29,350)( 30,349)( 31,348)( 32,347)
( 33,346)( 34,345)( 35,344)( 36,343)( 37,342)( 38,341)( 39,340)( 40,352)
( 41,364)( 42,363)( 43,362)( 44,361)( 45,360)( 46,359)( 47,358)( 48,357)
( 49,356)( 50,355)( 51,354)( 52,353)( 53,365)( 54,377)( 55,376)( 56,375)
( 57,374)( 58,373)( 59,372)( 60,371)( 61,370)( 62,369)( 63,368)( 64,367)
( 65,366)( 66,378)( 67,390)( 68,389)( 69,388)( 70,387)( 71,386)( 72,385)
( 73,384)( 74,383)( 75,382)( 76,381)( 77,380)( 78,379)( 79,391)( 80,403)
( 81,402)( 82,401)( 83,400)( 84,399)( 85,398)( 86,397)( 87,396)( 88,395)
( 89,394)( 90,393)( 91,392)( 92,404)( 93,416)( 94,415)( 95,414)( 96,413)
( 97,412)( 98,411)( 99,410)(100,409)(101,408)(102,407)(103,406)(104,405)
(105,209)(106,221)(107,220)(108,219)(109,218)(110,217)(111,216)(112,215)
(113,214)(114,213)(115,212)(116,211)(117,210)(118,222)(119,234)(120,233)
(121,232)(122,231)(123,230)(124,229)(125,228)(126,227)(127,226)(128,225)
(129,224)(130,223)(131,235)(132,247)(133,246)(134,245)(135,244)(136,243)
(137,242)(138,241)(139,240)(140,239)(141,238)(142,237)(143,236)(144,248)
(145,260)(146,259)(147,258)(148,257)(149,256)(150,255)(151,254)(152,253)
(153,252)(154,251)(155,250)(156,249)(157,261)(158,273)(159,272)(160,271)
(161,270)(162,269)(163,268)(164,267)(165,266)(166,265)(167,264)(168,263)
(169,262)(170,274)(171,286)(172,285)(173,284)(174,283)(175,282)(176,281)
(177,280)(178,279)(179,278)(180,277)(181,276)(182,275)(183,287)(184,299)
(185,298)(186,297)(187,296)(188,295)(189,294)(190,293)(191,292)(192,291)
(193,290)(194,289)(195,288)(196,300)(197,312)(198,311)(199,310)(200,309)
(201,308)(202,307)(203,306)(204,305)(205,304)(206,303)(207,302)(208,301)
(417,729)(418,741)(419,740)(420,739)(421,738)(422,737)(423,736)(424,735)
(425,734)(426,733)(427,732)(428,731)(429,730)(430,742)(431,754)(432,753)
(433,752)(434,751)(435,750)(436,749)(437,748)(438,747)(439,746)(440,745)
(441,744)(442,743)(443,755)(444,767)(445,766)(446,765)(447,764)(448,763)
(449,762)(450,761)(451,760)(452,759)(453,758)(454,757)(455,756)(456,768)
(457,780)(458,779)(459,778)(460,777)(461,776)(462,775)(463,774)(464,773)
(465,772)(466,771)(467,770)(468,769)(469,781)(470,793)(471,792)(472,791)
(473,790)(474,789)(475,788)(476,787)(477,786)(478,785)(479,784)(480,783)
(481,782)(482,794)(483,806)(484,805)(485,804)(486,803)(487,802)(488,801)
(489,800)(490,799)(491,798)(492,797)(493,796)(494,795)(495,807)(496,819)
(497,818)(498,817)(499,816)(500,815)(501,814)(502,813)(503,812)(504,811)
(505,810)(506,809)(507,808)(508,820)(509,832)(510,831)(511,830)(512,829)
(513,828)(514,827)(515,826)(516,825)(517,824)(518,823)(519,822)(520,821)
(521,625)(522,637)(523,636)(524,635)(525,634)(526,633)(527,632)(528,631)
(529,630)(530,629)(531,628)(532,627)(533,626)(534,638)(535,650)(536,649)
(537,648)(538,647)(539,646)(540,645)(541,644)(542,643)(543,642)(544,641)
(545,640)(546,639)(547,651)(548,663)(549,662)(550,661)(551,660)(552,659)
(553,658)(554,657)(555,656)(556,655)(557,654)(558,653)(559,652)(560,664)
(561,676)(562,675)(563,674)(564,673)(565,672)(566,671)(567,670)(568,669)
(569,668)(570,667)(571,666)(572,665)(573,677)(574,689)(575,688)(576,687)
(577,686)(578,685)(579,684)(580,683)(581,682)(582,681)(583,680)(584,679)
(585,678)(586,690)(587,702)(588,701)(589,700)(590,699)(591,698)(592,697)
(593,696)(594,695)(595,694)(596,693)(597,692)(598,691)(599,703)(600,715)
(601,714)(602,713)(603,712)(604,711)(605,710)(606,709)(607,708)(608,707)
(609,706)(610,705)(611,704)(612,716)(613,728)(614,727)(615,726)(616,725)
(617,724)(618,723)(619,722)(620,721)(621,720)(622,719)(623,718)(624,717);;
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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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)!( 1,417)( 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);
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)!( 1,313)( 2,325)( 3,324)( 4,323)( 5,322)( 6,321)( 7,320)
( 8,319)( 9,318)( 10,317)( 11,316)( 12,315)( 13,314)( 14,326)( 15,338)
( 16,337)( 17,336)( 18,335)( 19,334)( 20,333)( 21,332)( 22,331)( 23,330)
( 24,329)( 25,328)( 26,327)( 27,339)( 28,351)( 29,350)( 30,349)( 31,348)
( 32,347)( 33,346)( 34,345)( 35,344)( 36,343)( 37,342)( 38,341)( 39,340)
( 40,352)( 41,364)( 42,363)( 43,362)( 44,361)( 45,360)( 46,359)( 47,358)
( 48,357)( 49,356)( 50,355)( 51,354)( 52,353)( 53,365)( 54,377)( 55,376)
( 56,375)( 57,374)( 58,373)( 59,372)( 60,371)( 61,370)( 62,369)( 63,368)
( 64,367)( 65,366)( 66,378)( 67,390)( 68,389)( 69,388)( 70,387)( 71,386)
( 72,385)( 73,384)( 74,383)( 75,382)( 76,381)( 77,380)( 78,379)( 79,391)
( 80,403)( 81,402)( 82,401)( 83,400)( 84,399)( 85,398)( 86,397)( 87,396)
( 88,395)( 89,394)( 90,393)( 91,392)( 92,404)( 93,416)( 94,415)( 95,414)
( 96,413)( 97,412)( 98,411)( 99,410)(100,409)(101,408)(102,407)(103,406)
(104,405)(105,209)(106,221)(107,220)(108,219)(109,218)(110,217)(111,216)
(112,215)(113,214)(114,213)(115,212)(116,211)(117,210)(118,222)(119,234)
(120,233)(121,232)(122,231)(123,230)(124,229)(125,228)(126,227)(127,226)
(128,225)(129,224)(130,223)(131,235)(132,247)(133,246)(134,245)(135,244)
(136,243)(137,242)(138,241)(139,240)(140,239)(141,238)(142,237)(143,236)
(144,248)(145,260)(146,259)(147,258)(148,257)(149,256)(150,255)(151,254)
(152,253)(153,252)(154,251)(155,250)(156,249)(157,261)(158,273)(159,272)
(160,271)(161,270)(162,269)(163,268)(164,267)(165,266)(166,265)(167,264)
(168,263)(169,262)(170,274)(171,286)(172,285)(173,284)(174,283)(175,282)
(176,281)(177,280)(178,279)(179,278)(180,277)(181,276)(182,275)(183,287)
(184,299)(185,298)(186,297)(187,296)(188,295)(189,294)(190,293)(191,292)
(192,291)(193,290)(194,289)(195,288)(196,300)(197,312)(198,311)(199,310)
(200,309)(201,308)(202,307)(203,306)(204,305)(205,304)(206,303)(207,302)
(208,301)(417,729)(418,741)(419,740)(420,739)(421,738)(422,737)(423,736)
(424,735)(425,734)(426,733)(427,732)(428,731)(429,730)(430,742)(431,754)
(432,753)(433,752)(434,751)(435,750)(436,749)(437,748)(438,747)(439,746)
(440,745)(441,744)(442,743)(443,755)(444,767)(445,766)(446,765)(447,764)
(448,763)(449,762)(450,761)(451,760)(452,759)(453,758)(454,757)(455,756)
(456,768)(457,780)(458,779)(459,778)(460,777)(461,776)(462,775)(463,774)
(464,773)(465,772)(466,771)(467,770)(468,769)(469,781)(470,793)(471,792)
(472,791)(473,790)(474,789)(475,788)(476,787)(477,786)(478,785)(479,784)
(480,783)(481,782)(482,794)(483,806)(484,805)(485,804)(486,803)(487,802)
(488,801)(489,800)(490,799)(491,798)(492,797)(493,796)(494,795)(495,807)
(496,819)(497,818)(498,817)(499,816)(500,815)(501,814)(502,813)(503,812)
(504,811)(505,810)(506,809)(507,808)(508,820)(509,832)(510,831)(511,830)
(512,829)(513,828)(514,827)(515,826)(516,825)(517,824)(518,823)(519,822)
(520,821)(521,625)(522,637)(523,636)(524,635)(525,634)(526,633)(527,632)
(528,631)(529,630)(530,629)(531,628)(532,627)(533,626)(534,638)(535,650)
(536,649)(537,648)(538,647)(539,646)(540,645)(541,644)(542,643)(543,642)
(544,641)(545,640)(546,639)(547,651)(548,663)(549,662)(550,661)(551,660)
(552,659)(553,658)(554,657)(555,656)(556,655)(557,654)(558,653)(559,652)
(560,664)(561,676)(562,675)(563,674)(564,673)(565,672)(566,671)(567,670)
(568,669)(569,668)(570,667)(571,666)(572,665)(573,677)(574,689)(575,688)
(576,687)(577,686)(578,685)(579,684)(580,683)(581,682)(582,681)(583,680)
(584,679)(585,678)(586,690)(587,702)(588,701)(589,700)(590,699)(591,698)
(592,697)(593,696)(594,695)(595,694)(596,693)(597,692)(598,691)(599,703)
(600,715)(601,714)(602,713)(603,712)(604,711)(605,710)(606,709)(607,708)
(608,707)(609,706)(610,705)(611,704)(612,716)(613,728)(614,727)(615,726)
(616,725)(617,724)(618,723)(619,722)(620,721)(621,720)(622,719)(623,718)
(624,717);
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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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