Polytope of Type {4,4,56}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,56}*1792a
Also Known As : {{4,4|2},{4,56|2}}. if this polytope has another name.
Group : SmallGroup(1792,200568)
Rank : 4
Schlafli Type : {4,4,56}
Number of vertices, edges, etc : 4, 8, 112, 56
Order of s0s1s2s3 : 56
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 : {4,4,28}*896, {2,4,56}*896a, {4,2,56}*896
4-fold quotients : {2,4,28}*448, {4,2,28}*448, {4,4,14}*448, {2,2,56}*448
7-fold quotients : {4,4,8}*256a
8-fold quotients : {2,2,28}*224, {2,4,14}*224, {4,2,14}*224
14-fold quotients : {4,4,4}*128, {2,4,8}*128a, {4,2,8}*128
16-fold quotients : {4,2,7}*112, {2,2,14}*112
28-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64, {2,2,8}*64
32-fold quotients : {2,2,7}*56
56-fold quotients : {2,2,4}*32, {2,4,2}*32, {4,2,2}*32
112-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,561)( 2,562)( 3,563)( 4,564)( 5,565)( 6,566)( 7,567)( 8,568)
( 9,569)( 10,570)( 11,571)( 12,572)( 13,573)( 14,574)( 15,575)( 16,576)
( 17,577)( 18,578)( 19,579)( 20,580)( 21,581)( 22,582)( 23,583)( 24,584)
( 25,585)( 26,586)( 27,587)( 28,588)( 29,589)( 30,590)( 31,591)( 32,592)
( 33,593)( 34,594)( 35,595)( 36,596)( 37,597)( 38,598)( 39,599)( 40,600)
( 41,601)( 42,602)( 43,603)( 44,604)( 45,605)( 46,606)( 47,607)( 48,608)
( 49,609)( 50,610)( 51,611)( 52,612)( 53,613)( 54,614)( 55,615)( 56,616)
( 57,617)( 58,618)( 59,619)( 60,620)( 61,621)( 62,622)( 63,623)( 64,624)
( 65,625)( 66,626)( 67,627)( 68,628)( 69,629)( 70,630)( 71,631)( 72,632)
( 73,633)( 74,634)( 75,635)( 76,636)( 77,637)( 78,638)( 79,639)( 80,640)
( 81,641)( 82,642)( 83,643)( 84,644)( 85,645)( 86,646)( 87,647)( 88,648)
( 89,649)( 90,650)( 91,651)( 92,652)( 93,653)( 94,654)( 95,655)( 96,656)
( 97,657)( 98,658)( 99,659)(100,660)(101,661)(102,662)(103,663)(104,664)
(105,665)(106,666)(107,667)(108,668)(109,669)(110,670)(111,671)(112,672)
(113,449)(114,450)(115,451)(116,452)(117,453)(118,454)(119,455)(120,456)
(121,457)(122,458)(123,459)(124,460)(125,461)(126,462)(127,463)(128,464)
(129,465)(130,466)(131,467)(132,468)(133,469)(134,470)(135,471)(136,472)
(137,473)(138,474)(139,475)(140,476)(141,477)(142,478)(143,479)(144,480)
(145,481)(146,482)(147,483)(148,484)(149,485)(150,486)(151,487)(152,488)
(153,489)(154,490)(155,491)(156,492)(157,493)(158,494)(159,495)(160,496)
(161,497)(162,498)(163,499)(164,500)(165,501)(166,502)(167,503)(168,504)
(169,505)(170,506)(171,507)(172,508)(173,509)(174,510)(175,511)(176,512)
(177,513)(178,514)(179,515)(180,516)(181,517)(182,518)(183,519)(184,520)
(185,521)(186,522)(187,523)(188,524)(189,525)(190,526)(191,527)(192,528)
(193,529)(194,530)(195,531)(196,532)(197,533)(198,534)(199,535)(200,536)
(201,537)(202,538)(203,539)(204,540)(205,541)(206,542)(207,543)(208,544)
(209,545)(210,546)(211,547)(212,548)(213,549)(214,550)(215,551)(216,552)
(217,553)(218,554)(219,555)(220,556)(221,557)(222,558)(223,559)(224,560)
(225,799)(226,800)(227,801)(228,802)(229,803)(230,804)(231,805)(232,806)
(233,807)(234,808)(235,809)(236,810)(237,811)(238,812)(239,785)(240,786)
(241,787)(242,788)(243,789)(244,790)(245,791)(246,792)(247,793)(248,794)
(249,795)(250,796)(251,797)(252,798)(253,827)(254,828)(255,829)(256,830)
(257,831)(258,832)(259,833)(260,834)(261,835)(262,836)(263,837)(264,838)
(265,839)(266,840)(267,813)(268,814)(269,815)(270,816)(271,817)(272,818)
(273,819)(274,820)(275,821)(276,822)(277,823)(278,824)(279,825)(280,826)
(281,855)(282,856)(283,857)(284,858)(285,859)(286,860)(287,861)(288,862)
(289,863)(290,864)(291,865)(292,866)(293,867)(294,868)(295,841)(296,842)
(297,843)(298,844)(299,845)(300,846)(301,847)(302,848)(303,849)(304,850)
(305,851)(306,852)(307,853)(308,854)(309,883)(310,884)(311,885)(312,886)
(313,887)(314,888)(315,889)(316,890)(317,891)(318,892)(319,893)(320,894)
(321,895)(322,896)(323,869)(324,870)(325,871)(326,872)(327,873)(328,874)
(329,875)(330,876)(331,877)(332,878)(333,879)(334,880)(335,881)(336,882)
(337,687)(338,688)(339,689)(340,690)(341,691)(342,692)(343,693)(344,694)
(345,695)(346,696)(347,697)(348,698)(349,699)(350,700)(351,673)(352,674)
(353,675)(354,676)(355,677)(356,678)(357,679)(358,680)(359,681)(360,682)
(361,683)(362,684)(363,685)(364,686)(365,715)(366,716)(367,717)(368,718)
(369,719)(370,720)(371,721)(372,722)(373,723)(374,724)(375,725)(376,726)
(377,727)(378,728)(379,701)(380,702)(381,703)(382,704)(383,705)(384,706)
(385,707)(386,708)(387,709)(388,710)(389,711)(390,712)(391,713)(392,714)
(393,743)(394,744)(395,745)(396,746)(397,747)(398,748)(399,749)(400,750)
(401,751)(402,752)(403,753)(404,754)(405,755)(406,756)(407,729)(408,730)
(409,731)(410,732)(411,733)(412,734)(413,735)(414,736)(415,737)(416,738)
(417,739)(418,740)(419,741)(420,742)(421,771)(422,772)(423,773)(424,774)
(425,775)(426,776)(427,777)(428,778)(429,779)(430,780)(431,781)(432,782)
(433,783)(434,784)(435,757)(436,758)(437,759)(438,760)(439,761)(440,762)
(441,763)(442,764)(443,765)(444,766)(445,767)(446,768)(447,769)(448,770);;
s1 := ( 1,225)( 2,226)( 3,227)( 4,228)( 5,229)( 6,230)( 7,231)( 8,232)
( 9,233)( 10,234)( 11,235)( 12,236)( 13,237)( 14,238)( 15,239)( 16,240)
( 17,241)( 18,242)( 19,243)( 20,244)( 21,245)( 22,246)( 23,247)( 24,248)
( 25,249)( 26,250)( 27,251)( 28,252)( 29,253)( 30,254)( 31,255)( 32,256)
( 33,257)( 34,258)( 35,259)( 36,260)( 37,261)( 38,262)( 39,263)( 40,264)
( 41,265)( 42,266)( 43,267)( 44,268)( 45,269)( 46,270)( 47,271)( 48,272)
( 49,273)( 50,274)( 51,275)( 52,276)( 53,277)( 54,278)( 55,279)( 56,280)
( 57,281)( 58,282)( 59,283)( 60,284)( 61,285)( 62,286)( 63,287)( 64,288)
( 65,289)( 66,290)( 67,291)( 68,292)( 69,293)( 70,294)( 71,295)( 72,296)
( 73,297)( 74,298)( 75,299)( 76,300)( 77,301)( 78,302)( 79,303)( 80,304)
( 81,305)( 82,306)( 83,307)( 84,308)( 85,309)( 86,310)( 87,311)( 88,312)
( 89,313)( 90,314)( 91,315)( 92,316)( 93,317)( 94,318)( 95,319)( 96,320)
( 97,321)( 98,322)( 99,323)(100,324)(101,325)(102,326)(103,327)(104,328)
(105,329)(106,330)(107,331)(108,332)(109,333)(110,334)(111,335)(112,336)
(113,337)(114,338)(115,339)(116,340)(117,341)(118,342)(119,343)(120,344)
(121,345)(122,346)(123,347)(124,348)(125,349)(126,350)(127,351)(128,352)
(129,353)(130,354)(131,355)(132,356)(133,357)(134,358)(135,359)(136,360)
(137,361)(138,362)(139,363)(140,364)(141,365)(142,366)(143,367)(144,368)
(145,369)(146,370)(147,371)(148,372)(149,373)(150,374)(151,375)(152,376)
(153,377)(154,378)(155,379)(156,380)(157,381)(158,382)(159,383)(160,384)
(161,385)(162,386)(163,387)(164,388)(165,389)(166,390)(167,391)(168,392)
(169,393)(170,394)(171,395)(172,396)(173,397)(174,398)(175,399)(176,400)
(177,401)(178,402)(179,403)(180,404)(181,405)(182,406)(183,407)(184,408)
(185,409)(186,410)(187,411)(188,412)(189,413)(190,414)(191,415)(192,416)
(193,417)(194,418)(195,419)(196,420)(197,421)(198,422)(199,423)(200,424)
(201,425)(202,426)(203,427)(204,428)(205,429)(206,430)(207,431)(208,432)
(209,433)(210,434)(211,435)(212,436)(213,437)(214,438)(215,439)(216,440)
(217,441)(218,442)(219,443)(220,444)(221,445)(222,446)(223,447)(224,448)
(449,673)(450,674)(451,675)(452,676)(453,677)(454,678)(455,679)(456,680)
(457,681)(458,682)(459,683)(460,684)(461,685)(462,686)(463,687)(464,688)
(465,689)(466,690)(467,691)(468,692)(469,693)(470,694)(471,695)(472,696)
(473,697)(474,698)(475,699)(476,700)(477,701)(478,702)(479,703)(480,704)
(481,705)(482,706)(483,707)(484,708)(485,709)(486,710)(487,711)(488,712)
(489,713)(490,714)(491,715)(492,716)(493,717)(494,718)(495,719)(496,720)
(497,721)(498,722)(499,723)(500,724)(501,725)(502,726)(503,727)(504,728)
(505,729)(506,730)(507,731)(508,732)(509,733)(510,734)(511,735)(512,736)
(513,737)(514,738)(515,739)(516,740)(517,741)(518,742)(519,743)(520,744)
(521,745)(522,746)(523,747)(524,748)(525,749)(526,750)(527,751)(528,752)
(529,753)(530,754)(531,755)(532,756)(533,757)(534,758)(535,759)(536,760)
(537,761)(538,762)(539,763)(540,764)(541,765)(542,766)(543,767)(544,768)
(545,769)(546,770)(547,771)(548,772)(549,773)(550,774)(551,775)(552,776)
(553,777)(554,778)(555,779)(556,780)(557,781)(558,782)(559,783)(560,784)
(561,785)(562,786)(563,787)(564,788)(565,789)(566,790)(567,791)(568,792)
(569,793)(570,794)(571,795)(572,796)(573,797)(574,798)(575,799)(576,800)
(577,801)(578,802)(579,803)(580,804)(581,805)(582,806)(583,807)(584,808)
(585,809)(586,810)(587,811)(588,812)(589,813)(590,814)(591,815)(592,816)
(593,817)(594,818)(595,819)(596,820)(597,821)(598,822)(599,823)(600,824)
(601,825)(602,826)(603,827)(604,828)(605,829)(606,830)(607,831)(608,832)
(609,833)(610,834)(611,835)(612,836)(613,837)(614,838)(615,839)(616,840)
(617,841)(618,842)(619,843)(620,844)(621,845)(622,846)(623,847)(624,848)
(625,849)(626,850)(627,851)(628,852)(629,853)(630,854)(631,855)(632,856)
(633,857)(634,858)(635,859)(636,860)(637,861)(638,862)(639,863)(640,864)
(641,865)(642,866)(643,867)(644,868)(645,869)(646,870)(647,871)(648,872)
(649,873)(650,874)(651,875)(652,876)(653,877)(654,878)(655,879)(656,880)
(657,881)(658,882)(659,883)(660,884)(661,885)(662,886)(663,887)(664,888)
(665,889)(666,890)(667,891)(668,892)(669,893)(670,894)(671,895)(672,896);;
s2 := ( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 16, 21)( 17, 20)
( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)( 37, 42)
( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)( 53, 54)
( 57, 64)( 58, 70)( 59, 69)( 60, 68)( 61, 67)( 62, 66)( 63, 65)( 71, 78)
( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)( 85, 92)( 86, 98)
( 87, 97)( 88, 96)( 89, 95)( 90, 94)( 91, 93)( 99,106)(100,112)(101,111)
(102,110)(103,109)(104,108)(105,107)(113,169)(114,175)(115,174)(116,173)
(117,172)(118,171)(119,170)(120,176)(121,182)(122,181)(123,180)(124,179)
(125,178)(126,177)(127,183)(128,189)(129,188)(130,187)(131,186)(132,185)
(133,184)(134,190)(135,196)(136,195)(137,194)(138,193)(139,192)(140,191)
(141,197)(142,203)(143,202)(144,201)(145,200)(146,199)(147,198)(148,204)
(149,210)(150,209)(151,208)(152,207)(153,206)(154,205)(155,211)(156,217)
(157,216)(158,215)(159,214)(160,213)(161,212)(162,218)(163,224)(164,223)
(165,222)(166,221)(167,220)(168,219)(225,253)(226,259)(227,258)(228,257)
(229,256)(230,255)(231,254)(232,260)(233,266)(234,265)(235,264)(236,263)
(237,262)(238,261)(239,267)(240,273)(241,272)(242,271)(243,270)(244,269)
(245,268)(246,274)(247,280)(248,279)(249,278)(250,277)(251,276)(252,275)
(281,316)(282,322)(283,321)(284,320)(285,319)(286,318)(287,317)(288,309)
(289,315)(290,314)(291,313)(292,312)(293,311)(294,310)(295,330)(296,336)
(297,335)(298,334)(299,333)(300,332)(301,331)(302,323)(303,329)(304,328)
(305,327)(306,326)(307,325)(308,324)(337,421)(338,427)(339,426)(340,425)
(341,424)(342,423)(343,422)(344,428)(345,434)(346,433)(347,432)(348,431)
(349,430)(350,429)(351,435)(352,441)(353,440)(354,439)(355,438)(356,437)
(357,436)(358,442)(359,448)(360,447)(361,446)(362,445)(363,444)(364,443)
(365,393)(366,399)(367,398)(368,397)(369,396)(370,395)(371,394)(372,400)
(373,406)(374,405)(375,404)(376,403)(377,402)(378,401)(379,407)(380,413)
(381,412)(382,411)(383,410)(384,409)(385,408)(386,414)(387,420)(388,419)
(389,418)(390,417)(391,416)(392,415)(449,505)(450,511)(451,510)(452,509)
(453,508)(454,507)(455,506)(456,512)(457,518)(458,517)(459,516)(460,515)
(461,514)(462,513)(463,519)(464,525)(465,524)(466,523)(467,522)(468,521)
(469,520)(470,526)(471,532)(472,531)(473,530)(474,529)(475,528)(476,527)
(477,533)(478,539)(479,538)(480,537)(481,536)(482,535)(483,534)(484,540)
(485,546)(486,545)(487,544)(488,543)(489,542)(490,541)(491,547)(492,553)
(493,552)(494,551)(495,550)(496,549)(497,548)(498,554)(499,560)(500,559)
(501,558)(502,557)(503,556)(504,555)(562,567)(563,566)(564,565)(569,574)
(570,573)(571,572)(576,581)(577,580)(578,579)(583,588)(584,587)(585,586)
(590,595)(591,594)(592,593)(597,602)(598,601)(599,600)(604,609)(605,608)
(606,607)(611,616)(612,615)(613,614)(617,624)(618,630)(619,629)(620,628)
(621,627)(622,626)(623,625)(631,638)(632,644)(633,643)(634,642)(635,641)
(636,640)(637,639)(645,652)(646,658)(647,657)(648,656)(649,655)(650,654)
(651,653)(659,666)(660,672)(661,671)(662,670)(663,669)(664,668)(665,667)
(673,757)(674,763)(675,762)(676,761)(677,760)(678,759)(679,758)(680,764)
(681,770)(682,769)(683,768)(684,767)(685,766)(686,765)(687,771)(688,777)
(689,776)(690,775)(691,774)(692,773)(693,772)(694,778)(695,784)(696,783)
(697,782)(698,781)(699,780)(700,779)(701,729)(702,735)(703,734)(704,733)
(705,732)(706,731)(707,730)(708,736)(709,742)(710,741)(711,740)(712,739)
(713,738)(714,737)(715,743)(716,749)(717,748)(718,747)(719,746)(720,745)
(721,744)(722,750)(723,756)(724,755)(725,754)(726,753)(727,752)(728,751)
(785,813)(786,819)(787,818)(788,817)(789,816)(790,815)(791,814)(792,820)
(793,826)(794,825)(795,824)(796,823)(797,822)(798,821)(799,827)(800,833)
(801,832)(802,831)(803,830)(804,829)(805,828)(806,834)(807,840)(808,839)
(809,838)(810,837)(811,836)(812,835)(841,876)(842,882)(843,881)(844,880)
(845,879)(846,878)(847,877)(848,869)(849,875)(850,874)(851,873)(852,872)
(853,871)(854,870)(855,890)(856,896)(857,895)(858,894)(859,893)(860,892)
(861,891)(862,883)(863,889)(864,888)(865,887)(866,886)(867,885)(868,884);;
s3 := ( 1,114)( 2,113)( 3,119)( 4,118)( 5,117)( 6,116)( 7,115)( 8,121)
( 9,120)( 10,126)( 11,125)( 12,124)( 13,123)( 14,122)( 15,128)( 16,127)
( 17,133)( 18,132)( 19,131)( 20,130)( 21,129)( 22,135)( 23,134)( 24,140)
( 25,139)( 26,138)( 27,137)( 28,136)( 29,142)( 30,141)( 31,147)( 32,146)
( 33,145)( 34,144)( 35,143)( 36,149)( 37,148)( 38,154)( 39,153)( 40,152)
( 41,151)( 42,150)( 43,156)( 44,155)( 45,161)( 46,160)( 47,159)( 48,158)
( 49,157)( 50,163)( 51,162)( 52,168)( 53,167)( 54,166)( 55,165)( 56,164)
( 57,177)( 58,176)( 59,182)( 60,181)( 61,180)( 62,179)( 63,178)( 64,170)
( 65,169)( 66,175)( 67,174)( 68,173)( 69,172)( 70,171)( 71,191)( 72,190)
( 73,196)( 74,195)( 75,194)( 76,193)( 77,192)( 78,184)( 79,183)( 80,189)
( 81,188)( 82,187)( 83,186)( 84,185)( 85,205)( 86,204)( 87,210)( 88,209)
( 89,208)( 90,207)( 91,206)( 92,198)( 93,197)( 94,203)( 95,202)( 96,201)
( 97,200)( 98,199)( 99,219)(100,218)(101,224)(102,223)(103,222)(104,221)
(105,220)(106,212)(107,211)(108,217)(109,216)(110,215)(111,214)(112,213)
(225,338)(226,337)(227,343)(228,342)(229,341)(230,340)(231,339)(232,345)
(233,344)(234,350)(235,349)(236,348)(237,347)(238,346)(239,352)(240,351)
(241,357)(242,356)(243,355)(244,354)(245,353)(246,359)(247,358)(248,364)
(249,363)(250,362)(251,361)(252,360)(253,366)(254,365)(255,371)(256,370)
(257,369)(258,368)(259,367)(260,373)(261,372)(262,378)(263,377)(264,376)
(265,375)(266,374)(267,380)(268,379)(269,385)(270,384)(271,383)(272,382)
(273,381)(274,387)(275,386)(276,392)(277,391)(278,390)(279,389)(280,388)
(281,401)(282,400)(283,406)(284,405)(285,404)(286,403)(287,402)(288,394)
(289,393)(290,399)(291,398)(292,397)(293,396)(294,395)(295,415)(296,414)
(297,420)(298,419)(299,418)(300,417)(301,416)(302,408)(303,407)(304,413)
(305,412)(306,411)(307,410)(308,409)(309,429)(310,428)(311,434)(312,433)
(313,432)(314,431)(315,430)(316,422)(317,421)(318,427)(319,426)(320,425)
(321,424)(322,423)(323,443)(324,442)(325,448)(326,447)(327,446)(328,445)
(329,444)(330,436)(331,435)(332,441)(333,440)(334,439)(335,438)(336,437)
(449,562)(450,561)(451,567)(452,566)(453,565)(454,564)(455,563)(456,569)
(457,568)(458,574)(459,573)(460,572)(461,571)(462,570)(463,576)(464,575)
(465,581)(466,580)(467,579)(468,578)(469,577)(470,583)(471,582)(472,588)
(473,587)(474,586)(475,585)(476,584)(477,590)(478,589)(479,595)(480,594)
(481,593)(482,592)(483,591)(484,597)(485,596)(486,602)(487,601)(488,600)
(489,599)(490,598)(491,604)(492,603)(493,609)(494,608)(495,607)(496,606)
(497,605)(498,611)(499,610)(500,616)(501,615)(502,614)(503,613)(504,612)
(505,625)(506,624)(507,630)(508,629)(509,628)(510,627)(511,626)(512,618)
(513,617)(514,623)(515,622)(516,621)(517,620)(518,619)(519,639)(520,638)
(521,644)(522,643)(523,642)(524,641)(525,640)(526,632)(527,631)(528,637)
(529,636)(530,635)(531,634)(532,633)(533,653)(534,652)(535,658)(536,657)
(537,656)(538,655)(539,654)(540,646)(541,645)(542,651)(543,650)(544,649)
(545,648)(546,647)(547,667)(548,666)(549,672)(550,671)(551,670)(552,669)
(553,668)(554,660)(555,659)(556,665)(557,664)(558,663)(559,662)(560,661)
(673,786)(674,785)(675,791)(676,790)(677,789)(678,788)(679,787)(680,793)
(681,792)(682,798)(683,797)(684,796)(685,795)(686,794)(687,800)(688,799)
(689,805)(690,804)(691,803)(692,802)(693,801)(694,807)(695,806)(696,812)
(697,811)(698,810)(699,809)(700,808)(701,814)(702,813)(703,819)(704,818)
(705,817)(706,816)(707,815)(708,821)(709,820)(710,826)(711,825)(712,824)
(713,823)(714,822)(715,828)(716,827)(717,833)(718,832)(719,831)(720,830)
(721,829)(722,835)(723,834)(724,840)(725,839)(726,838)(727,837)(728,836)
(729,849)(730,848)(731,854)(732,853)(733,852)(734,851)(735,850)(736,842)
(737,841)(738,847)(739,846)(740,845)(741,844)(742,843)(743,863)(744,862)
(745,868)(746,867)(747,866)(748,865)(749,864)(750,856)(751,855)(752,861)
(753,860)(754,859)(755,858)(756,857)(757,877)(758,876)(759,882)(760,881)
(761,880)(762,879)(763,878)(764,870)(765,869)(766,875)(767,874)(768,873)
(769,872)(770,871)(771,891)(772,890)(773,896)(774,895)(775,894)(776,893)
(777,892)(778,884)(779,883)(780,889)(781,888)(782,887)(783,886)(784,885);;
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*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(896)!( 1,561)( 2,562)( 3,563)( 4,564)( 5,565)( 6,566)( 7,567)
( 8,568)( 9,569)( 10,570)( 11,571)( 12,572)( 13,573)( 14,574)( 15,575)
( 16,576)( 17,577)( 18,578)( 19,579)( 20,580)( 21,581)( 22,582)( 23,583)
( 24,584)( 25,585)( 26,586)( 27,587)( 28,588)( 29,589)( 30,590)( 31,591)
( 32,592)( 33,593)( 34,594)( 35,595)( 36,596)( 37,597)( 38,598)( 39,599)
( 40,600)( 41,601)( 42,602)( 43,603)( 44,604)( 45,605)( 46,606)( 47,607)
( 48,608)( 49,609)( 50,610)( 51,611)( 52,612)( 53,613)( 54,614)( 55,615)
( 56,616)( 57,617)( 58,618)( 59,619)( 60,620)( 61,621)( 62,622)( 63,623)
( 64,624)( 65,625)( 66,626)( 67,627)( 68,628)( 69,629)( 70,630)( 71,631)
( 72,632)( 73,633)( 74,634)( 75,635)( 76,636)( 77,637)( 78,638)( 79,639)
( 80,640)( 81,641)( 82,642)( 83,643)( 84,644)( 85,645)( 86,646)( 87,647)
( 88,648)( 89,649)( 90,650)( 91,651)( 92,652)( 93,653)( 94,654)( 95,655)
( 96,656)( 97,657)( 98,658)( 99,659)(100,660)(101,661)(102,662)(103,663)
(104,664)(105,665)(106,666)(107,667)(108,668)(109,669)(110,670)(111,671)
(112,672)(113,449)(114,450)(115,451)(116,452)(117,453)(118,454)(119,455)
(120,456)(121,457)(122,458)(123,459)(124,460)(125,461)(126,462)(127,463)
(128,464)(129,465)(130,466)(131,467)(132,468)(133,469)(134,470)(135,471)
(136,472)(137,473)(138,474)(139,475)(140,476)(141,477)(142,478)(143,479)
(144,480)(145,481)(146,482)(147,483)(148,484)(149,485)(150,486)(151,487)
(152,488)(153,489)(154,490)(155,491)(156,492)(157,493)(158,494)(159,495)
(160,496)(161,497)(162,498)(163,499)(164,500)(165,501)(166,502)(167,503)
(168,504)(169,505)(170,506)(171,507)(172,508)(173,509)(174,510)(175,511)
(176,512)(177,513)(178,514)(179,515)(180,516)(181,517)(182,518)(183,519)
(184,520)(185,521)(186,522)(187,523)(188,524)(189,525)(190,526)(191,527)
(192,528)(193,529)(194,530)(195,531)(196,532)(197,533)(198,534)(199,535)
(200,536)(201,537)(202,538)(203,539)(204,540)(205,541)(206,542)(207,543)
(208,544)(209,545)(210,546)(211,547)(212,548)(213,549)(214,550)(215,551)
(216,552)(217,553)(218,554)(219,555)(220,556)(221,557)(222,558)(223,559)
(224,560)(225,799)(226,800)(227,801)(228,802)(229,803)(230,804)(231,805)
(232,806)(233,807)(234,808)(235,809)(236,810)(237,811)(238,812)(239,785)
(240,786)(241,787)(242,788)(243,789)(244,790)(245,791)(246,792)(247,793)
(248,794)(249,795)(250,796)(251,797)(252,798)(253,827)(254,828)(255,829)
(256,830)(257,831)(258,832)(259,833)(260,834)(261,835)(262,836)(263,837)
(264,838)(265,839)(266,840)(267,813)(268,814)(269,815)(270,816)(271,817)
(272,818)(273,819)(274,820)(275,821)(276,822)(277,823)(278,824)(279,825)
(280,826)(281,855)(282,856)(283,857)(284,858)(285,859)(286,860)(287,861)
(288,862)(289,863)(290,864)(291,865)(292,866)(293,867)(294,868)(295,841)
(296,842)(297,843)(298,844)(299,845)(300,846)(301,847)(302,848)(303,849)
(304,850)(305,851)(306,852)(307,853)(308,854)(309,883)(310,884)(311,885)
(312,886)(313,887)(314,888)(315,889)(316,890)(317,891)(318,892)(319,893)
(320,894)(321,895)(322,896)(323,869)(324,870)(325,871)(326,872)(327,873)
(328,874)(329,875)(330,876)(331,877)(332,878)(333,879)(334,880)(335,881)
(336,882)(337,687)(338,688)(339,689)(340,690)(341,691)(342,692)(343,693)
(344,694)(345,695)(346,696)(347,697)(348,698)(349,699)(350,700)(351,673)
(352,674)(353,675)(354,676)(355,677)(356,678)(357,679)(358,680)(359,681)
(360,682)(361,683)(362,684)(363,685)(364,686)(365,715)(366,716)(367,717)
(368,718)(369,719)(370,720)(371,721)(372,722)(373,723)(374,724)(375,725)
(376,726)(377,727)(378,728)(379,701)(380,702)(381,703)(382,704)(383,705)
(384,706)(385,707)(386,708)(387,709)(388,710)(389,711)(390,712)(391,713)
(392,714)(393,743)(394,744)(395,745)(396,746)(397,747)(398,748)(399,749)
(400,750)(401,751)(402,752)(403,753)(404,754)(405,755)(406,756)(407,729)
(408,730)(409,731)(410,732)(411,733)(412,734)(413,735)(414,736)(415,737)
(416,738)(417,739)(418,740)(419,741)(420,742)(421,771)(422,772)(423,773)
(424,774)(425,775)(426,776)(427,777)(428,778)(429,779)(430,780)(431,781)
(432,782)(433,783)(434,784)(435,757)(436,758)(437,759)(438,760)(439,761)
(440,762)(441,763)(442,764)(443,765)(444,766)(445,767)(446,768)(447,769)
(448,770);
s1 := Sym(896)!( 1,225)( 2,226)( 3,227)( 4,228)( 5,229)( 6,230)( 7,231)
( 8,232)( 9,233)( 10,234)( 11,235)( 12,236)( 13,237)( 14,238)( 15,239)
( 16,240)( 17,241)( 18,242)( 19,243)( 20,244)( 21,245)( 22,246)( 23,247)
( 24,248)( 25,249)( 26,250)( 27,251)( 28,252)( 29,253)( 30,254)( 31,255)
( 32,256)( 33,257)( 34,258)( 35,259)( 36,260)( 37,261)( 38,262)( 39,263)
( 40,264)( 41,265)( 42,266)( 43,267)( 44,268)( 45,269)( 46,270)( 47,271)
( 48,272)( 49,273)( 50,274)( 51,275)( 52,276)( 53,277)( 54,278)( 55,279)
( 56,280)( 57,281)( 58,282)( 59,283)( 60,284)( 61,285)( 62,286)( 63,287)
( 64,288)( 65,289)( 66,290)( 67,291)( 68,292)( 69,293)( 70,294)( 71,295)
( 72,296)( 73,297)( 74,298)( 75,299)( 76,300)( 77,301)( 78,302)( 79,303)
( 80,304)( 81,305)( 82,306)( 83,307)( 84,308)( 85,309)( 86,310)( 87,311)
( 88,312)( 89,313)( 90,314)( 91,315)( 92,316)( 93,317)( 94,318)( 95,319)
( 96,320)( 97,321)( 98,322)( 99,323)(100,324)(101,325)(102,326)(103,327)
(104,328)(105,329)(106,330)(107,331)(108,332)(109,333)(110,334)(111,335)
(112,336)(113,337)(114,338)(115,339)(116,340)(117,341)(118,342)(119,343)
(120,344)(121,345)(122,346)(123,347)(124,348)(125,349)(126,350)(127,351)
(128,352)(129,353)(130,354)(131,355)(132,356)(133,357)(134,358)(135,359)
(136,360)(137,361)(138,362)(139,363)(140,364)(141,365)(142,366)(143,367)
(144,368)(145,369)(146,370)(147,371)(148,372)(149,373)(150,374)(151,375)
(152,376)(153,377)(154,378)(155,379)(156,380)(157,381)(158,382)(159,383)
(160,384)(161,385)(162,386)(163,387)(164,388)(165,389)(166,390)(167,391)
(168,392)(169,393)(170,394)(171,395)(172,396)(173,397)(174,398)(175,399)
(176,400)(177,401)(178,402)(179,403)(180,404)(181,405)(182,406)(183,407)
(184,408)(185,409)(186,410)(187,411)(188,412)(189,413)(190,414)(191,415)
(192,416)(193,417)(194,418)(195,419)(196,420)(197,421)(198,422)(199,423)
(200,424)(201,425)(202,426)(203,427)(204,428)(205,429)(206,430)(207,431)
(208,432)(209,433)(210,434)(211,435)(212,436)(213,437)(214,438)(215,439)
(216,440)(217,441)(218,442)(219,443)(220,444)(221,445)(222,446)(223,447)
(224,448)(449,673)(450,674)(451,675)(452,676)(453,677)(454,678)(455,679)
(456,680)(457,681)(458,682)(459,683)(460,684)(461,685)(462,686)(463,687)
(464,688)(465,689)(466,690)(467,691)(468,692)(469,693)(470,694)(471,695)
(472,696)(473,697)(474,698)(475,699)(476,700)(477,701)(478,702)(479,703)
(480,704)(481,705)(482,706)(483,707)(484,708)(485,709)(486,710)(487,711)
(488,712)(489,713)(490,714)(491,715)(492,716)(493,717)(494,718)(495,719)
(496,720)(497,721)(498,722)(499,723)(500,724)(501,725)(502,726)(503,727)
(504,728)(505,729)(506,730)(507,731)(508,732)(509,733)(510,734)(511,735)
(512,736)(513,737)(514,738)(515,739)(516,740)(517,741)(518,742)(519,743)
(520,744)(521,745)(522,746)(523,747)(524,748)(525,749)(526,750)(527,751)
(528,752)(529,753)(530,754)(531,755)(532,756)(533,757)(534,758)(535,759)
(536,760)(537,761)(538,762)(539,763)(540,764)(541,765)(542,766)(543,767)
(544,768)(545,769)(546,770)(547,771)(548,772)(549,773)(550,774)(551,775)
(552,776)(553,777)(554,778)(555,779)(556,780)(557,781)(558,782)(559,783)
(560,784)(561,785)(562,786)(563,787)(564,788)(565,789)(566,790)(567,791)
(568,792)(569,793)(570,794)(571,795)(572,796)(573,797)(574,798)(575,799)
(576,800)(577,801)(578,802)(579,803)(580,804)(581,805)(582,806)(583,807)
(584,808)(585,809)(586,810)(587,811)(588,812)(589,813)(590,814)(591,815)
(592,816)(593,817)(594,818)(595,819)(596,820)(597,821)(598,822)(599,823)
(600,824)(601,825)(602,826)(603,827)(604,828)(605,829)(606,830)(607,831)
(608,832)(609,833)(610,834)(611,835)(612,836)(613,837)(614,838)(615,839)
(616,840)(617,841)(618,842)(619,843)(620,844)(621,845)(622,846)(623,847)
(624,848)(625,849)(626,850)(627,851)(628,852)(629,853)(630,854)(631,855)
(632,856)(633,857)(634,858)(635,859)(636,860)(637,861)(638,862)(639,863)
(640,864)(641,865)(642,866)(643,867)(644,868)(645,869)(646,870)(647,871)
(648,872)(649,873)(650,874)(651,875)(652,876)(653,877)(654,878)(655,879)
(656,880)(657,881)(658,882)(659,883)(660,884)(661,885)(662,886)(663,887)
(664,888)(665,889)(666,890)(667,891)(668,892)(669,893)(670,894)(671,895)
(672,896);
s2 := Sym(896)!( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 16, 21)
( 17, 20)( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)
( 37, 42)( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)
( 53, 54)( 57, 64)( 58, 70)( 59, 69)( 60, 68)( 61, 67)( 62, 66)( 63, 65)
( 71, 78)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)( 85, 92)
( 86, 98)( 87, 97)( 88, 96)( 89, 95)( 90, 94)( 91, 93)( 99,106)(100,112)
(101,111)(102,110)(103,109)(104,108)(105,107)(113,169)(114,175)(115,174)
(116,173)(117,172)(118,171)(119,170)(120,176)(121,182)(122,181)(123,180)
(124,179)(125,178)(126,177)(127,183)(128,189)(129,188)(130,187)(131,186)
(132,185)(133,184)(134,190)(135,196)(136,195)(137,194)(138,193)(139,192)
(140,191)(141,197)(142,203)(143,202)(144,201)(145,200)(146,199)(147,198)
(148,204)(149,210)(150,209)(151,208)(152,207)(153,206)(154,205)(155,211)
(156,217)(157,216)(158,215)(159,214)(160,213)(161,212)(162,218)(163,224)
(164,223)(165,222)(166,221)(167,220)(168,219)(225,253)(226,259)(227,258)
(228,257)(229,256)(230,255)(231,254)(232,260)(233,266)(234,265)(235,264)
(236,263)(237,262)(238,261)(239,267)(240,273)(241,272)(242,271)(243,270)
(244,269)(245,268)(246,274)(247,280)(248,279)(249,278)(250,277)(251,276)
(252,275)(281,316)(282,322)(283,321)(284,320)(285,319)(286,318)(287,317)
(288,309)(289,315)(290,314)(291,313)(292,312)(293,311)(294,310)(295,330)
(296,336)(297,335)(298,334)(299,333)(300,332)(301,331)(302,323)(303,329)
(304,328)(305,327)(306,326)(307,325)(308,324)(337,421)(338,427)(339,426)
(340,425)(341,424)(342,423)(343,422)(344,428)(345,434)(346,433)(347,432)
(348,431)(349,430)(350,429)(351,435)(352,441)(353,440)(354,439)(355,438)
(356,437)(357,436)(358,442)(359,448)(360,447)(361,446)(362,445)(363,444)
(364,443)(365,393)(366,399)(367,398)(368,397)(369,396)(370,395)(371,394)
(372,400)(373,406)(374,405)(375,404)(376,403)(377,402)(378,401)(379,407)
(380,413)(381,412)(382,411)(383,410)(384,409)(385,408)(386,414)(387,420)
(388,419)(389,418)(390,417)(391,416)(392,415)(449,505)(450,511)(451,510)
(452,509)(453,508)(454,507)(455,506)(456,512)(457,518)(458,517)(459,516)
(460,515)(461,514)(462,513)(463,519)(464,525)(465,524)(466,523)(467,522)
(468,521)(469,520)(470,526)(471,532)(472,531)(473,530)(474,529)(475,528)
(476,527)(477,533)(478,539)(479,538)(480,537)(481,536)(482,535)(483,534)
(484,540)(485,546)(486,545)(487,544)(488,543)(489,542)(490,541)(491,547)
(492,553)(493,552)(494,551)(495,550)(496,549)(497,548)(498,554)(499,560)
(500,559)(501,558)(502,557)(503,556)(504,555)(562,567)(563,566)(564,565)
(569,574)(570,573)(571,572)(576,581)(577,580)(578,579)(583,588)(584,587)
(585,586)(590,595)(591,594)(592,593)(597,602)(598,601)(599,600)(604,609)
(605,608)(606,607)(611,616)(612,615)(613,614)(617,624)(618,630)(619,629)
(620,628)(621,627)(622,626)(623,625)(631,638)(632,644)(633,643)(634,642)
(635,641)(636,640)(637,639)(645,652)(646,658)(647,657)(648,656)(649,655)
(650,654)(651,653)(659,666)(660,672)(661,671)(662,670)(663,669)(664,668)
(665,667)(673,757)(674,763)(675,762)(676,761)(677,760)(678,759)(679,758)
(680,764)(681,770)(682,769)(683,768)(684,767)(685,766)(686,765)(687,771)
(688,777)(689,776)(690,775)(691,774)(692,773)(693,772)(694,778)(695,784)
(696,783)(697,782)(698,781)(699,780)(700,779)(701,729)(702,735)(703,734)
(704,733)(705,732)(706,731)(707,730)(708,736)(709,742)(710,741)(711,740)
(712,739)(713,738)(714,737)(715,743)(716,749)(717,748)(718,747)(719,746)
(720,745)(721,744)(722,750)(723,756)(724,755)(725,754)(726,753)(727,752)
(728,751)(785,813)(786,819)(787,818)(788,817)(789,816)(790,815)(791,814)
(792,820)(793,826)(794,825)(795,824)(796,823)(797,822)(798,821)(799,827)
(800,833)(801,832)(802,831)(803,830)(804,829)(805,828)(806,834)(807,840)
(808,839)(809,838)(810,837)(811,836)(812,835)(841,876)(842,882)(843,881)
(844,880)(845,879)(846,878)(847,877)(848,869)(849,875)(850,874)(851,873)
(852,872)(853,871)(854,870)(855,890)(856,896)(857,895)(858,894)(859,893)
(860,892)(861,891)(862,883)(863,889)(864,888)(865,887)(866,886)(867,885)
(868,884);
s3 := Sym(896)!( 1,114)( 2,113)( 3,119)( 4,118)( 5,117)( 6,116)( 7,115)
( 8,121)( 9,120)( 10,126)( 11,125)( 12,124)( 13,123)( 14,122)( 15,128)
( 16,127)( 17,133)( 18,132)( 19,131)( 20,130)( 21,129)( 22,135)( 23,134)
( 24,140)( 25,139)( 26,138)( 27,137)( 28,136)( 29,142)( 30,141)( 31,147)
( 32,146)( 33,145)( 34,144)( 35,143)( 36,149)( 37,148)( 38,154)( 39,153)
( 40,152)( 41,151)( 42,150)( 43,156)( 44,155)( 45,161)( 46,160)( 47,159)
( 48,158)( 49,157)( 50,163)( 51,162)( 52,168)( 53,167)( 54,166)( 55,165)
( 56,164)( 57,177)( 58,176)( 59,182)( 60,181)( 61,180)( 62,179)( 63,178)
( 64,170)( 65,169)( 66,175)( 67,174)( 68,173)( 69,172)( 70,171)( 71,191)
( 72,190)( 73,196)( 74,195)( 75,194)( 76,193)( 77,192)( 78,184)( 79,183)
( 80,189)( 81,188)( 82,187)( 83,186)( 84,185)( 85,205)( 86,204)( 87,210)
( 88,209)( 89,208)( 90,207)( 91,206)( 92,198)( 93,197)( 94,203)( 95,202)
( 96,201)( 97,200)( 98,199)( 99,219)(100,218)(101,224)(102,223)(103,222)
(104,221)(105,220)(106,212)(107,211)(108,217)(109,216)(110,215)(111,214)
(112,213)(225,338)(226,337)(227,343)(228,342)(229,341)(230,340)(231,339)
(232,345)(233,344)(234,350)(235,349)(236,348)(237,347)(238,346)(239,352)
(240,351)(241,357)(242,356)(243,355)(244,354)(245,353)(246,359)(247,358)
(248,364)(249,363)(250,362)(251,361)(252,360)(253,366)(254,365)(255,371)
(256,370)(257,369)(258,368)(259,367)(260,373)(261,372)(262,378)(263,377)
(264,376)(265,375)(266,374)(267,380)(268,379)(269,385)(270,384)(271,383)
(272,382)(273,381)(274,387)(275,386)(276,392)(277,391)(278,390)(279,389)
(280,388)(281,401)(282,400)(283,406)(284,405)(285,404)(286,403)(287,402)
(288,394)(289,393)(290,399)(291,398)(292,397)(293,396)(294,395)(295,415)
(296,414)(297,420)(298,419)(299,418)(300,417)(301,416)(302,408)(303,407)
(304,413)(305,412)(306,411)(307,410)(308,409)(309,429)(310,428)(311,434)
(312,433)(313,432)(314,431)(315,430)(316,422)(317,421)(318,427)(319,426)
(320,425)(321,424)(322,423)(323,443)(324,442)(325,448)(326,447)(327,446)
(328,445)(329,444)(330,436)(331,435)(332,441)(333,440)(334,439)(335,438)
(336,437)(449,562)(450,561)(451,567)(452,566)(453,565)(454,564)(455,563)
(456,569)(457,568)(458,574)(459,573)(460,572)(461,571)(462,570)(463,576)
(464,575)(465,581)(466,580)(467,579)(468,578)(469,577)(470,583)(471,582)
(472,588)(473,587)(474,586)(475,585)(476,584)(477,590)(478,589)(479,595)
(480,594)(481,593)(482,592)(483,591)(484,597)(485,596)(486,602)(487,601)
(488,600)(489,599)(490,598)(491,604)(492,603)(493,609)(494,608)(495,607)
(496,606)(497,605)(498,611)(499,610)(500,616)(501,615)(502,614)(503,613)
(504,612)(505,625)(506,624)(507,630)(508,629)(509,628)(510,627)(511,626)
(512,618)(513,617)(514,623)(515,622)(516,621)(517,620)(518,619)(519,639)
(520,638)(521,644)(522,643)(523,642)(524,641)(525,640)(526,632)(527,631)
(528,637)(529,636)(530,635)(531,634)(532,633)(533,653)(534,652)(535,658)
(536,657)(537,656)(538,655)(539,654)(540,646)(541,645)(542,651)(543,650)
(544,649)(545,648)(546,647)(547,667)(548,666)(549,672)(550,671)(551,670)
(552,669)(553,668)(554,660)(555,659)(556,665)(557,664)(558,663)(559,662)
(560,661)(673,786)(674,785)(675,791)(676,790)(677,789)(678,788)(679,787)
(680,793)(681,792)(682,798)(683,797)(684,796)(685,795)(686,794)(687,800)
(688,799)(689,805)(690,804)(691,803)(692,802)(693,801)(694,807)(695,806)
(696,812)(697,811)(698,810)(699,809)(700,808)(701,814)(702,813)(703,819)
(704,818)(705,817)(706,816)(707,815)(708,821)(709,820)(710,826)(711,825)
(712,824)(713,823)(714,822)(715,828)(716,827)(717,833)(718,832)(719,831)
(720,830)(721,829)(722,835)(723,834)(724,840)(725,839)(726,838)(727,837)
(728,836)(729,849)(730,848)(731,854)(732,853)(733,852)(734,851)(735,850)
(736,842)(737,841)(738,847)(739,846)(740,845)(741,844)(742,843)(743,863)
(744,862)(745,868)(746,867)(747,866)(748,865)(749,864)(750,856)(751,855)
(752,861)(753,860)(754,859)(755,858)(756,857)(757,877)(758,876)(759,882)
(760,881)(761,880)(762,879)(763,878)(764,870)(765,869)(766,875)(767,874)
(768,873)(769,872)(770,871)(771,891)(772,890)(773,896)(774,895)(775,894)
(776,893)(777,892)(778,884)(779,883)(780,889)(781,888)(782,887)(783,886)
(784,885);
poly := sub<Sym(896)|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*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope