Polytope of Type {8,4,26}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,26}*1664b
if this polytope has a name.
Group : SmallGroup(1664,13831)
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
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 : {8,4,2}*128b
16-fold quotients : {2,2,13}*104
26-fold quotients : {4,4,2}*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)( 27,456)( 28,457)( 29,458)( 30,459)( 31,460)( 32,461)
( 33,462)( 34,463)( 35,464)( 36,465)( 37,466)( 38,467)( 39,468)( 40,443)
( 41,444)( 42,445)( 43,446)( 44,447)( 45,448)( 46,449)( 47,450)( 48,451)
( 49,452)( 50,453)( 51,454)( 52,455)( 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)( 79,495)( 80,496)
( 81,497)( 82,498)( 83,499)( 84,500)( 85,501)( 86,502)( 87,503)( 88,504)
( 89,505)( 90,506)( 91,507)( 92,508)( 93,509)( 94,510)( 95,511)( 96,512)
( 97,513)( 98,514)( 99,515)(100,516)(101,517)(102,518)(103,519)(104,520)
(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)(131,560)(132,561)(133,562)(134,563)(135,564)(136,565)
(137,566)(138,567)(139,568)(140,569)(141,570)(142,571)(143,572)(144,547)
(145,548)(146,549)(147,550)(148,551)(149,552)(150,553)(151,554)(152,555)
(153,556)(154,557)(155,558)(156,559)(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)(183,599)(184,600)
(185,601)(186,602)(187,603)(188,604)(189,605)(190,606)(191,607)(192,608)
(193,609)(194,610)(195,611)(196,612)(197,613)(198,614)(199,615)(200,616)
(201,617)(202,618)(203,619)(204,620)(205,621)(206,622)(207,623)(208,624)
(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)(235,664)(236,665)(237,666)(238,667)(239,668)(240,669)
(241,670)(242,671)(243,672)(244,673)(245,674)(246,675)(247,676)(248,651)
(249,652)(250,653)(251,654)(252,655)(253,656)(254,657)(255,658)(256,659)
(257,660)(258,661)(259,662)(260,663)(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)(287,703)(288,704)
(289,705)(290,706)(291,707)(292,708)(293,709)(294,710)(295,711)(296,712)
(297,713)(298,714)(299,715)(300,716)(301,717)(302,718)(303,719)(304,720)
(305,721)(306,722)(307,723)(308,724)(309,725)(310,726)(311,727)(312,728)
(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)(339,768)(340,769)(341,770)(342,771)(343,772)(344,773)
(345,774)(346,775)(347,776)(348,777)(349,778)(350,779)(351,780)(352,755)
(353,756)(354,757)(355,758)(356,759)(357,760)(358,761)(359,762)(360,763)
(361,764)(362,765)(363,766)(364,767)(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)(391,807)(392,808)
(393,809)(394,810)(395,811)(396,812)(397,813)(398,814)(399,815)(400,816)
(401,817)(402,818)(403,819)(404,820)(405,821)(406,822)(407,823)(408,824)
(409,825)(410,826)(411,827)(412,828)(413,829)(414,830)(415,831)(416,832);;
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)(625,716)(626,717)(627,718)(628,719)
(629,720)(630,721)(631,722)(632,723)(633,724)(634,725)(635,726)(636,727)
(637,728)(638,703)(639,704)(640,705)(641,706)(642,707)(643,708)(644,709)
(645,710)(646,711)(647,712)(648,713)(649,714)(650,715)(651,690)(652,691)
(653,692)(654,693)(655,694)(656,695)(657,696)(658,697)(659,698)(660,699)
(661,700)(662,701)(663,702)(664,677)(665,678)(666,679)(667,680)(668,681)
(669,682)(670,683)(671,684)(672,685)(673,686)(674,687)(675,688)(676,689)
(729,820)(730,821)(731,822)(732,823)(733,824)(734,825)(735,826)(736,827)
(737,828)(738,829)(739,830)(740,831)(741,832)(742,807)(743,808)(744,809)
(745,810)(746,811)(747,812)(748,813)(749,814)(750,815)(751,816)(752,817)
(753,818)(754,819)(755,794)(756,795)(757,796)(758,797)(759,798)(760,799)
(761,800)(762,801)(763,802)(764,803)(765,804)(766,805)(767,806)(768,781)
(769,782)(770,783)(771,784)(772,785)(773,786)(774,787)(775,788)(776,789)
(777,790)(778,791)(779,792)(780,793);;
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)( 53,378)( 54,390)( 55,389)( 56,388)
( 57,387)( 58,386)( 59,385)( 60,384)( 61,383)( 62,382)( 63,381)( 64,380)
