Polytope of Type {26,8,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,8,4}*1664b
if this polytope has a name.
Group : SmallGroup(1664,13831)
Rank : 4
Schlafli Type : {26,8,4}
Number of vertices, edges, etc : 26, 104, 16, 4
Order of s0s1s2s3 : 104
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {26,4,4}*832
4-fold quotients : {26,2,4}*416, {26,4,2}*416
8-fold quotients : {13,2,4}*208, {26,2,2}*208
13-fold quotients : {2,8,4}*128b
16-fold quotients : {13,2,2}*104
26-fold quotients : {2,4,4}*64
52-fold quotients : {2,2,4}*32, {2,4,2}*32
104-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,105)( 2,117)( 3,116)( 4,115)( 5,114)( 6,113)( 7,112)( 8,111)
( 9,110)( 10,109)( 11,108)( 12,107)( 13,106)( 14,118)( 15,130)( 16,129)
( 17,128)( 18,127)( 19,126)( 20,125)( 21,124)( 22,123)( 23,122)( 24,121)
( 25,120)( 26,119)( 27,131)( 28,143)( 29,142)( 30,141)( 31,140)( 32,139)
( 33,138)( 34,137)( 35,136)( 36,135)( 37,134)( 38,133)( 39,132)( 40,144)
( 41,156)( 42,155)( 43,154)( 44,153)( 45,152)( 46,151)( 47,150)( 48,149)
( 49,148)( 50,147)( 51,146)( 52,145)( 53,157)( 54,169)( 55,168)( 56,167)
( 57,166)( 58,165)( 59,164)( 60,163)( 61,162)( 62,161)( 63,160)( 64,159)
( 65,158)( 66,170)( 67,182)( 68,181)( 69,180)( 70,179)( 71,178)( 72,177)
( 73,176)( 74,175)( 75,174)( 76,173)( 77,172)( 78,171)( 79,183)( 80,195)
( 81,194)( 82,193)( 83,192)( 84,191)( 85,190)( 86,189)( 87,188)( 88,187)
( 89,186)( 90,185)( 91,184)( 92,196)( 93,208)( 94,207)( 95,206)( 96,205)
( 97,204)( 98,203)( 99,202)(100,201)(101,200)(102,199)(103,198)(104,197)
(209,313)(210,325)(211,324)(212,323)(213,322)(214,321)(215,320)(216,319)
(217,318)(218,317)(219,316)(220,315)(221,314)(222,326)(223,338)(224,337)
(225,336)(226,335)(227,334)(228,333)(229,332)(230,331)(231,330)(232,329)
(233,328)(234,327)(235,339)(236,351)(237,350)(238,349)(239,348)(240,347)
(241,346)(242,345)(243,344)(244,343)(245,342)(246,341)(247,340)(248,352)
(249,364)(250,363)(251,362)(252,361)(253,360)(254,359)(255,358)(256,357)
(257,356)(258,355)(259,354)(260,353)(261,365)(262,377)(263,376)(264,375)
(265,374)(266,373)(267,372)(268,371)(269,370)(270,369)(271,368)(272,367)
(273,366)(274,378)(275,390)(276,389)(277,388)(278,387)(279,386)(280,385)
(281,384)(282,383)(283,382)(284,381)(285,380)(286,379)(287,391)(288,403)
(289,402)(290,401)(291,400)(292,399)(293,398)(294,397)(295,396)(296,395)
(297,394)(298,393)(299,392)(300,404)(301,416)(302,415)(303,414)(304,413)
(305,412)(306,411)(307,410)(308,409)(309,408)(310,407)(311,406)(312,405)
(417,521)(418,533)(419,532)(420,531)(421,530)(422,529)(423,528)(424,527)
(425,526)(426,525)(427,524)(428,523)(429,522)(430,534)(431,546)(432,545)
(433,544)(434,543)(435,542)(436,541)(437,540)(438,539)(439,538)(440,537)
(441,536)(442,535)(443,547)(444,559)(445,558)(446,557)(447,556)(448,555)
(449,554)(450,553)(451,552)(452,551)(453,550)(454,549)(455,548)(456,560)
(457,572)(458,571)(459,570)(460,569)(461,568)(462,567)(463,566)(464,565)
(465,564)(466,563)(467,562)(468,561)(469,573)(470,585)(471,584)(472,583)
(473,582)(474,581)(475,580)(476,579)(477,578)(478,577)(479,576)(480,575)
(481,574)(482,586)(483,598)(484,597)(485,596)(486,595)(487,594)(488,593)
