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