( 65,379)( 66,365)( 67,377)( 68,376)( 69,375)( 70,374)( 71,373)( 72,372)
( 73,371)( 74,370)( 75,369)( 76,368)( 77,367)( 78,366)( 79,404)( 80,416)
( 81,415)( 82,414)( 83,413)( 84,412)( 85,411)( 86,410)( 87,409)( 88,408)
( 89,407)( 90,406)( 91,405)( 92,391)( 93,403)( 94,402)( 95,401)( 96,400)
( 97,399)( 98,398)( 99,397)(100,396)(101,395)(102,394)(103,393)(104,392)
(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)(157,274)(158,286)(159,285)(160,284)
(161,283)(162,282)(163,281)(164,280)(165,279)(166,278)(167,277)(168,276)
(169,275)(170,261)(171,273)(172,272)(173,271)(174,270)(175,269)(176,268)
(177,267)(178,266)(179,265)(180,264)(181,263)(182,262)(183,300)(184,312)
(185,311)(186,310)(187,309)(188,308)(189,307)(190,306)(191,305)(192,304)
(193,303)(194,302)(195,301)(196,287)(197,299)(198,298)(199,297)(200,296)
(201,295)(202,294)(203,293)(204,292)(205,291)(206,290)(207,289)(208,288)
(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)(469,794)(470,806)(471,805)(472,804)
(473,803)(474,802)(475,801)(476,800)(477,799)(478,798)(479,797)(480,796)
(481,795)(482,781)(483,793)(484,792)(485,791)(486,790)(487,789)(488,788)
(489,787)(490,786)(491,785)(492,784)(493,783)(494,782)(495,820)(496,832)
(497,831)(498,830)(499,829)(500,828)(501,827)(502,826)(503,825)(504,824)
(505,823)(506,822)(507,821)(508,807)(509,819)(510,818)(511,817)(512,816)
(513,815)(514,814)(515,813)(516,812)(517,811)(518,810)(519,809)(520,808)
(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)(573,690)(574,702)(575,701)(576,700)
(577,699)(578,698)(579,697)(580,696)(581,695)(582,694)(583,693)(584,692)
(585,691)(586,677)(587,689)(588,688)(589,687)(590,686)(591,685)(592,684)
(593,683)(594,682)(595,681)(596,680)(597,679)(598,678)(599,716)(600,728)
(601,727)(602,726)(603,725)(604,724)(605,723)(606,722)(607,721)(608,720)
(609,719)(610,718)(611,717)(612,703)(613,715)(614,714)(615,713)(616,712)
(617,711)(618,710)(619,709)(620,708)(621,707)(622,706)(623,705)(624,704);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s0*s1*s2*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)( 27,456)( 28,457)( 29,458)( 30,459)( 31,460)
( 32,461)( 33,462)( 34,463)( 35,464)( 36,465)( 37,466)( 38,467)( 39,468)
( 40,443)( 41,444)( 42,445)( 43,446)( 44,447)( 45,448)( 46,449)( 47,450)
( 48,451)( 49,452)( 50,453)( 51,454)( 52,455)( 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)( 79,495)
( 80,496)( 81,497)( 82,498)( 83,499)( 84,500)( 85,501)( 86,502)( 87,503)
( 88,504)( 89,505)( 90,506)( 91,507)( 92,508)( 93,509)( 94,510)( 95,511)
( 96,512)( 97,513)( 98,514)( 99,515)(100,516)(101,517)(102,518)(103,519)
(104,520)(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)(131,560)(132,561)(133,562)(134,563)(135,564)
(136,565)(137,566)(138,567)(139,568)(140,569)(141,570)(142,571)(143,572)
(144,547)(145,548)(146,549)(147,550)(148,551)(149,552)(150,553)(151,554)
(152,555)(153,556)(154,557)(155,558)(156,559)(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)(183,599)
(184,600)(185,601)(186,602)(187,603)(188,604)(189,605)(190,606)(191,607)
(192,608)(193,609)(194,610)(195,611)(196,612)(197,613)(198,614)(199,615)
(200,616)(201,617)(202,618)(203,619)(204,620)(205,621)(206,622)(207,623)
(208,624)(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)(235,664)(236,665)(237,666)(238,667)(239,668)
(240,669)(241,670)(242,671)(243,672)(244,673)(245,674)(246,675)(247,676)
(248,651)(249,652)(250,653)(251,654)(252,655)(253,656)(254,657)(255,658)
(256,659)(257,660)(258,661)(259,662)(260,663)(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)(287,703)
(288,704)(289,705)(290,706)(291,707)(292,708)(293,709)(294,710)(295,711)
(296,712)(297,713)(298,714)(299,715)(300,716)(301,717)(302,718)(303,719)
(304,720)(305,721)(306,722)(307,723)(308,724)(309,725)(310,726)(311,727)
(312,728)(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)(339,768)(340,769)(341,770)(342,771)(343,772)