(489,592)(490,591)(491,590)(492,589)(493,588)(494,587)(495,599)(496,611)
(497,610)(498,609)(499,608)(500,607)(501,606)(502,605)(503,604)(504,603)
(505,602)(506,601)(507,600)(508,612)(509,624)(510,623)(511,622)(512,621)
(513,620)(514,619)(515,618)(516,617)(517,616)(518,615)(519,614)(520,613)
(625,729)(626,741)(627,740)(628,739)(629,738)(630,737)(631,736)(632,735)
(633,734)(634,733)(635,732)(636,731)(637,730)(638,742)(639,754)(640,753)
(641,752)(642,751)(643,750)(644,749)(645,748)(646,747)(647,746)(648,745)
(649,744)(650,743)(651,755)(652,767)(653,766)(654,765)(655,764)(656,763)
(657,762)(658,761)(659,760)(660,759)(661,758)(662,757)(663,756)(664,768)
(665,780)(666,779)(667,778)(668,777)(669,776)(670,775)(671,774)(672,773)
(673,772)(674,771)(675,770)(676,769)(677,781)(678,793)(679,792)(680,791)
(681,790)(682,789)(683,788)(684,787)(685,786)(686,785)(687,784)(688,783)
(689,782)(690,794)(691,806)(692,805)(693,804)(694,803)(695,802)(696,801)
(697,800)(698,799)(699,798)(700,797)(701,796)(702,795)(703,807)(704,819)
(705,818)(706,817)(707,816)(708,815)(709,814)(710,813)(711,812)(712,811)
(713,810)(714,809)(715,808)(716,820)(717,832)(718,831)(719,830)(720,829)
(721,828)(722,827)(723,826)(724,825)(725,824)(726,823)(727,822)(728,821);;
s1 := ( 1,522)( 2,521)( 3,533)( 4,532)( 5,531)( 6,530)( 7,529)( 8,528)
( 9,527)( 10,526)( 11,525)( 12,524)( 13,523)( 14,535)( 15,534)( 16,546)
( 17,545)( 18,544)( 19,543)( 20,542)( 21,541)( 22,540)( 23,539)( 24,538)
( 25,537)( 26,536)( 27,561)( 28,560)( 29,572)( 30,571)( 31,570)( 32,569)
( 33,568)( 34,567)( 35,566)( 36,565)( 37,564)( 38,563)( 39,562)( 40,548)
( 41,547)( 42,559)( 43,558)( 44,557)( 45,556)( 46,555)( 47,554)( 48,553)
( 49,552)( 50,551)( 51,550)( 52,549)( 53,587)( 54,586)( 55,598)( 56,597)
( 57,596)( 58,595)( 59,594)( 60,593)( 61,592)( 62,591)( 63,590)( 64,589)
( 65,588)( 66,574)( 67,573)( 68,585)( 69,584)( 70,583)( 71,582)( 72,581)
( 73,580)( 74,579)( 75,578)( 76,577)( 77,576)( 78,575)( 79,600)( 80,599)
( 81,611)( 82,610)( 83,609)( 84,608)( 85,607)( 86,606)( 87,605)( 88,604)
( 89,603)( 90,602)( 91,601)( 92,613)( 93,612)( 94,624)( 95,623)( 96,622)
( 97,621)( 98,620)( 99,619)(100,618)(101,617)(102,616)(103,615)(104,614)
(105,418)(106,417)(107,429)(108,428)(109,427)(110,426)(111,425)(112,424)
(113,423)(114,422)(115,421)(116,420)(117,419)(118,431)(119,430)(120,442)
(121,441)(122,440)(123,439)(124,438)(125,437)(126,436)(127,435)(128,434)
(129,433)(130,432)(131,457)(132,456)(133,468)(134,467)(135,466)(136,465)
(137,464)(138,463)(139,462)(140,461)(141,460)(142,459)(143,458)(144,444)
(145,443)(146,455)(147,454)(148,453)(149,452)(150,451)(151,450)(152,449)
(153,448)(154,447)(155,446)(156,445)(157,483)(158,482)(159,494)(160,493)
(161,492)(162,491)(163,490)(164,489)(165,488)(166,487)(167,486)(168,485)
(169,484)(170,470)(171,469)(172,481)(173,480)(174,479)(175,478)(176,477)
(177,476)(178,475)(179,474)(180,473)(181,472)(182,471)(183,496)(184,495)
(185,507)(186,506)(187,505)(188,504)(189,503)(190,502)(191,501)(192,500)
(193,499)(194,498)(195,497)(196,509)(197,508)(198,520)(199,519)(200,518)
(201,517)(202,516)(203,515)(204,514)(205,513)(206,512)(207,511)(208,510)
(209,730)(210,729)(211,741)(212,740)(213,739)(214,738)(215,737)(216,736)
(217,735)(218,734)(219,733)(220,732)(221,731)(222,743)(223,742)(224,754)
(225,753)(226,752)(227,751)(228,750)(229,749)(230,748)(231,747)(232,746)
(233,745)(234,744)(235,769)(236,768)(237,780)(238,779)(239,778)(240,777)
(241,776)(242,775)(243,774)(244,773)(245,772)(246,771)(247,770)(248,756)
(249,755)(250,767)(251,766)(252,765)(253,764)(254,763)(255,762)(256,761)
(257,760)(258,759)(259,758)(260,757)(261,795)(262,794)(263,806)(264,805)
(265,804)(266,803)(267,802)(268,801)(269,800)(270,799)(271,798)(272,797)
(273,796)(274,782)(275,781)(276,793)(277,792)(278,791)(279,790)(280,789)
(281,788)(282,787)(283,786)(284,785)(285,784)(286,783)(287,808)(288,807)
(289,819)(290,818)(291,817)(292,816)(293,815)(294,814)(295,813)(296,812)
(297,811)(298,810)(299,809)(300,821)(301,820)(302,832)(303,831)(304,830)
(305,829)(306,828)(307,827)(308,826)(309,825)(310,824)(311,823)(312,822)
(313,626)(314,625)(315,637)(316,636)(317,635)(318,634)(319,633)(320,632)
(321,631)(322,630)(323,629)(324,628)(325,627)(326,639)(327,638)(328,650)
(329,649)(330,648)(331,647)(332,646)(333,645)(334,644)(335,643)(336,642)
(337,641)(338,640)(339,665)(340,664)(341,676)(342,675)(343,674)(344,673)
(345,672)(346,671)(347,670)(348,669)(349,668)(350,667)(351,666)(352,652)
(353,651)(354,663)(355,662)(356,661)(357,660)(358,659)(359,658)(360,657)
(361,656)(362,655)(363,654)(364,653)(365,691)(366,690)(367,702)(368,701)
(369,700)(370,699)(371,698)(372,697)(373,696)(374,695)(375,694)(376,693)
(377,692)(378,678)(379,677)(380,689)(381,688)(382,687)(383,686)(384,685)
(385,684)(386,683)(387,682)(388,681)(389,680)(390,679)(391,704)(392,703)
(393,715)(394,714)(395,713)(396,712)(397,711)(398,710)(399,709)(400,708)
(401,707)(402,706)(403,705)(404,717)(405,716)(406,728)(407,727)(408,726)
(409,725)(410,724)(411,723)(412,722)(413,721)(414,720)(415,719)(416,718);;
s2 := ( 53, 66)( 54, 67)( 55, 68)( 56, 69)( 57, 70)( 58, 71)( 59, 72)( 60, 73)
( 61, 74)( 62, 75)( 63, 76)( 64, 77)( 65, 78)( 79, 92)( 80, 93)( 81, 94)
( 82, 95)( 83, 96)( 84, 97)( 85, 98)( 86, 99)( 87,100)( 88,101)( 89,102)
( 90,103)( 91,104)(157,170)(158,171)(159,172)(160,173)(161,174)(162,175)
(163,176)(164,177)(165,178)(166,179)(167,180)(168,181)(169,182)(183,196)
(184,197)(185,198)(186,199)(187,200)(188,201)(189,202)(190,203)(191,204)
(192,205)(193,206)(194,207)(195,208)(209,235)(210,236)(211,237)(212,238)
(213,239)(214,240)(215,241)(216,242)(217,243)(218,244)(219,245)(220,246)
(221,247)(222,248)(223,249)(224,250)(225,251)(226,252)(227,253)(228,254)
(229,255)(230,256)(231,257)(232,258)(233,259)(234,260)(261,300)(262,301)
(263,302)(264,303)(265,304)(266,305)(267,306)(268,307)(269,308)(270,309)
(271,310)(272,311)(273,312)(274,287)(275,288)(276,289)(277,290)(278,291)
(279,292)(280,293)(281,294)(282,295)(283,296)(284,297)(285,298)(286,299)
(313,339)(314,340)(315,341)(316,342)(317,343)(318,344)(319,345)(320,346)
(321,347)(322,348)(323,349)(324,350)(325,351)(326,352)(327,353)(328,354)
(329,355)(330,356)(331,357)(332,358)(333,359)(334,360)(335,361)(336,362)
(337,363)(338,364)(365,404)(366,405)(367,406)(368,407)(369,408)(370,409)
