Polytope of Type {4,4,52}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,52}*1664
Also Known As : {{4,4|2},{4,52|2}}. if this polytope has another name.
Group : SmallGroup(1664,7822)
Rank : 4
Schlafli Type : {4,4,52}
Number of vertices, edges, etc : 4, 8, 104, 52
Order of s0s1s2s3 : 52
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 : {2,4,52}*832, {4,2,52}*832, {4,4,26}*832
4-fold quotients : {2,2,52}*416, {2,4,26}*416, {4,2,26}*416
8-fold quotients : {4,2,13}*208, {2,2,26}*208
13-fold quotients : {4,4,4}*128
16-fold quotients : {2,2,13}*104
26-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
52-fold quotients : {2,2,4}*32, {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 := ( 1,105)( 2,106)( 3,107)( 4,108)( 5,109)( 6,110)( 7,111)( 8,112)
( 9,113)( 10,114)( 11,115)( 12,116)( 13,117)( 14,118)( 15,119)( 16,120)
( 17,121)( 18,122)( 19,123)( 20,124)( 21,125)( 22,126)( 23,127)( 24,128)
( 25,129)( 26,130)( 27,131)( 28,132)( 29,133)( 30,134)( 31,135)( 32,136)
( 33,137)( 34,138)( 35,139)( 36,140)( 37,141)( 38,142)( 39,143)( 40,144)
( 41,145)( 42,146)( 43,147)( 44,148)( 45,149)( 46,150)( 47,151)( 48,152)
( 49,153)( 50,154)( 51,155)( 52,156)( 53,157)( 54,158)( 55,159)( 56,160)
( 57,161)( 58,162)( 59,163)( 60,164)( 61,165)( 62,166)( 63,167)( 64,168)
( 65,169)( 66,170)( 67,171)( 68,172)( 69,173)( 70,174)( 71,175)( 72,176)
( 73,177)( 74,178)( 75,179)( 76,180)( 77,181)( 78,182)( 79,183)( 80,184)
( 81,185)( 82,186)( 83,187)( 84,188)( 85,189)( 86,190)( 87,191)( 88,192)
( 89,193)( 90,194)( 91,195)( 92,196)( 93,197)( 94,198)( 95,199)( 96,200)
( 97,201)( 98,202)( 99,203)(100,204)(101,205)(102,206)(103,207)(104,208)
(209,313)(210,314)(211,315)(212,316)(213,317)(214,318)(215,319)(216,320)
(217,321)(218,322)(219,323)(220,324)(221,325)(222,326)(223,327)(224,328)
(225,329)(226,330)(227,331)(228,332)(229,333)(230,334)(231,335)(232,336)
(233,337)(234,338)(235,339)(236,340)(237,341)(238,342)(239,343)(240,344)
(241,345)(242,346)(243,347)(244,348)(245,349)(246,350)(247,351)(248,352)
(249,353)(250,354)(251,355)(252,356)(253,357)(254,358)(255,359)(256,360)
(257,361)(258,362)(259,363)(260,364)(261,365)(262,366)(263,367)(264,368)
(265,369)(266,370)(267,371)(268,372)(269,373)(270,374)(271,375)(272,376)
(273,377)(274,378)(275,379)(276,380)(277,381)(278,382)(279,383)(280,384)
(281,385)(282,386)(283,387)(284,388)(285,389)(286,390)(287,391)(288,392)
(289,393)(290,394)(291,395)(292,396)(293,397)(294,398)(295,399)(296,400)
(297,401)(298,402)(299,403)(300,404)(301,405)(302,406)(303,407)(304,408)
(305,409)(306,410)(307,411)(308,412)(309,413)(310,414)(311,415)(312,416)
(417,521)(418,522)(419,523)(420,524)(421,525)(422,526)(423,527)(424,528)
(425,529)(426,530)(427,531)(428,532)(429,533)(430,534)(431,535)(432,536)
(433,537)(434,538)(435,539)(436,540)(437,541)(438,542)(439,543)(440,544)
(441,545)(442,546)(443,547)(444,548)(445,549)(446,550)(447,551)(448,552)
(449,553)(450,554)(451,555)(452,556)(453,557)(454,558)(455,559)(456,560)
(457,561)(458,562)(459,563)(460,564)(461,565)(462,566)(463,567)(464,568)
(465,569)(466,570)(467,571)(468,572)(469,573)(470,574)(471,575)(472,576)
(473,577)(474,578)(475,579)(476,580)(477,581)(478,582)(479,583)(480,584)
(481,585)(482,586)(483,587)(484,588)(485,589)(486,590)(487,591)(488,592)
(489,593)(490,594)(491,595)(492,596)(493,597)(494,598)(495,599)(496,600)
(497,601)(498,602)(499,603)(500,604)(501,605)(502,606)(503,607)(504,608)
(505,609)(506,610)(507,611)(508,612)(509,613)(510,614)(511,615)(512,616)
(513,617)(514,618)(515,619)(516,620)(517,621)(518,622)(519,623)(520,624)
(625,729)(626,730)(627,731)(628,732)(629,733)(630,734)(631,735)(632,736)
(633,737)(634,738)(635,739)(636,740)(637,741)(638,742)(639,743)(640,744)
(641,745)(642,746)(643,747)(644,748)(645,749)(646,750)(647,751)(648,752)
(649,753)(650,754)(651,755)(652,756)(653,757)(654,758)(655,759)(656,760)
(657,761)(658,762)(659,763)(660,764)(661,765)(662,766)(663,767)(664,768)
(665,769)(666,770)(667,771)(668,772)(669,773)(670,774)(671,775)(672,776)
(673,777)(674,778)(675,779)(676,780)(677,781)(678,782)(679,783)(680,784)
(681,785)(682,786)(683,787)(684,788)(685,789)(686,790)(687,791)(688,792)
(689,793)(690,794)(691,795)(692,796)(693,797)(694,798)(695,799)(696,800)
(697,801)(698,802)(699,803)(700,804)(701,805)(702,806)(703,807)(704,808)
(705,809)(706,810)(707,811)(708,812)(709,813)(710,814)(711,815)(712,816)
(713,817)(714,818)(715,819)(716,820)(717,821)(718,822)(719,823)(720,824)
(721,825)(722,826)(723,827)(724,828)(725,829)(726,830)(727,831)(728,832);;
s1 := (105,157)(106,158)(107,159)(108,160)(109,161)(110,162)(111,163)(112,164)
(113,165)(114,166)(115,167)(116,168)(117,169)(118,170)(119,171)(120,172)
(121,173)(122,174)(123,175)(124,176)(125,177)(126,178)(127,179)(128,180)
(129,181)(130,182)(131,183)(132,184)(133,185)(134,186)(135,187)(136,188)
(137,189)(138,190)(139,191)(140,192)(141,193)(142,194)(143,195)(144,196)
(145,197)(146,198)(147,199)(148,200)(149,201)(150,202)(151,203)(152,204)
(153,205)(154,206)(155,207)(156,208)(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)(261,287)(262,288)
(263,289)(264,290)(265,291)(266,292)(267,293)(268,294)(269,295)(270,296)
(271,297)(272,298)(273,299)(274,300)(275,301)(276,302)(277,303)(278,304)
(279,305)(280,306)(281,307)(282,308)(283,309)(284,310)(285,311)(286,312)
(313,391)(314,392)(315,393)(316,394)(317,395)(318,396)(319,397)(320,398)
(321,399)(322,400)(323,401)(324,402)(325,403)(326,404)(327,405)(328,406)
(329,407)(330,408)(331,409)(332,410)(333,411)(334,412)(335,413)(336,414)
(337,415)(338,416)(339,365)(340,366)(341,367)(342,368)(343,369)(344,370)
(345,371)(346,372)(347,373)(348,374)(349,375)(350,376)(351,377)(352,378)
(353,379)(354,380)(355,381)(356,382)(357,383)(358,384)(359,385)(360,386)
(361,387)(362,388)(363,389)(364,390)(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)
(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)(729,755)(730,756)(731,757)(732,758)
(733,759)(734,760)(735,761)(736,762)(737,763)(738,764)(739,765)(740,766)
(741,767)(742,768)(743,769)(744,770)(745,771)(746,772)(747,773)(748,774)
(749,775)(750,776)(751,777)(752,778)(753,779)(754,780)(781,807)(782,808)
(783,809)(784,810)(785,811)(786,812)(787,813)(788,814)(789,815)(790,816)
(791,817)(792,818)(793,819)(794,820)(795,821)(796,822)(797,823)(798,824)
(799,825)(800,826)(801,827)(802,828)(803,829)(804,830)(805,831)(806,832);;
s2 := ( 1,209)( 2,221)( 3,220)( 4,219)( 5,218)( 6,217)( 7,216)( 8,215)
( 9,214)( 10,213)( 11,212)( 12,211)( 13,210)( 14,222)( 15,234)( 16,233)
( 17,232)( 18,231)( 19,230)( 20,229)( 21,228)( 22,227)( 23,226)( 24,225)
( 25,224)( 26,223)( 27,235)( 28,247)( 29,246)( 30,245)( 31,244)( 32,243)
( 33,242)( 34,241)( 35,240)( 36,239)( 37,238)( 38,237)( 39,236)( 40,248)
( 41,260)( 42,259)( 43,258)( 44,257)( 45,256)( 46,255)( 47,254)( 48,253)
( 49,252)( 50,251)( 51,250)( 52,249)( 53,261)( 54,273)( 55,272)( 56,271)
( 57,270)( 58,269)( 59,268)( 60,267)( 61,266)( 62,265)( 63,264)( 64,263)
( 65,262)( 66,274)( 67,286)( 68,285)( 69,284)( 70,283)( 71,282)( 72,281)
( 73,280)( 74,279)( 75,278)( 76,277)( 77,276)( 78,275)( 79,287)( 80,299)
( 81,298)( 82,297)( 83,296)( 84,295)( 85,294)( 86,293)( 87,292)( 88,291)
( 89,290)( 90,289)( 91,288)( 92,300)( 93,312)( 94,311)( 95,310)( 96,309)
( 97,308)( 98,307)( 99,306)(100,305)(101,304)(102,303)(103,302)(104,301)
(105,313)(106,325)(107,324)(108,323)(109,322)(110,321)(111,320)(112,319)
(113,318)(114,317)(115,316)(116,315)(117,314)(118,326)(119,338)(120,337)
(121,336)(122,335)(123,334)(124,333)(125,332)(126,331)(127,330)(128,329)
(129,328)(130,327)(131,339)(132,351)(133,350)(134,349)(135,348)(136,347)
(137,346)(138,345)(139,344)(140,343)(141,342)(142,341)(143,340)(144,352)
(145,364)(146,363)(147,362)(148,361)(149,360)(150,359)(151,358)(152,357)
(153,356)(154,355)(155,354)(156,353)(157,365)(158,377)(159,376)(160,375)
(161,374)(162,373)(163,372)(164,371)(165,370)(166,369)(167,368)(168,367)
(169,366)(170,378)(171,390)(172,389)(173,388)(174,387)(175,386)(176,385)
(177,384)(178,383)(179,382)(180,381)(181,380)(182,379)(183,391)(184,403)
(185,402)(186,401)(187,400)(188,399)(189,398)(190,397)(191,396)(192,395)
(193,394)(194,393)(195,392)(196,404)(197,416)(198,415)(199,414)(200,413)
(201,412)(202,411)(203,410)(204,409)(205,408)(206,407)(207,406)(208,405)
(417,625)(418,637)(419,636)(420,635)(421,634)(422,633)(423,632)(424,631)
(425,630)(426,629)(427,628)(428,627)(429,626)(430,638)(431,650)(432,649)
(433,648)(434,647)(435,646)(436,645)(437,644)(438,643)(439,642)(440,641)
(441,640)(442,639)(443,651)(444,663)(445,662)(446,661)(447,660)(448,659)
(449,658)(450,657)(451,656)(452,655)(453,654)(454,653)(455,652)(456,664)
(457,676)(458,675)(459,674)(460,673)(461,672)(462,671)(463,670)(464,669)
(465,668)(466,667)(467,666)(468,665)(469,677)(470,689)(471,688)(472,687)
(473,686)(474,685)(475,684)(476,683)(477,682)(478,681)(479,680)(480,679)
(481,678)(482,690)(483,702)(484,701)(485,700)(486,699)(487,698)(488,697)
(489,696)(490,695)(491,694)(492,693)(493,692)(494,691)(495,703)(496,715)
(497,714)(498,713)(499,712)(500,711)(501,710)(502,709)(503,708)(504,707)
(505,706)(506,705)(507,704)(508,716)(509,728)(510,727)(511,726)(512,725)
(513,724)(514,723)(515,722)(516,721)(517,720)(518,719)(519,718)(520,717)
(521,729)(522,741)(523,740)(524,739)(525,738)(526,737)(527,736)(528,735)
(529,734)(530,733)(531,732)(532,731)(533,730)(534,742)(535,754)(536,753)
(537,752)(538,751)(539,750)(540,749)(541,748)(542,747)(543,746)(544,745)
(545,744)(546,743)(547,755)(548,767)(549,766)(550,765)(551,764)(552,763)
(553,762)(554,761)(555,760)(556,759)(557,758)(558,757)(559,756)(560,768)
(561,780)(562,779)(563,778)(564,777)(565,776)(566,775)(567,774)(568,773)
(569,772)(570,771)(571,770)(572,769)(573,781)(574,793)(575,792)(576,791)
(577,790)(578,789)(579,788)(580,787)(581,786)(582,785)(583,784)(584,783)
(585,782)(586,794)(587,806)(588,805)(589,804)(590,803)(591,802)(592,801)
(593,800)(594,799)(595,798)(596,797)(597,796)(598,795)(599,807)(600,819)
(601,818)(602,817)(603,816)(604,815)(605,814)(606,813)(607,812)(608,811)
(609,810)(610,809)(611,808)(612,820)(613,832)(614,831)(615,830)(616,829)
(617,828)(618,827)(619,826)(620,825)(621,824)(622,823)(623,822)(624,821);;
s3 := ( 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)( 53,574)( 54,573)( 55,585)( 56,584)
( 57,583)( 58,582)( 59,581)( 60,580)( 61,579)( 62,578)( 63,577)( 64,576)
( 65,575)( 66,587)( 67,586)( 68,598)( 69,597)( 70,596)( 71,595)( 72,594)
( 73,593)( 74,592)( 75,591)( 76,590)( 77,589)( 78,588)( 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)(131,444)(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)(157,470)(158,469)(159,481)(160,480)
(161,479)(162,478)(163,477)(164,476)(165,475)(166,474)(167,473)(168,472)
(169,471)(170,483)(171,482)(172,494)(173,493)(174,492)(175,491)(176,490)
(177,489)(178,488)(179,487)(180,486)(181,485)(182,484)(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)
(209,743)(210,742)(211,754)(212,753)(213,752)(214,751)(215,750)(216,749)
(217,748)(218,747)(219,746)(220,745)(221,744)(222,730)(223,729)(224,741)
(225,740)(226,739)(227,738)(228,737)(229,736)(230,735)(231,734)(232,733)
(233,732)(234,731)(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)(287,821)(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)
(313,639)(314,638)(315,650)(316,649)(317,648)(318,647)(319,646)(320,645)
(321,644)(322,643)(323,642)(324,641)(325,640)(326,626)(327,625)(328,637)
(329,636)(330,635)(331,634)(332,633)(333,632)(334,631)(335,630)(336,629)
(337,628)(338,627)(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)(391,717)(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);;
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,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, 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*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)!( 1,105)( 2,106)( 3,107)( 4,108)( 5,109)( 6,110)( 7,111)
( 8,112)( 9,113)( 10,114)( 11,115)( 12,116)( 13,117)( 14,118)( 15,119)
( 16,120)( 17,121)( 18,122)( 19,123)( 20,124)( 21,125)( 22,126)( 23,127)
( 24,128)( 25,129)( 26,130)( 27,131)( 28,132)( 29,133)( 30,134)( 31,135)
( 32,136)( 33,137)( 34,138)( 35,139)( 36,140)( 37,141)( 38,142)( 39,143)
( 40,144)( 41,145)( 42,146)( 43,147)( 44,148)( 45,149)( 46,150)( 47,151)
( 48,152)( 49,153)( 50,154)( 51,155)( 52,156)( 53,157)( 54,158)( 55,159)
( 56,160)( 57,161)( 58,162)( 59,163)( 60,164)( 61,165)( 62,166)( 63,167)
( 64,168)( 65,169)( 66,170)( 67,171)( 68,172)( 69,173)( 70,174)( 71,175)
( 72,176)( 73,177)( 74,178)( 75,179)( 76,180)( 77,181)( 78,182)( 79,183)
( 80,184)( 81,185)( 82,186)( 83,187)( 84,188)( 85,189)( 86,190)( 87,191)
( 88,192)( 89,193)( 90,194)( 91,195)( 92,196)( 93,197)( 94,198)( 95,199)
( 96,200)( 97,201)( 98,202)( 99,203)(100,204)(101,205)(102,206)(103,207)
(104,208)(209,313)(210,314)(211,315)(212,316)(213,317)(214,318)(215,319)
(216,320)(217,321)(218,322)(219,323)(220,324)(221,325)(222,326)(223,327)
(224,328)(225,329)(226,330)(227,331)(228,332)(229,333)(230,334)(231,335)
(232,336)(233,337)(234,338)(235,339)(236,340)(237,341)(238,342)(239,343)
(240,344)(241,345)(242,346)(243,347)(244,348)(245,349)(246,350)(247,351)
(248,352)(249,353)(250,354)(251,355)(252,356)(253,357)(254,358)(255,359)
(256,360)(257,361)(258,362)(259,363)(260,364)(261,365)(262,366)(263,367)
(264,368)(265,369)(266,370)(267,371)(268,372)(269,373)(270,374)(271,375)
(272,376)(273,377)(274,378)(275,379)(276,380)(277,381)(278,382)(279,383)
(280,384)(281,385)(282,386)(283,387)(284,388)(285,389)(286,390)(287,391)
(288,392)(289,393)(290,394)(291,395)(292,396)(293,397)(294,398)(295,399)
(296,400)(297,401)(298,402)(299,403)(300,404)(301,405)(302,406)(303,407)
(304,408)(305,409)(306,410)(307,411)(308,412)(309,413)(310,414)(311,415)
(312,416)(417,521)(418,522)(419,523)(420,524)(421,525)(422,526)(423,527)
(424,528)(425,529)(426,530)(427,531)(428,532)(429,533)(430,534)(431,535)
(432,536)(433,537)(434,538)(435,539)(436,540)(437,541)(438,542)(439,543)
(440,544)(441,545)(442,546)(443,547)(444,548)(445,549)(446,550)(447,551)
(448,552)(449,553)(450,554)(451,555)(452,556)(453,557)(454,558)(455,559)
(456,560)(457,561)(458,562)(459,563)(460,564)(461,565)(462,566)(463,567)
(464,568)(465,569)(466,570)(467,571)(468,572)(469,573)(470,574)(471,575)
(472,576)(473,577)(474,578)(475,579)(476,580)(477,581)(478,582)(479,583)
(480,584)(481,585)(482,586)(483,587)(484,588)(485,589)(486,590)(487,591)
(488,592)(489,593)(490,594)(491,595)(492,596)(493,597)(494,598)(495,599)
(496,600)(497,601)(498,602)(499,603)(500,604)(501,605)(502,606)(503,607)
(504,608)(505,609)(506,610)(507,611)(508,612)(509,613)(510,614)(511,615)
(512,616)(513,617)(514,618)(515,619)(516,620)(517,621)(518,622)(519,623)
(520,624)(625,729)(626,730)(627,731)(628,732)(629,733)(630,734)(631,735)
(632,736)(633,737)(634,738)(635,739)(636,740)(637,741)(638,742)(639,743)
(640,744)(641,745)(642,746)(643,747)(644,748)(645,749)(646,750)(647,751)
(648,752)(649,753)(650,754)(651,755)(652,756)(653,757)(654,758)(655,759)
(656,760)(657,761)(658,762)(659,763)(660,764)(661,765)(662,766)(663,767)
(664,768)(665,769)(666,770)(667,771)(668,772)(669,773)(670,774)(671,775)
(672,776)(673,777)(674,778)(675,779)(676,780)(677,781)(678,782)(679,783)
(680,784)(681,785)(682,786)(683,787)(684,788)(685,789)(686,790)(687,791)
(688,792)(689,793)(690,794)(691,795)(692,796)(693,797)(694,798)(695,799)
(696,800)(697,801)(698,802)(699,803)(700,804)(701,805)(702,806)(703,807)
(704,808)(705,809)(706,810)(707,811)(708,812)(709,813)(710,814)(711,815)
(712,816)(713,817)(714,818)(715,819)(716,820)(717,821)(718,822)(719,823)
(720,824)(721,825)(722,826)(723,827)(724,828)(725,829)(726,830)(727,831)
(728,832);
s1 := Sym(832)!(105,157)(106,158)(107,159)(108,160)(109,161)(110,162)(111,163)
(112,164)(113,165)(114,166)(115,167)(116,168)(117,169)(118,170)(119,171)
(120,172)(121,173)(122,174)(123,175)(124,176)(125,177)(126,178)(127,179)
(128,180)(129,181)(130,182)(131,183)(132,184)(133,185)(134,186)(135,187)
(136,188)(137,189)(138,190)(139,191)(140,192)(141,193)(142,194)(143,195)
(144,196)(145,197)(146,198)(147,199)(148,200)(149,201)(150,202)(151,203)
(152,204)(153,205)(154,206)(155,207)(156,208)(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)(261,287)
(262,288)(263,289)(264,290)(265,291)(266,292)(267,293)(268,294)(269,295)
(270,296)(271,297)(272,298)(273,299)(274,300)(275,301)(276,302)(277,303)
(278,304)(279,305)(280,306)(281,307)(282,308)(283,309)(284,310)(285,311)
(286,312)(313,391)(314,392)(315,393)(316,394)(317,395)(318,396)(319,397)
(320,398)(321,399)(322,400)(323,401)(324,402)(325,403)(326,404)(327,405)
(328,406)(329,407)(330,408)(331,409)(332,410)(333,411)(334,412)(335,413)
(336,414)(337,415)(338,416)(339,365)(340,366)(341,367)(342,368)(343,369)
(344,370)(345,371)(346,372)(347,373)(348,374)(349,375)(350,376)(351,377)
(352,378)(353,379)(354,380)(355,381)(356,382)(357,383)(358,384)(359,385)
(360,386)(361,387)(362,388)(363,389)(364,390)(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)(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)(729,755)(730,756)(731,757)
(732,758)(733,759)(734,760)(735,761)(736,762)(737,763)(738,764)(739,765)
(740,766)(741,767)(742,768)(743,769)(744,770)(745,771)(746,772)(747,773)
(748,774)(749,775)(750,776)(751,777)(752,778)(753,779)(754,780)(781,807)
(782,808)(783,809)(784,810)(785,811)(786,812)(787,813)(788,814)(789,815)
(790,816)(791,817)(792,818)(793,819)(794,820)(795,821)(796,822)(797,823)
(798,824)(799,825)(800,826)(801,827)(802,828)(803,829)(804,830)(805,831)
(806,832);
s2 := Sym(832)!( 1,209)( 2,221)( 3,220)( 4,219)( 5,218)( 6,217)( 7,216)
( 8,215)( 9,214)( 10,213)( 11,212)( 12,211)( 13,210)( 14,222)( 15,234)
( 16,233)( 17,232)( 18,231)( 19,230)( 20,229)( 21,228)( 22,227)( 23,226)
( 24,225)( 25,224)( 26,223)( 27,235)( 28,247)( 29,246)( 30,245)( 31,244)
( 32,243)( 33,242)( 34,241)( 35,240)( 36,239)( 37,238)( 38,237)( 39,236)
( 40,248)( 41,260)( 42,259)( 43,258)( 44,257)( 45,256)( 46,255)( 47,254)
( 48,253)( 49,252)( 50,251)( 51,250)( 52,249)( 53,261)( 54,273)( 55,272)
( 56,271)( 57,270)( 58,269)( 59,268)( 60,267)( 61,266)( 62,265)( 63,264)
( 64,263)( 65,262)( 66,274)( 67,286)( 68,285)( 69,284)( 70,283)( 71,282)
( 72,281)( 73,280)( 74,279)( 75,278)( 76,277)( 77,276)( 78,275)( 79,287)
( 80,299)( 81,298)( 82,297)( 83,296)( 84,295)( 85,294)( 86,293)( 87,292)
( 88,291)( 89,290)( 90,289)( 91,288)( 92,300)( 93,312)( 94,311)( 95,310)
( 96,309)( 97,308)( 98,307)( 99,306)(100,305)(101,304)(102,303)(103,302)
(104,301)(105,313)(106,325)(107,324)(108,323)(109,322)(110,321)(111,320)
(112,319)(113,318)(114,317)(115,316)(116,315)(117,314)(118,326)(119,338)
(120,337)(121,336)(122,335)(123,334)(124,333)(125,332)(126,331)(127,330)
(128,329)(129,328)(130,327)(131,339)(132,351)(133,350)(134,349)(135,348)
(136,347)(137,346)(138,345)(139,344)(140,343)(141,342)(142,341)(143,340)
(144,352)(145,364)(146,363)(147,362)(148,361)(149,360)(150,359)(151,358)
(152,357)(153,356)(154,355)(155,354)(156,353)(157,365)(158,377)(159,376)
(160,375)(161,374)(162,373)(163,372)(164,371)(165,370)(166,369)(167,368)
(168,367)(169,366)(170,378)(171,390)(172,389)(173,388)(174,387)(175,386)
(176,385)(177,384)(178,383)(179,382)(180,381)(181,380)(182,379)(183,391)
(184,403)(185,402)(186,401)(187,400)(188,399)(189,398)(190,397)(191,396)
(192,395)(193,394)(194,393)(195,392)(196,404)(197,416)(198,415)(199,414)
(200,413)(201,412)(202,411)(203,410)(204,409)(205,408)(206,407)(207,406)
(208,405)(417,625)(418,637)(419,636)(420,635)(421,634)(422,633)(423,632)
(424,631)(425,630)(426,629)(427,628)(428,627)(429,626)(430,638)(431,650)
(432,649)(433,648)(434,647)(435,646)(436,645)(437,644)(438,643)(439,642)
(440,641)(441,640)(442,639)(443,651)(444,663)(445,662)(446,661)(447,660)
(448,659)(449,658)(450,657)(451,656)(452,655)(453,654)(454,653)(455,652)
(456,664)(457,676)(458,675)(459,674)(460,673)(461,672)(462,671)(463,670)
(464,669)(465,668)(466,667)(467,666)(468,665)(469,677)(470,689)(471,688)
(472,687)(473,686)(474,685)(475,684)(476,683)(477,682)(478,681)(479,680)
(480,679)(481,678)(482,690)(483,702)(484,701)(485,700)(486,699)(487,698)
(488,697)(489,696)(490,695)(491,694)(492,693)(493,692)(494,691)(495,703)
(496,715)(497,714)(498,713)(499,712)(500,711)(501,710)(502,709)(503,708)
(504,707)(505,706)(506,705)(507,704)(508,716)(509,728)(510,727)(511,726)
(512,725)(513,724)(514,723)(515,722)(516,721)(517,720)(518,719)(519,718)
(520,717)(521,729)(522,741)(523,740)(524,739)(525,738)(526,737)(527,736)
(528,735)(529,734)(530,733)(531,732)(532,731)(533,730)(534,742)(535,754)
(536,753)(537,752)(538,751)(539,750)(540,749)(541,748)(542,747)(543,746)
(544,745)(545,744)(546,743)(547,755)(548,767)(549,766)(550,765)(551,764)
(552,763)(553,762)(554,761)(555,760)(556,759)(557,758)(558,757)(559,756)
(560,768)(561,780)(562,779)(563,778)(564,777)(565,776)(566,775)(567,774)
(568,773)(569,772)(570,771)(571,770)(572,769)(573,781)(574,793)(575,792)
(576,791)(577,790)(578,789)(579,788)(580,787)(581,786)(582,785)(583,784)
(584,783)(585,782)(586,794)(587,806)(588,805)(589,804)(590,803)(591,802)
(592,801)(593,800)(594,799)(595,798)(596,797)(597,796)(598,795)(599,807)
(600,819)(601,818)(602,817)(603,816)(604,815)(605,814)(606,813)(607,812)
(608,811)(609,810)(610,809)(611,808)(612,820)(613,832)(614,831)(615,830)
(616,829)(617,828)(618,827)(619,826)(620,825)(621,824)(622,823)(623,822)
(624,821);
s3 := 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)( 53,574)( 54,573)( 55,585)
( 56,584)( 57,583)( 58,582)( 59,581)( 60,580)( 61,579)( 62,578)( 63,577)
( 64,576)( 65,575)( 66,587)( 67,586)( 68,598)( 69,597)( 70,596)( 71,595)
( 72,594)( 73,593)( 74,592)( 75,591)( 76,590)( 77,589)( 78,588)( 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)(131,444)(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)(157,470)(158,469)(159,481)
(160,480)(161,479)(162,478)(163,477)(164,476)(165,475)(166,474)(167,473)
(168,472)(169,471)(170,483)(171,482)(172,494)(173,493)(174,492)(175,491)
(176,490)(177,489)(178,488)(179,487)(180,486)(181,485)(182,484)(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)(209,743)(210,742)(211,754)(212,753)(213,752)(214,751)(215,750)
(216,749)(217,748)(218,747)(219,746)(220,745)(221,744)(222,730)(223,729)
(224,741)(225,740)(226,739)(227,738)(228,737)(229,736)(230,735)(231,734)
(232,733)(233,732)(234,731)(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)(287,821)
(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)(313,639)(314,638)(315,650)(316,649)(317,648)(318,647)(319,646)
(320,645)(321,644)(322,643)(323,642)(324,641)(325,640)(326,626)(327,625)
(328,637)(329,636)(330,635)(331,634)(332,633)(333,632)(334,631)(335,630)
(336,629)(337,628)(338,627)(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)(391,717)
(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);
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, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
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*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