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