(371,410)(372,411)(373,412)(374,413)(375,414)(376,415)(377,416)(378,391)
(379,392)(380,393)(381,394)(382,395)(383,396)(384,397)(385,398)(386,399)
(387,400)(388,401)(389,402)(390,403)(417,469)(418,470)(419,471)(420,472)
(421,473)(422,474)(423,475)(424,476)(425,477)(426,478)(427,479)(428,480)
(429,481)(430,482)(431,483)(432,484)(433,485)(434,486)(435,487)(436,488)
(437,489)(438,490)(439,491)(440,492)(441,493)(442,494)(443,495)(444,496)
(445,497)(446,498)(447,499)(448,500)(449,501)(450,502)(451,503)(452,504)
(453,505)(454,506)(455,507)(456,508)(457,509)(458,510)(459,511)(460,512)
(461,513)(462,514)(463,515)(464,516)(465,517)(466,518)(467,519)(468,520)
(521,573)(522,574)(523,575)(524,576)(525,577)(526,578)(527,579)(528,580)
(529,581)(530,582)(531,583)(532,584)(533,585)(534,586)(535,587)(536,588)
(537,589)(538,590)(539,591)(540,592)(541,593)(542,594)(543,595)(544,596)
(545,597)(546,598)(547,599)(548,600)(549,601)(550,602)(551,603)(552,604)
(553,605)(554,606)(555,607)(556,608)(557,609)(558,610)(559,611)(560,612)
(561,613)(562,614)(563,615)(564,616)(565,617)(566,618)(567,619)(568,620)
(569,621)(570,622)(571,623)(572,624)(625,716)(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);;
s3 := ( 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)( 53,274)( 54,275)( 55,276)( 56,277)
( 57,278)( 58,279)( 59,280)( 60,281)( 61,282)( 62,283)( 63,284)( 64,285)
( 65,286)( 66,261)( 67,262)( 68,263)( 69,264)( 70,265)( 71,266)( 72,267)
( 73,268)( 74,269)( 75,270)( 76,271)( 77,272)( 78,273)( 79,300)( 80,301)
( 81,302)( 82,303)( 83,304)( 84,305)( 85,306)( 86,307)( 87,308)( 88,309)
( 89,310)( 90,311)( 91,312)( 92,287)( 93,288)( 94,289)( 95,290)( 96,291)
( 97,292)( 98,293)( 99,294)(100,295)(101,296)(102,297)(103,298)(104,299)
(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)(157,378)(158,379)(159,380)(160,381)
(161,382)(162,383)(163,384)(164,385)(165,386)(166,387)(167,388)(168,389)
(169,390)(170,365)(171,366)(172,367)(173,368)(174,369)(175,370)(176,371)
(177,372)(178,373)(179,374)(180,375)(181,376)(182,377)(183,404)(184,405)
(185,406)(186,407)(187,408)(188,409)(189,410)(190,411)(191,412)(192,413)
(193,414)(194,415)(195,416)(196,391)(197,392)(198,393)(199,394)(200,395)
(201,396)(202,397)(203,398)(204,399)(205,400)(206,401)(207,402)(208,403)
(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)(469,690)(470,691)(471,692)(472,693)
(473,694)(474,695)(475,696)(476,697)(477,698)(478,699)(479,700)(480,701)
(481,702)(482,677)(483,678)(484,679)(485,680)(486,681)(487,682)(488,683)
(489,684)(490,685)(491,686)(492,687)(493,688)(494,689)(495,716)(496,717)
(497,718)(498,719)(499,720)(500,721)(501,722)(502,723)(503,724)(504,725)
(505,726)(506,727)(507,728)(508,703)(509,704)(510,705)(511,706)(512,707)
(513,708)(514,709)(515,710)(516,711)(517,712)(518,713)(519,714)(520,715)
(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)(573,794)(574,795)(575,796)(576,797)
(577,798)(578,799)(579,800)(580,801)(581,802)(582,803)(583,804)(584,805)
(585,806)(586,781)(587,782)(588,783)(589,784)(590,785)(591,786)(592,787)
(593,788)(594,789)(595,790)(596,791)(597,792)(598,793)(599,820)(600,821)
(601,822)(602,823)(603,824)(604,825)(605,826)(606,827)(607,828)(608,829)
(609,830)(610,831)(611,832)(612,807)(613,808)(614,809)(615,810)(616,811)
(617,812)(618,813)(619,814)(620,815)(621,816)(622,817)(623,818)(624,819);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(832)!( 1,105)( 2,117)( 3,116)( 4,115)( 5,114)( 6,113)( 7,112)
( 8,111)( 9,110)( 10,109)( 11,108)( 12,107)( 13,106)( 14,118)( 15,130)
( 16,129)( 17,128)( 18,127)( 19,126)( 20,125)( 21,124)( 22,123)( 23,122)
( 24,121)( 25,120)( 26,119)( 27,131)( 28,143)( 29,142)( 30,141)( 31,140)
( 32,139)( 33,138)( 34,137)( 35,136)( 36,135)( 37,134)( 38,133)( 39,132)
( 40,144)( 41,156)( 42,155)( 43,154)( 44,153)( 45,152)( 46,151)( 47,150)
( 48,149)( 49,148)( 50,147)( 51,146)( 52,145)( 53,157)( 54,169)( 55,168)
( 56,167)( 57,166)( 58,165)( 59,164)( 60,163)( 61,162)( 62,161)( 63,160)
( 64,159)( 65,158)( 66,170)( 67,182)( 68,181)( 69,180)( 70,179)( 71,178)
( 72,177)( 73,176)( 74,175)( 75,174)( 76,173)( 77,172)( 78,171)( 79,183)
( 80,195)( 81,194)( 82,193)( 83,192)( 84,191)( 85,190)( 86,189)( 87,188)
( 88,187)( 89,186)( 90,185)( 91,184)( 92,196)( 93,208)( 94,207)( 95,206)
( 96,205)( 97,204)( 98,203)( 99,202)(100,201)(101,200)(102,199)(103,198)
(104,197)(209,313)(210,325)(211,324)(212,323)(213,322)(214,321)(215,320)
(216,319)(217,318)(218,317)(219,316)(220,315)(221,314)(222,326)(223,338)
(224,337)(225,336)(226,335)(227,334)(228,333)(229,332)(230,331)(231,330)
(232,329)(233,328)(234,327)(235,339)(236,351)(237,350)(238,349)(239,348)
(240,347)(241,346)(242,345)(243,344)(244,343)(245,342)(246,341)(247,340)
(248,352)(249,364)(250,363)(251,362)(252,361)(253,360)(254,359)(255,358)
(256,357)(257,356)(258,355)(259,354)(260,353)(261,365)(262,377)(263,376)
(264,375)(265,374)(266,373)(267,372)(268,371)(269,370)(270,369)(271,368)
(272,367)(273,366)(274,378)(275,390)(276,389)(277,388)(278,387)(279,386)
(280,385)(281,384)(282,383)(283,382)(284,381)(285,380)(286,379)(287,391)
(288,403)(289,402)(290,401)(291,400)(292,399)(293,398)(294,397)(295,396)
(296,395)(297,394)(298,393)(299,392)(300,404)(301,416)(302,415)(303,414)
(304,413)(305,412)(306,411)(307,410)(308,409)(309,408)(310,407)(311,406)
(312,405)(417,521)(418,533)(419,532)(420,531)(421,530)(422,529)(423,528)
(424,527)(425,526)(426,525)(427,524)(428,523)(429,522)(430,534)(431,546)
(432,545)(433,544)(434,543)(435,542)(436,541)(437,540)(438,539)(439,538)
(440,537)(441,536)(442,535)(443,547)(444,559)(445,558)(446,557)(447,556)
(448,555)(449,554)(450,553)(451,552)(452,551)(453,550)(454,549)(455,548)
(456,560)(457,572)(458,571)(459,570)(460,569)(461,568)(462,567)(463,566)
(464,565)(465,564)(466,563)(467,562)(468,561)(469,573)(470,585)(471,584)
(472,583)(473,582)(474,581)(475,580)(476,579)(477,578)(478,577)(479,576)
(480,575)(481,574)(482,586)(483,598)(484,597)(485,596)(486,595)(487,594)
(488,593)(489,592)(490,591)(491,590)(492,589)(493,588)(494,587)(495,599)
(496,611)(497,610)(498,609)(499,608)(500,607)(501,606)(502,605)(503,604)
(504,603)(505,602)(506,601)(507,600)(508,612)(509,624)(510,623)(511,622)
(512,621)(513,620)(514,619)(515,618)(516,617)(517,616)(518,615)(519,614)
(520,613)(625,729)(626,741)(627,740)(628,739)(629,738)(630,737)(631,736)
(632,735)(633,734)(634,733)(635,732)(636,731)(637,730)(638,742)(639,754)
(640,753)(641,752)(642,751)(643,750)(644,749)(645,748)(646,747)(647,746)
(648,745)(649,744)(650,743)(651,755)(652,767)(653,766)(654,765)(655,764)
(656,763)(657,762)(658,761)(659,760)(660,759)(661,758)(662,757)(663,756)
(664,768)(665,780)(666,779)(667,778)(668,777)(669,776)(670,775)(671,774)
(672,773)(673,772)(674,771)(675,770)(676,769)(677,781)(678,793)(679,792)
(680,791)(681,790)(682,789)(683,788)(684,787)(685,786)(686,785)(687,784)
(688,783)(689,782)(690,794)(691,806)(692,805)(693,804)(694,803)(695,802)
(696,801)(697,800)(698,799)(699,798)(700,797)(701,796)(702,795)(703,807)
(704,819)(705,818)(706,817)(707,816)(708,815)(709,814)(710,813)(711,812)
(712,811)(713,810)(714,809)(715,808)(716,820)(717,832)(718,831)(719,830)
(720,829)(721,828)(722,827)(723,826)(724,825)(725,824)(726,823)(727,822)
(728,821);
s1 := Sym(832)!( 1,522)( 2,521)( 3,533)( 4,532)( 5,531)( 6,530)( 7,529)
( 8,528)( 9,527)( 10,526)( 11,525)( 12,524)( 13,523)( 14,535)( 15,534)
( 16,546)( 17,545)( 18,544)( 19,543)( 20,542)( 21,541)( 22,540)( 23,539)
( 24,538)( 25,537)( 26,536)( 27,561)( 28,560)( 29,572)( 30,571)( 31,570)
( 32,569)( 33,568)( 34,567)( 35,566)( 36,565)( 37,564)( 38,563)( 39,562)
( 40,548)( 41,547)( 42,559)( 43,558)( 44,557)( 45,556)( 46,555)( 47,554)
( 48,553)( 49,552)( 50,551)( 51,550)( 52,549)( 53,587)( 54,586)( 55,598)
( 56,597)( 57,596)( 58,595)( 59,594)( 60,593)( 61,592)( 62,591)( 63,590)
( 64,589)( 65,588)( 66,574)( 67,573)( 68,585)( 69,584)( 70,583)( 71,582)
( 72,581)( 73,580)( 74,579)( 75,578)( 76,577)( 77,576)( 78,575)( 79,600)
( 80,599)( 81,611)( 82,610)( 83,609)( 84,608)( 85,607)( 86,606)( 87,605)
( 88,604)( 89,603)( 90,602)( 91,601)( 92,613)( 93,612)( 94,624)( 95,623)
( 96,622)( 97,621)( 98,620)( 99,619)(100,618)(101,617)(102,616)(103,615)
(104,614)(105,418)(106,417)(107,429)(108,428)(109,427)(110,426)(111,425)
(112,424)(113,423)(114,422)(115,421)(116,420)(117,419)(118,431)(119,430)
(120,442)(121,441)(122,440)(123,439)(124,438)(125,437)(126,436)(127,435)
(128,434)(129,433)(130,432)(131,457)(132,456)(133,468)(134,467)(135,466)
(136,465)(137,464)(138,463)(139,462)(140,461)(141,460)(142,459)(143,458)
(144,444)(145,443)(146,455)(147,454)(148,453)(149,452)(150,451)(151,450)
(152,449)(153,448)(154,447)(155,446)(156,445)(157,483)(158,482)(159,494)
(160,493)(161,492)(162,491)(163,490)(164,489)(165,488)(166,487)(167,486)
(168,485)(169,484)(170,470)(171,469)(172,481)(173,480)(174,479)(175,478)
(176,477)(177,476)(178,475)(179,474)(180,473)(181,472)(182,471)(183,496)
(184,495)(185,507)(186,506)(187,505)(188,504)(189,503)(190,502)(191,501)
(192,500)(193,499)(194,498)(195,497)(196,509)(197,508)(198,520)(199,519)
(200,518)(201,517)(202,516)(203,515)(204,514)(205,513)(206,512)(207,511)
(208,510)(209,730)(210,729)(211,741)(212,740)(213,739)(214,738)(215,737)
(216,736)(217,735)(218,734)(219,733)(220,732)(221,731)(222,743)(223,742)
(224,754)(225,753)(226,752)(227,751)(228,750)(229,749)(230,748)(231,747)
(232,746)(233,745)(234,744)(235,769)(236,768)(237,780)(238,779)(239,778)
(240,777)(241,776)(242,775)(243,774)(244,773)(245,772)(246,771)(247,770)
(248,756)(249,755)(250,767)(251,766)(252,765)(253,764)(254,763)(255,762)
(256,761)(257,760)(258,759)(259,758)(260,757)(261,795)(262,794)(263,806)
(264,805)(265,804)(266,803)(267,802)(268,801)(269,800)(270,799)(271,798)
(272,797)(273,796)(274,782)(275,781)(276,793)(277,792)(278,791)(279,790)
(280,789)(281,788)(282,787)(283,786)(284,785)(285,784)(286,783)(287,808)
(288,807)(289,819)(290,818)(291,817)(292,816)(293,815)(294,814)(295,813)
(296,812)(297,811)(298,810)(299,809)(300,821)(301,820)(302,832)(303,831)
(304,830)(305,829)(306,828)(307,827)(308,826)(309,825)(310,824)(311,823)
(312,822)(313,626)(314,625)(315,637)(316,636)(317,635)(318,634)(319,633)
(320,632)(321,631)(322,630)(323,629)(324,628)(325,627)(326,639)(327,638)
(328,650)(329,649)(330,648)(331,647)(332,646)(333,645)(334,644)(335,643)
(336,642)(337,641)(338,640)(339,665)(340,664)(341,676)(342,675)(343,674)
(344,673)(345,672)(346,671)(347,670)(348,669)(349,668)(350,667)(351,666)
(352,652)(353,651)(354,663)(355,662)(356,661)(357,660)(358,659)(359,658)
(360,657)(361,656)(362,655)(363,654)(364,653)(365,691)(366,690)(367,702)
(368,701)(369,700)(370,699)(371,698)(372,697)(373,696)(374,695)(375,694)
(376,693)(377,692)(378,678)(379,677)(380,689)(381,688)(382,687)(383,686)
(384,685)(385,684)(386,683)(387,682)(388,681)(389,680)(390,679)(391,704)
(392,703)(393,715)(394,714)(395,713)(396,712)(397,711)(398,710)(399,709)
(400,708)(401,707)(402,706)(403,705)(404,717)(405,716)(406,728)(407,727)
(408,726)(409,725)(410,724)(411,723)(412,722)(413,721)(414,720)(415,719)
(416,718);
s2 := Sym(832)!( 53, 66)( 54, 67)( 55, 68)( 56, 69)( 57, 70)( 58, 71)( 59, 72)
( 60, 73)( 61, 74)( 62, 75)( 63, 76)( 64, 77)( 65, 78)( 79, 92)( 80, 93)
( 81, 94)( 82, 95)( 83, 96)( 84, 97)( 85, 98)( 86, 99)( 87,100)( 88,101)
( 89,102)( 90,103)( 91,104)(157,170)(158,171)(159,172)(160,173)(161,174)
(162,175)(163,176)(164,177)(165,178)(166,179)(167,180)(168,181)(169,182)
(183,196)(184,197)(185,198)(186,199)(187,200)(188,201)(189,202)(190,203)
(191,204)(192,205)(193,206)(194,207)(195,208)(209,235)(210,236)(211,237)
(212,238)(213,239)(214,240)(215,241)(216,242)(217,243)(218,244)(219,245)
(220,246)(221,247)(222,248)(223,249)(224,250)(225,251)(226,252)(227,253)
(228,254)(229,255)(230,256)(231,257)(232,258)(233,259)(234,260)(261,300)
(262,301)(263,302)(264,303)(265,304)(266,305)(267,306)(268,307)(269,308)
(270,309)(271,310)(272,311)(273,312)(274,287)(275,288)(276,289)(277,290)
(278,291)(279,292)(280,293)(281,294)(282,295)(283,296)(284,297)(285,298)
(286,299)(313,339)(314,340)(315,341)(316,342)(317,343)(318,344)(319,345)
(320,346)(321,347)(322,348)(323,349)(324,350)(325,351)(326,352)(327,353)
(328,354)(329,355)(330,356)(331,357)(332,358)(333,359)(334,360)(335,361)
(336,362)(337,363)(338,364)(365,404)(366,405)(367,406)(368,407)(369,408)
(370,409)(371,410)(372,411)(373,412)(374,413)(375,414)(376,415)(377,416)
(378,391)(379,392)(380,393)(381,394)(382,395)(383,396)(384,397)(385,398)
(386,399)(387,400)(388,401)(389,402)(390,403)(417,469)(418,470)(419,471)
(420,472)(421,473)(422,474)(423,475)(424,476)(425,477)(426,478)(427,479)
(428,480)(429,481)(430,482)(431,483)(432,484)(433,485)(434,486)(435,487)
(436,488)(437,489)(438,490)(439,491)(440,492)(441,493)(442,494)(443,495)
(444,496)(445,497)(446,498)(447,499)(448,500)(449,501)(450,502)(451,503)
(452,504)(453,505)(454,506)(455,507)(456,508)(457,509)(458,510)(459,511)
(460,512)(461,513)(462,514)(463,515)(464,516)(465,517)(466,518)(467,519)
(468,520)(521,573)(522,574)(523,575)(524,576)(525,577)(526,578)(527,579)
(528,580)(529,581)(530,582)(531,583)(532,584)(533,585)(534,586)(535,587)
(536,588)(537,589)(538,590)(539,591)(540,592)(541,593)(542,594)(543,595)
(544,596)(545,597)(546,598)(547,599)(548,600)(549,601)(550,602)(551,603)
(552,604)(553,605)(554,606)(555,607)(556,608)(557,609)(558,610)(559,611)
(560,612)(561,613)(562,614)(563,615)(564,616)(565,617)(566,618)(567,619)
(568,620)(569,621)(570,622)(571,623)(572,624)(625,716)(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);
s3 := 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)( 53,274)( 54,275)( 55,276)
( 56,277)( 57,278)( 58,279)( 59,280)( 60,281)( 61,282)( 62,283)( 63,284)
( 64,285)( 65,286)( 66,261)( 67,262)( 68,263)( 69,264)( 70,265)( 71,266)
( 72,267)( 73,268)( 74,269)( 75,270)( 76,271)( 77,272)( 78,273)( 79,300)
( 80,301)( 81,302)( 82,303)( 83,304)( 84,305)( 85,306)( 86,307)( 87,308)
( 88,309)( 89,310)( 90,311)( 91,312)( 92,287)( 93,288)( 94,289)( 95,290)
( 96,291)( 97,292)( 98,293)( 99,294)(100,295)(101,296)(102,297)(103,298)
(104,299)(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)(157,378)(158,379)(159,380)
(160,381)(161,382)(162,383)(163,384)(164,385)(165,386)(166,387)(167,388)
(168,389)(169,390)(170,365)(171,366)(172,367)(173,368)(174,369)(175,370)
(176,371)(177,372)(178,373)(179,374)(180,375)(181,376)(182,377)(183,404)
(184,405)(185,406)(186,407)(187,408)(188,409)(189,410)(190,411)(191,412)
(192,413)(193,414)(194,415)(195,416)(196,391)(197,392)(198,393)(199,394)
(200,395)(201,396)(202,397)(203,398)(204,399)(205,400)(206,401)(207,402)
(208,403)(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)(469,690)(470,691)(471,692)
(472,693)(473,694)(474,695)(475,696)(476,697)(477,698)(478,699)(479,700)
(480,701)(481,702)(482,677)(483,678)(484,679)(485,680)(486,681)(487,682)
(488,683)(489,684)(490,685)(491,686)(492,687)(493,688)(494,689)(495,716)
(496,717)(497,718)(498,719)(499,720)(500,721)(501,722)(502,723)(503,724)
(504,725)(505,726)(506,727)(507,728)(508,703)(509,704)(510,705)(511,706)
(512,707)(513,708)(514,709)(515,710)(516,711)(517,712)(518,713)(519,714)
(520,715)(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)(573,794)(574,795)(575,796)
(576,797)(577,798)(578,799)(579,800)(580,801)(581,802)(582,803)(583,804)
(584,805)(585,806)(586,781)(587,782)(588,783)(589,784)(590,785)(591,786)
(592,787)(593,788)(594,789)(595,790)(596,791)(597,792)(598,793)(599,820)
(600,821)(601,822)(602,823)(603,824)(604,825)(605,826)(606,827)(607,828)
(608,829)(609,830)(610,831)(611,832)(612,807)(613,808)(614,809)(615,810)
(616,811)(617,812)(618,813)(619,814)(620,815)(621,816)(622,817)(623,818)
(624,819);
poly := sub<Sym(832)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope