Polytope of Type {4,52,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,52,4}*1664
Also Known As : {{4,52|2},{52,4|2}}. if this polytope has another name.
Group : SmallGroup(1664,7823)
Rank : 4
Schlafli Type : {4,52,4}
Number of vertices, edges, etc : 4, 104, 104, 4
Order of s0s1s2s3 : 52
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Self-Dual
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 : {2,52,4}*832, {4,52,2}*832, {4,26,4}*832
4-fold quotients : {2,52,2}*416, {2,26,4}*416, {4,26,2}*416
8-fold quotients : {2,26,2}*208
13-fold quotients : {4,4,4}*128
16-fold quotients : {2,13,2}*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 := ( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 15, 26)( 16, 25)
( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 28, 39)( 29, 38)( 30, 37)( 31, 36)
( 32, 35)( 33, 34)( 41, 52)( 42, 51)( 43, 50)( 44, 49)( 45, 48)( 46, 47)
( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 67, 78)( 68, 77)
( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 80, 91)( 81, 90)( 82, 89)( 83, 88)
( 84, 87)( 85, 86)( 93,104)( 94,103)( 95,102)( 96,101)( 97,100)( 98, 99)
(105,157)(106,169)(107,168)(108,167)(109,166)(110,165)(111,164)(112,163)
(113,162)(114,161)(115,160)(116,159)(117,158)(118,170)(119,182)(120,181)
(121,180)(122,179)(123,178)(124,177)(125,176)(126,175)(127,174)(128,173)
(129,172)(130,171)(131,183)(132,195)(133,194)(134,193)(135,192)(136,191)
(137,190)(138,189)(139,188)(140,187)(141,186)(142,185)(143,184)(144,196)
(145,208)(146,207)(147,206)(148,205)(149,204)(150,203)(151,202)(152,201)
(153,200)(154,199)(155,198)(156,197)(209,235)(210,247)(211,246)(212,245)
(213,244)(214,243)(215,242)(216,241)(217,240)(218,239)(219,238)(220,237)
(221,236)(222,248)(223,260)(224,259)(225,258)(226,257)(227,256)(228,255)
(229,254)(230,253)(231,252)(232,251)(233,250)(234,249)(261,287)(262,299)
(263,298)(264,297)(265,296)(266,295)(267,294)(268,293)(269,292)(270,291)
(271,290)(272,289)(273,288)(274,300)(275,312)(276,311)(277,310)(278,309)
(279,308)(280,307)(281,306)(282,305)(283,304)(284,303)(285,302)(286,301)
(313,391)(314,403)(315,402)(316,401)(317,400)(318,399)(319,398)(320,397)
(321,396)(322,395)(323,394)(324,393)(325,392)(326,404)(327,416)(328,415)
(329,414)(330,413)(331,412)(332,411)(333,410)(334,409)(335,408)(336,407)
(337,406)(338,405)(339,365)(340,377)(341,376)(342,375)(343,374)(344,373)
(345,372)(346,371)(347,370)(348,369)(349,368)(350,367)(351,366)(352,378)
(353,390)(354,389)(355,388)(356,387)(357,386)(358,385)(359,384)(360,383)
(361,382)(362,381)(363,380)(364,379)(417,469)(418,481)(419,480)(420,479)
(421,478)(422,477)(423,476)(424,475)(425,474)(426,473)(427,472)(428,471)
(429,470)(430,482)(431,494)(432,493)(433,492)(434,491)(435,490)(436,489)
(437,488)(438,487)(439,486)(440,485)(441,484)(442,483)(443,495)(444,507)
(445,506)(446,505)(447,504)(448,503)(449,502)(450,501)(451,500)(452,499)
(453,498)(454,497)(455,496)(456,508)(457,520)(458,519)(459,518)(460,517)
(461,516)(462,515)(463,514)(464,513)(465,512)(466,511)(467,510)(468,509)
(522,533)(523,532)(524,531)(525,530)(526,529)(527,528)(535,546)(536,545)
(537,544)(538,543)(539,542)(540,541)(548,559)(549,558)(550,557)(551,556)
(552,555)(553,554)(561,572)(562,571)(563,570)(564,569)(565,568)(566,567)
(574,585)(575,584)(576,583)(577,582)(578,581)(579,580)(587,598)(588,597)
(589,596)(590,595)(591,594)(592,593)(600,611)(601,610)(602,609)(603,608)
(604,607)(605,606)(613,624)(614,623)(615,622)(616,621)(617,620)(618,619)
(625,703)(626,715)(627,714)(628,713)(629,712)(630,711)(631,710)(632,709)
(633,708)(634,707)(635,706)(636,705)(637,704)(638,716)(639,728)(640,727)
(641,726)(642,725)(643,724)(644,723)(645,722)(646,721)(647,720)(648,719)
(649,718)(650,717)(651,677)(652,689)(653,688)(654,687)(655,686)(656,685)
(657,684)(658,683)(659,682)(660,681)(661,680)(662,679)(663,678)(664,690)
(665,702)(666,701)(667,700)(668,699)(669,698)(670,697)(671,696)(672,695)
(673,694)(674,693)(675,692)(676,691)(729,755)(730,767)(731,766)(732,765)
(733,764)(734,763)(735,762)(736,761)(737,760)(738,759)(739,758)(740,757)
(741,756)(742,768)(743,780)(744,779)(745,778)(746,777)(747,776)(748,775)
(749,774)(750,773)(751,772)(752,771)(753,770)(754,769)(781,807)(782,819)
(783,818)(784,817)(785,816)(786,815)(787,814)(788,813)(789,812)(790,811)
(791,810)(792,809)(793,808)(794,820)(795,832)(796,831)(797,830)(798,829)
(799,828)(800,827)(801,826)(802,825)(803,824)(804,823)(805,822)(806,821);;
s2 := ( 1,210)( 2,209)( 3,221)( 4,220)( 5,219)( 6,218)( 7,217)( 8,216)
( 9,215)( 10,214)( 11,213)( 12,212)( 13,211)( 14,223)( 15,222)( 16,234)
( 17,233)( 18,232)( 19,231)( 20,230)( 21,229)( 22,228)( 23,227)( 24,226)
( 25,225)( 26,224)( 27,236)( 28,235)( 29,247)( 30,246)( 31,245)( 32,244)
( 33,243)( 34,242)( 35,241)( 36,240)( 37,239)( 38,238)( 39,237)( 40,249)
( 41,248)( 42,260)( 43,259)( 44,258)( 45,257)( 46,256)( 47,255)( 48,254)
( 49,253)( 50,252)( 51,251)( 52,250)( 53,262)( 54,261)( 55,273)( 56,272)
( 57,271)( 58,270)( 59,269)( 60,268)( 61,267)( 62,266)( 63,265)( 64,264)
( 65,263)( 66,275)( 67,274)( 68,286)( 69,285)( 70,284)( 71,283)( 72,282)
( 73,281)( 74,280)( 75,279)( 76,278)( 77,277)( 78,276)( 79,288)( 80,287)
( 81,299)( 82,298)( 83,297)( 84,296)( 85,295)( 86,294)( 87,293)( 88,292)
( 89,291)( 90,290)( 91,289)( 92,301)( 93,300)( 94,312)( 95,311)( 96,310)
( 97,309)( 98,308)( 99,307)(100,306)(101,305)(102,304)(103,303)(104,302)
(105,314)(106,313)(107,325)(108,324)(109,323)(110,322)(111,321)(112,320)
(113,319)(114,318)(115,317)(116,316)(117,315)(118,327)(119,326)(120,338)
(121,337)(122,336)(123,335)(124,334)(125,333)(126,332)(127,331)(128,330)
(129,329)(130,328)(131,340)(132,339)(133,351)(134,350)(135,349)(136,348)
(137,347)(138,346)(139,345)(140,344)(141,343)(142,342)(143,341)(144,353)
(145,352)(146,364)(147,363)(148,362)(149,361)(150,360)(151,359)(152,358)
(153,357)(154,356)(155,355)(156,354)(157,366)(158,365)(159,377)(160,376)
(161,375)(162,374)(163,373)(164,372)(165,371)(166,370)(167,369)(168,368)
(169,367)(170,379)(171,378)(172,390)(173,389)(174,388)(175,387)(176,386)
(177,385)(178,384)(179,383)(180,382)(181,381)(182,380)(183,392)(184,391)
(185,403)(186,402)(187,401)(188,400)(189,399)(190,398)(191,397)(192,396)
(193,395)(194,394)(195,393)(196,405)(197,404)(198,416)(199,415)(200,414)
(201,413)(202,412)(203,411)(204,410)(205,409)(206,408)(207,407)(208,406)
(417,626)(418,625)(419,637)(420,636)(421,635)(422,634)(423,633)(424,632)
(425,631)(426,630)(427,629)(428,628)(429,627)(430,639)(431,638)(432,650)
(433,649)(434,648)(435,647)(436,646)(437,645)(438,644)(439,643)(440,642)
(441,641)(442,640)(443,652)(444,651)(445,663)(446,662)(447,661)(448,660)
(449,659)(450,658)(451,657)(452,656)(453,655)(454,654)(455,653)(456,665)
(457,664)(458,676)(459,675)(460,674)(461,673)(462,672)(463,671)(464,670)
(465,669)(466,668)(467,667)(468,666)(469,678)(470,677)(471,689)(472,688)
(473,687)(474,686)(475,685)(476,684)(477,683)(478,682)(479,681)(480,680)
(481,679)(482,691)(483,690)(484,702)(485,701)(486,700)(487,699)(488,698)
(489,697)(490,696)(491,695)(492,694)(493,693)(494,692)(495,704)(496,703)
(497,715)(498,714)(499,713)(500,712)(501,711)(502,710)(503,709)(504,708)
(505,707)(506,706)(507,705)(508,717)(509,716)(510,728)(511,727)(512,726)
(513,725)(514,724)(515,723)(516,722)(517,721)(518,720)(519,719)(520,718)
(521,730)(522,729)(523,741)(524,740)(525,739)(526,738)(527,737)(528,736)
(529,735)(530,734)(531,733)(532,732)(533,731)(534,743)(535,742)(536,754)
(537,753)(538,752)(539,751)(540,750)(541,749)(542,748)(543,747)(544,746)
(545,745)(546,744)(547,756)(548,755)(549,767)(550,766)(551,765)(552,764)
(553,763)(554,762)(555,761)(556,760)(557,759)(558,758)(559,757)(560,769)
(561,768)(562,780)(563,779)(564,778)(565,777)(566,776)(567,775)(568,774)
(569,773)(570,772)(571,771)(572,770)(573,782)(574,781)(575,793)(576,792)
(577,791)(578,790)(579,789)(580,788)(581,787)(582,786)(583,785)(584,784)
(585,783)(586,795)(587,794)(588,806)(589,805)(590,804)(591,803)(592,802)
(593,801)(594,800)(595,799)(596,798)(597,797)(598,796)(599,808)(600,807)
(601,819)(602,818)(603,817)(604,816)(605,815)(606,814)(607,813)(608,812)
(609,811)(610,810)(611,809)(612,821)(613,820)(614,832)(615,831)(616,830)
(617,829)(618,828)(619,827)(620,826)(621,825)(622,824)(623,823)(624,822);;
s3 := ( 1,521)( 2,522)( 3,523)( 4,524)( 5,525)( 6,526)( 7,527)( 8,528)
( 9,529)( 10,530)( 11,531)( 12,532)( 13,533)( 14,534)( 15,535)( 16,536)
( 17,537)( 18,538)( 19,539)( 20,540)( 21,541)( 22,542)( 23,543)( 24,544)
( 25,545)( 26,546)( 27,547)( 28,548)( 29,549)( 30,550)( 31,551)( 32,552)
( 33,553)( 34,554)( 35,555)( 36,556)( 37,557)( 38,558)( 39,559)( 40,560)
( 41,561)( 42,562)( 43,563)( 44,564)( 45,565)( 46,566)( 47,567)( 48,568)
( 49,569)( 50,570)( 51,571)( 52,572)( 53,573)( 54,574)( 55,575)( 56,576)
( 57,577)( 58,578)( 59,579)( 60,580)( 61,581)( 62,582)( 63,583)( 64,584)
( 65,585)( 66,586)( 67,587)( 68,588)( 69,589)( 70,590)( 71,591)( 72,592)
( 73,593)( 74,594)( 75,595)( 76,596)( 77,597)( 78,598)( 79,599)( 80,600)
( 81,601)( 82,602)( 83,603)( 84,604)( 85,605)( 86,606)( 87,607)( 88,608)
( 89,609)( 90,610)( 91,611)( 92,612)( 93,613)( 94,614)( 95,615)( 96,616)
( 97,617)( 98,618)( 99,619)(100,620)(101,621)(102,622)(103,623)(104,624)
(105,417)(106,418)(107,419)(108,420)(109,421)(110,422)(111,423)(112,424)
(113,425)(114,426)(115,427)(116,428)(117,429)(118,430)(119,431)(120,432)
(121,433)(122,434)(123,435)(124,436)(125,437)(126,438)(127,439)(128,440)
(129,441)(130,442)(131,443)(132,444)(133,445)(134,446)(135,447)(136,448)
(137,449)(138,450)(139,451)(140,452)(141,453)(142,454)(143,455)(144,456)
(145,457)(146,458)(147,459)(148,460)(149,461)(150,462)(151,463)(152,464)
(153,465)(154,466)(155,467)(156,468)(157,469)(158,470)(159,471)(160,472)
(161,473)(162,474)(163,475)(164,476)(165,477)(166,478)(167,479)(168,480)
(169,481)(170,482)(171,483)(172,484)(173,485)(174,486)(175,487)(176,488)
(177,489)(178,490)(179,491)(180,492)(181,493)(182,494)(183,495)(184,496)
(185,497)(186,498)(187,499)(188,500)(189,501)(190,502)(191,503)(192,504)
(193,505)(194,506)(195,507)(196,508)(197,509)(198,510)(199,511)(200,512)
(201,513)(202,514)(203,515)(204,516)(205,517)(206,518)(207,519)(208,520)
(209,742)(210,743)(211,744)(212,745)(213,746)(214,747)(215,748)(216,749)
(217,750)(218,751)(219,752)(220,753)(221,754)(222,729)(223,730)(224,731)
(225,732)(226,733)(227,734)(228,735)(229,736)(230,737)(231,738)(232,739)
(233,740)(234,741)(235,768)(236,769)(237,770)(238,771)(239,772)(240,773)
(241,774)(242,775)(243,776)(244,777)(245,778)(246,779)(247,780)(248,755)
(249,756)(250,757)(251,758)(252,759)(253,760)(254,761)(255,762)(256,763)
(257,764)(258,765)(259,766)(260,767)(261,794)(262,795)(263,796)(264,797)
(265,798)(266,799)(267,800)(268,801)(269,802)(270,803)(271,804)(272,805)
(273,806)(274,781)(275,782)(276,783)(277,784)(278,785)(279,786)(280,787)
(281,788)(282,789)(283,790)(284,791)(285,792)(286,793)(287,820)(288,821)
(289,822)(290,823)(291,824)(292,825)(293,826)(294,827)(295,828)(296,829)
(297,830)(298,831)(299,832)(300,807)(301,808)(302,809)(303,810)(304,811)
(305,812)(306,813)(307,814)(308,815)(309,816)(310,817)(311,818)(312,819)
(313,638)(314,639)(315,640)(316,641)(317,642)(318,643)(319,644)(320,645)
(321,646)(322,647)(323,648)(324,649)(325,650)(326,625)(327,626)(328,627)
(329,628)(330,629)(331,630)(332,631)(333,632)(334,633)(335,634)(336,635)
(337,636)(338,637)(339,664)(340,665)(341,666)(342,667)(343,668)(344,669)
(345,670)(346,671)(347,672)(348,673)(349,674)(350,675)(351,676)(352,651)
(353,652)(354,653)(355,654)(356,655)(357,656)(358,657)(359,658)(360,659)
(361,660)(362,661)(363,662)(364,663)(365,690)(366,691)(367,692)(368,693)
(369,694)(370,695)(371,696)(372,697)(373,698)(374,699)(375,700)(376,701)
(377,702)(378,677)(379,678)(380,679)(381,680)(382,681)(383,682)(384,683)
(385,684)(386,685)(387,686)(388,687)(389,688)(390,689)(391,716)(392,717)
(393,718)(394,719)(395,720)(396,721)(397,722)(398,723)(399,724)(400,725)
(401,726)(402,727)(403,728)(404,703)(405,704)(406,705)(407,706)(408,707)
(409,708)(410,709)(411,710)(412,711)(413,712)(414,713)(415,714)(416,715);;
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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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)!( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 15, 26)
( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 28, 39)( 29, 38)( 30, 37)
( 31, 36)( 32, 35)( 33, 34)( 41, 52)( 42, 51)( 43, 50)( 44, 49)( 45, 48)
( 46, 47)( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 67, 78)
( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 80, 91)( 81, 90)( 82, 89)
( 83, 88)( 84, 87)( 85, 86)( 93,104)( 94,103)( 95,102)( 96,101)( 97,100)
( 98, 99)(105,157)(106,169)(107,168)(108,167)(109,166)(110,165)(111,164)
(112,163)(113,162)(114,161)(115,160)(116,159)(117,158)(118,170)(119,182)
(120,181)(121,180)(122,179)(123,178)(124,177)(125,176)(126,175)(127,174)
(128,173)(129,172)(130,171)(131,183)(132,195)(133,194)(134,193)(135,192)
(136,191)(137,190)(138,189)(139,188)(140,187)(141,186)(142,185)(143,184)
(144,196)(145,208)(146,207)(147,206)(148,205)(149,204)(150,203)(151,202)
(152,201)(153,200)(154,199)(155,198)(156,197)(209,235)(210,247)(211,246)
(212,245)(213,244)(214,243)(215,242)(216,241)(217,240)(218,239)(219,238)
(220,237)(221,236)(222,248)(223,260)(224,259)(225,258)(226,257)(227,256)
(228,255)(229,254)(230,253)(231,252)(232,251)(233,250)(234,249)(261,287)
(262,299)(263,298)(264,297)(265,296)(266,295)(267,294)(268,293)(269,292)
(270,291)(271,290)(272,289)(273,288)(274,300)(275,312)(276,311)(277,310)
(278,309)(279,308)(280,307)(281,306)(282,305)(283,304)(284,303)(285,302)
(286,301)(313,391)(314,403)(315,402)(316,401)(317,400)(318,399)(319,398)
(320,397)(321,396)(322,395)(323,394)(324,393)(325,392)(326,404)(327,416)
(328,415)(329,414)(330,413)(331,412)(332,411)(333,410)(334,409)(335,408)
(336,407)(337,406)(338,405)(339,365)(340,377)(341,376)(342,375)(343,374)
(344,373)(345,372)(346,371)(347,370)(348,369)(349,368)(350,367)(351,366)
(352,378)(353,390)(354,389)(355,388)(356,387)(357,386)(358,385)(359,384)
(360,383)(361,382)(362,381)(363,380)(364,379)(417,469)(418,481)(419,480)
(420,479)(421,478)(422,477)(423,476)(424,475)(425,474)(426,473)(427,472)
(428,471)(429,470)(430,482)(431,494)(432,493)(433,492)(434,491)(435,490)
(436,489)(437,488)(438,487)(439,486)(440,485)(441,484)(442,483)(443,495)
(444,507)(445,506)(446,505)(447,504)(448,503)(449,502)(450,501)(451,500)
(452,499)(453,498)(454,497)(455,496)(456,508)(457,520)(458,519)(459,518)
(460,517)(461,516)(462,515)(463,514)(464,513)(465,512)(466,511)(467,510)
(468,509)(522,533)(523,532)(524,531)(525,530)(526,529)(527,528)(535,546)
(536,545)(537,544)(538,543)(539,542)(540,541)(548,559)(549,558)(550,557)
(551,556)(552,555)(553,554)(561,572)(562,571)(563,570)(564,569)(565,568)
(566,567)(574,585)(575,584)(576,583)(577,582)(578,581)(579,580)(587,598)
(588,597)(589,596)(590,595)(591,594)(592,593)(600,611)(601,610)(602,609)
(603,608)(604,607)(605,606)(613,624)(614,623)(615,622)(616,621)(617,620)
(618,619)(625,703)(626,715)(627,714)(628,713)(629,712)(630,711)(631,710)
(632,709)(633,708)(634,707)(635,706)(636,705)(637,704)(638,716)(639,728)
(640,727)(641,726)(642,725)(643,724)(644,723)(645,722)(646,721)(647,720)
(648,719)(649,718)(650,717)(651,677)(652,689)(653,688)(654,687)(655,686)
(656,685)(657,684)(658,683)(659,682)(660,681)(661,680)(662,679)(663,678)
(664,690)(665,702)(666,701)(667,700)(668,699)(669,698)(670,697)(671,696)
(672,695)(673,694)(674,693)(675,692)(676,691)(729,755)(730,767)(731,766)
(732,765)(733,764)(734,763)(735,762)(736,761)(737,760)(738,759)(739,758)
(740,757)(741,756)(742,768)(743,780)(744,779)(745,778)(746,777)(747,776)
(748,775)(749,774)(750,773)(751,772)(752,771)(753,770)(754,769)(781,807)
(782,819)(783,818)(784,817)(785,816)(786,815)(787,814)(788,813)(789,812)
(790,811)(791,810)(792,809)(793,808)(794,820)(795,832)(796,831)(797,830)
(798,829)(799,828)(800,827)(801,826)(802,825)(803,824)(804,823)(805,822)
(806,821);
s2 := Sym(832)!( 1,210)( 2,209)( 3,221)( 4,220)( 5,219)( 6,218)( 7,217)
( 8,216)( 9,215)( 10,214)( 11,213)( 12,212)( 13,211)( 14,223)( 15,222)
( 16,234)( 17,233)( 18,232)( 19,231)( 20,230)( 21,229)( 22,228)( 23,227)
( 24,226)( 25,225)( 26,224)( 27,236)( 28,235)( 29,247)( 30,246)( 31,245)
( 32,244)( 33,243)( 34,242)( 35,241)( 36,240)( 37,239)( 38,238)( 39,237)
( 40,249)( 41,248)( 42,260)( 43,259)( 44,258)( 45,257)( 46,256)( 47,255)
( 48,254)( 49,253)( 50,252)( 51,251)( 52,250)( 53,262)( 54,261)( 55,273)
( 56,272)( 57,271)( 58,270)( 59,269)( 60,268)( 61,267)( 62,266)( 63,265)
( 64,264)( 65,263)( 66,275)( 67,274)( 68,286)( 69,285)( 70,284)( 71,283)
( 72,282)( 73,281)( 74,280)( 75,279)( 76,278)( 77,277)( 78,276)( 79,288)
( 80,287)( 81,299)( 82,298)( 83,297)( 84,296)( 85,295)( 86,294)( 87,293)
( 88,292)( 89,291)( 90,290)( 91,289)( 92,301)( 93,300)( 94,312)( 95,311)
( 96,310)( 97,309)( 98,308)( 99,307)(100,306)(101,305)(102,304)(103,303)
(104,302)(105,314)(106,313)(107,325)(108,324)(109,323)(110,322)(111,321)
(112,320)(113,319)(114,318)(115,317)(116,316)(117,315)(118,327)(119,326)
(120,338)(121,337)(122,336)(123,335)(124,334)(125,333)(126,332)(127,331)
(128,330)(129,329)(130,328)(131,340)(132,339)(133,351)(134,350)(135,349)
(136,348)(137,347)(138,346)(139,345)(140,344)(141,343)(142,342)(143,341)
(144,353)(145,352)(146,364)(147,363)(148,362)(149,361)(150,360)(151,359)
(152,358)(153,357)(154,356)(155,355)(156,354)(157,366)(158,365)(159,377)
(160,376)(161,375)(162,374)(163,373)(164,372)(165,371)(166,370)(167,369)
(168,368)(169,367)(170,379)(171,378)(172,390)(173,389)(174,388)(175,387)
(176,386)(177,385)(178,384)(179,383)(180,382)(181,381)(182,380)(183,392)
(184,391)(185,403)(186,402)(187,401)(188,400)(189,399)(190,398)(191,397)
(192,396)(193,395)(194,394)(195,393)(196,405)(197,404)(198,416)(199,415)
(200,414)(201,413)(202,412)(203,411)(204,410)(205,409)(206,408)(207,407)
(208,406)(417,626)(418,625)(419,637)(420,636)(421,635)(422,634)(423,633)
(424,632)(425,631)(426,630)(427,629)(428,628)(429,627)(430,639)(431,638)
(432,650)(433,649)(434,648)(435,647)(436,646)(437,645)(438,644)(439,643)
(440,642)(441,641)(442,640)(443,652)(444,651)(445,663)(446,662)(447,661)
(448,660)(449,659)(450,658)(451,657)(452,656)(453,655)(454,654)(455,653)
(456,665)(457,664)(458,676)(459,675)(460,674)(461,673)(462,672)(463,671)
(464,670)(465,669)(466,668)(467,667)(468,666)(469,678)(470,677)(471,689)
(472,688)(473,687)(474,686)(475,685)(476,684)(477,683)(478,682)(479,681)
(480,680)(481,679)(482,691)(483,690)(484,702)(485,701)(486,700)(487,699)
(488,698)(489,697)(490,696)(491,695)(492,694)(493,693)(494,692)(495,704)
(496,703)(497,715)(498,714)(499,713)(500,712)(501,711)(502,710)(503,709)
(504,708)(505,707)(506,706)(507,705)(508,717)(509,716)(510,728)(511,727)
(512,726)(513,725)(514,724)(515,723)(516,722)(517,721)(518,720)(519,719)
(520,718)(521,730)(522,729)(523,741)(524,740)(525,739)(526,738)(527,737)
(528,736)(529,735)(530,734)(531,733)(532,732)(533,731)(534,743)(535,742)
(536,754)(537,753)(538,752)(539,751)(540,750)(541,749)(542,748)(543,747)
(544,746)(545,745)(546,744)(547,756)(548,755)(549,767)(550,766)(551,765)
(552,764)(553,763)(554,762)(555,761)(556,760)(557,759)(558,758)(559,757)
(560,769)(561,768)(562,780)(563,779)(564,778)(565,777)(566,776)(567,775)
(568,774)(569,773)(570,772)(571,771)(572,770)(573,782)(574,781)(575,793)
(576,792)(577,791)(578,790)(579,789)(580,788)(581,787)(582,786)(583,785)
(584,784)(585,783)(586,795)(587,794)(588,806)(589,805)(590,804)(591,803)
(592,802)(593,801)(594,800)(595,799)(596,798)(597,797)(598,796)(599,808)
(600,807)(601,819)(602,818)(603,817)(604,816)(605,815)(606,814)(607,813)
(608,812)(609,811)(610,810)(611,809)(612,821)(613,820)(614,832)(615,831)
(616,830)(617,829)(618,828)(619,827)(620,826)(621,825)(622,824)(623,823)
(624,822);
s3 := Sym(832)!( 1,521)( 2,522)( 3,523)( 4,524)( 5,525)( 6,526)( 7,527)
( 8,528)( 9,529)( 10,530)( 11,531)( 12,532)( 13,533)( 14,534)( 15,535)
( 16,536)( 17,537)( 18,538)( 19,539)( 20,540)( 21,541)( 22,542)( 23,543)
( 24,544)( 25,545)( 26,546)( 27,547)( 28,548)( 29,549)( 30,550)( 31,551)
( 32,552)( 33,553)( 34,554)( 35,555)( 36,556)( 37,557)( 38,558)( 39,559)
( 40,560)( 41,561)( 42,562)( 43,563)( 44,564)( 45,565)( 46,566)( 47,567)
( 48,568)( 49,569)( 50,570)( 51,571)( 52,572)( 53,573)( 54,574)( 55,575)
( 56,576)( 57,577)( 58,578)( 59,579)( 60,580)( 61,581)( 62,582)( 63,583)
( 64,584)( 65,585)( 66,586)( 67,587)( 68,588)( 69,589)( 70,590)( 71,591)
( 72,592)( 73,593)( 74,594)( 75,595)( 76,596)( 77,597)( 78,598)( 79,599)
( 80,600)( 81,601)( 82,602)( 83,603)( 84,604)( 85,605)( 86,606)( 87,607)
( 88,608)( 89,609)( 90,610)( 91,611)( 92,612)( 93,613)( 94,614)( 95,615)
( 96,616)( 97,617)( 98,618)( 99,619)(100,620)(101,621)(102,622)(103,623)
(104,624)(105,417)(106,418)(107,419)(108,420)(109,421)(110,422)(111,423)
(112,424)(113,425)(114,426)(115,427)(116,428)(117,429)(118,430)(119,431)
(120,432)(121,433)(122,434)(123,435)(124,436)(125,437)(126,438)(127,439)
(128,440)(129,441)(130,442)(131,443)(132,444)(133,445)(134,446)(135,447)
(136,448)(137,449)(138,450)(139,451)(140,452)(141,453)(142,454)(143,455)
(144,456)(145,457)(146,458)(147,459)(148,460)(149,461)(150,462)(151,463)
(152,464)(153,465)(154,466)(155,467)(156,468)(157,469)(158,470)(159,471)
(160,472)(161,473)(162,474)(163,475)(164,476)(165,477)(166,478)(167,479)
(168,480)(169,481)(170,482)(171,483)(172,484)(173,485)(174,486)(175,487)
(176,488)(177,489)(178,490)(179,491)(180,492)(181,493)(182,494)(183,495)
(184,496)(185,497)(186,498)(187,499)(188,500)(189,501)(190,502)(191,503)
(192,504)(193,505)(194,506)(195,507)(196,508)(197,509)(198,510)(199,511)
(200,512)(201,513)(202,514)(203,515)(204,516)(205,517)(206,518)(207,519)
(208,520)(209,742)(210,743)(211,744)(212,745)(213,746)(214,747)(215,748)
(216,749)(217,750)(218,751)(219,752)(220,753)(221,754)(222,729)(223,730)
(224,731)(225,732)(226,733)(227,734)(228,735)(229,736)(230,737)(231,738)
(232,739)(233,740)(234,741)(235,768)(236,769)(237,770)(238,771)(239,772)
(240,773)(241,774)(242,775)(243,776)(244,777)(245,778)(246,779)(247,780)
(248,755)(249,756)(250,757)(251,758)(252,759)(253,760)(254,761)(255,762)
(256,763)(257,764)(258,765)(259,766)(260,767)(261,794)(262,795)(263,796)
(264,797)(265,798)(266,799)(267,800)(268,801)(269,802)(270,803)(271,804)
(272,805)(273,806)(274,781)(275,782)(276,783)(277,784)(278,785)(279,786)
(280,787)(281,788)(282,789)(283,790)(284,791)(285,792)(286,793)(287,820)
(288,821)(289,822)(290,823)(291,824)(292,825)(293,826)(294,827)(295,828)
(296,829)(297,830)(298,831)(299,832)(300,807)(301,808)(302,809)(303,810)
(304,811)(305,812)(306,813)(307,814)(308,815)(309,816)(310,817)(311,818)
(312,819)(313,638)(314,639)(315,640)(316,641)(317,642)(318,643)(319,644)
(320,645)(321,646)(322,647)(323,648)(324,649)(325,650)(326,625)(327,626)
(328,627)(329,628)(330,629)(331,630)(332,631)(333,632)(334,633)(335,634)
(336,635)(337,636)(338,637)(339,664)(340,665)(341,666)(342,667)(343,668)
(344,669)(345,670)(346,671)(347,672)(348,673)(349,674)(350,675)(351,676)
(352,651)(353,652)(354,653)(355,654)(356,655)(357,656)(358,657)(359,658)
(360,659)(361,660)(362,661)(363,662)(364,663)(365,690)(366,691)(367,692)
(368,693)(369,694)(370,695)(371,696)(372,697)(373,698)(374,699)(375,700)
(376,701)(377,702)(378,677)(379,678)(380,679)(381,680)(382,681)(383,682)
(384,683)(385,684)(386,685)(387,686)(388,687)(389,688)(390,689)(391,716)
(392,717)(393,718)(394,719)(395,720)(396,721)(397,722)(398,723)(399,724)
(400,725)(401,726)(402,727)(403,728)(404,703)(405,704)(406,705)(407,706)
(408,707)(409,708)(410,709)(411,710)(412,711)(413,712)(414,713)(415,714)
(416,715);
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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope