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