(344,773)(345,774)(346,775)(347,776)(348,777)(349,778)(350,779)(351,780)
(352,755)(353,756)(354,757)(355,758)(356,759)(357,760)(358,761)(359,762)
(360,763)(361,764)(362,765)(363,766)(364,767)(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)(391,807)
(392,808)(393,809)(394,810)(395,811)(396,812)(397,813)(398,814)(399,815)
(400,816)(401,817)(402,818)(403,819)(404,820)(405,821)(406,822)(407,823)
(408,824)(409,825)(410,826)(411,827)(412,828)(413,829)(414,830)(415,831)
(416,832);
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)(625,716)(626,717)(627,718)
(628,719)(629,720)(630,721)(631,722)(632,723)(633,724)(634,725)(635,726)
(636,727)(637,728)(638,703)(639,704)(640,705)(641,706)(642,707)(643,708)
(644,709)(645,710)(646,711)(647,712)(648,713)(649,714)(650,715)(651,690)
(652,691)(653,692)(654,693)(655,694)(656,695)(657,696)(658,697)(659,698)
(660,699)(661,700)(662,701)(663,702)(664,677)(665,678)(666,679)(667,680)
(668,681)(669,682)(670,683)(671,684)(672,685)(673,686)(674,687)(675,688)
(676,689)(729,820)(730,821)(731,822)(732,823)(733,824)(734,825)(735,826)
(736,827)(737,828)(738,829)(739,830)(740,831)(741,832)(742,807)(743,808)
(744,809)(745,810)(746,811)(747,812)(748,813)(749,814)(750,815)(751,816)
(752,817)(753,818)(754,819)(755,794)(756,795)(757,796)(758,797)(759,798)
(760,799)(761,800)(762,801)(763,802)(764,803)(765,804)(766,805)(767,806)
(768,781)(769,782)(770,783)(771,784)(772,785)(773,786)(774,787)(775,788)
(776,789)(777,790)(778,791)(779,792)(780,793);
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)( 53,378)( 54,390)( 55,389)
( 56,388)( 57,387)( 58,386)( 59,385)( 60,384)( 61,383)( 62,382)( 63,381)
( 64,380)( 65,379)( 66,365)( 67,377)( 68,376)( 69,375)( 70,374)( 71,373)
( 72,372)( 73,371)( 74,370)( 75,369)( 76,368)( 77,367)( 78,366)( 79,404)
( 80,416)( 81,415)( 82,414)( 83,413)( 84,412)( 85,411)( 86,410)( 87,409)
( 88,408)( 89,407)( 90,406)( 91,405)( 92,391)( 93,403)( 94,402)( 95,401)
( 96,400)( 97,399)( 98,398)( 99,397)(100,396)(101,395)(102,394)(103,393)
(104,392)(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)(157,274)(158,286)(159,285)
(160,284)(161,283)(162,282)(163,281)(164,280)(165,279)(166,278)(167,277)
(168,276)(169,275)(170,261)(171,273)(172,272)(173,271)(174,270)(175,269)
(176,268)(177,267)(178,266)(179,265)(180,264)(181,263)(182,262)(183,300)
(184,312)(185,311)(186,310)(187,309)(188,308)(189,307)(190,306)(191,305)
(192,304)(193,303)(194,302)(195,301)(196,287)(197,299)(198,298)(199,297)
(200,296)(201,295)(202,294)(203,293)(204,292)(205,291)(206,290)(207,289)
(208,288)(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)(469,794)(470,806)(471,805)
(472,804)(473,803)(474,802)(475,801)(476,800)(477,799)(478,798)(479,797)
(480,796)(481,795)(482,781)(483,793)(484,792)(485,791)(486,790)(487,789)
(488,788)(489,787)(490,786)(491,785)(492,784)(493,783)(494,782)(495,820)
(496,832)(497,831)(498,830)(499,829)(500,828)(501,827)(502,826)(503,825)
(504,824)(505,823)(506,822)(507,821)(508,807)(509,819)(510,818)(511,817)
(512,816)(513,815)(514,814)(515,813)(516,812)(517,811)(518,810)(519,809)
(520,808)(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)(573,690)(574,702)(575,701)
(576,700)(577,699)(578,698)(579,697)(580,696)(581,695)(582,694)(583,693)
(584,692)(585,691)(586,677)(587,689)(588,688)(589,687)(590,686)(591,685)
(592,684)(593,683)(594,682)(595,681)(596,680)(597,679)(598,678)(599,716)
(600,728)(601,727)(602,726)(603,725)(604,724)(605,723)(606,722)(607,721)
(608,720)(609,719)(610,718)(611,717)(612,703)(613,715)(614,714)(615,713)
(616,712)(617,711)(618,710)(619,709)(620,708)(621,707)(622,706)(623,705)
(624,704);
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,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s0*s1*s0*s1*s2*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