Polytope of Type {4,56,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,56,4}*1792d
Also Known As : {{4,56|2},{56,4|2}}. if this polytope has another name.
Group : SmallGroup(1792,201310)
Rank : 4
Schlafli Type : {4,56,4}
Number of vertices, edges, etc : 4, 112, 112, 4
Order of s0s1s2s3 : 56
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 : {4,28,4}*896, {2,56,4}*896a, {4,56,2}*896a
4-fold quotients : {2,28,4}*448, {4,28,2}*448, {4,14,4}*448, {2,56,2}*448
7-fold quotients : {4,8,4}*256d
8-fold quotients : {2,28,2}*224, {2,14,4}*224, {4,14,2}*224
14-fold quotients : {4,4,4}*128, {2,8,4}*128a, {4,8,2}*128a
16-fold quotients : {2,14,2}*112
28-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64, {2,8,2}*64
32-fold quotients : {2,7,2}*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)( 2,114)( 3,115)( 4,116)( 5,117)( 6,118)( 7,119)( 8,120)
( 9,121)( 10,122)( 11,123)( 12,124)( 13,125)( 14,126)( 15,127)( 16,128)
( 17,129)( 18,130)( 19,131)( 20,132)( 21,133)( 22,134)( 23,135)( 24,136)
( 25,137)( 26,138)( 27,139)( 28,140)( 29,141)( 30,142)( 31,143)( 32,144)
( 33,145)( 34,146)( 35,147)( 36,148)( 37,149)( 38,150)( 39,151)( 40,152)
( 41,153)( 42,154)( 43,155)( 44,156)( 45,157)( 46,158)( 47,159)( 48,160)
( 49,161)( 50,162)( 51,163)( 52,164)( 53,165)( 54,166)( 55,167)( 56,168)
( 57,169)( 58,170)( 59,171)( 60,172)( 61,173)( 62,174)( 63,175)( 64,176)
( 65,177)( 66,178)( 67,179)( 68,180)( 69,181)( 70,182)( 71,183)( 72,184)
( 73,185)( 74,186)( 75,187)( 76,188)( 77,189)( 78,190)( 79,191)( 80,192)
( 81,193)( 82,194)( 83,195)( 84,196)( 85,197)( 86,198)( 87,199)( 88,200)
( 89,201)( 90,202)( 91,203)( 92,204)( 93,205)( 94,206)( 95,207)( 96,208)
( 97,209)( 98,210)( 99,211)(100,212)(101,213)(102,214)(103,215)(104,216)
(105,217)(106,218)(107,219)(108,220)(109,221)(110,222)(111,223)(112,224)
(225,337)(226,338)(227,339)(228,340)(229,341)(230,342)(231,343)(232,344)
(233,345)(234,346)(235,347)(236,348)(237,349)(238,350)(239,351)(240,352)
(241,353)(242,354)(243,355)(244,356)(245,357)(246,358)(247,359)(248,360)
(249,361)(250,362)(251,363)(252,364)(253,365)(254,366)(255,367)(256,368)
(257,369)(258,370)(259,371)(260,372)(261,373)(262,374)(263,375)(264,376)
(265,377)(266,378)(267,379)(268,380)(269,381)(270,382)(271,383)(272,384)
(273,385)(274,386)(275,387)(276,388)(277,389)(278,390)(279,391)(280,392)
(281,393)(282,394)(283,395)(284,396)(285,397)(286,398)(287,399)(288,400)
(289,401)(290,402)(291,403)(292,404)(293,405)(294,406)(295,407)(296,408)
(297,409)(298,410)(299,411)(300,412)(301,413)(302,414)(303,415)(304,416)
(305,417)(306,418)(307,419)(308,420)(309,421)(310,422)(311,423)(312,424)
(313,425)(314,426)(315,427)(316,428)(317,429)(318,430)(319,431)(320,432)
(321,433)(322,434)(323,435)(324,436)(325,437)(326,438)(327,439)(328,440)
(329,441)(330,442)(331,443)(332,444)(333,445)(334,446)(335,447)(336,448)
(449,561)(450,562)(451,563)(452,564)(453,565)(454,566)(455,567)(456,568)
(457,569)(458,570)(459,571)(460,572)(461,573)(462,574)(463,575)(464,576)
(465,577)(466,578)(467,579)(468,580)(469,581)(470,582)(471,583)(472,584)
(473,585)(474,586)(475,587)(476,588)(477,589)(478,590)(479,591)(480,592)
(481,593)(482,594)(483,595)(484,596)(485,597)(486,598)(487,599)(488,600)
(489,601)(490,602)(491,603)(492,604)(493,605)(494,606)(495,607)(496,608)
(497,609)(498,610)(499,611)(500,612)(501,613)(502,614)(503,615)(504,616)
(505,617)(506,618)(507,619)(508,620)(509,621)(510,622)(511,623)(512,624)
(513,625)(514,626)(515,627)(516,628)(517,629)(518,630)(519,631)(520,632)
(521,633)(522,634)(523,635)(524,636)(525,637)(526,638)(527,639)(528,640)
(529,641)(530,642)(531,643)(532,644)(533,645)(534,646)(535,647)(536,648)
(537,649)(538,650)(539,651)(540,652)(541,653)(542,654)(543,655)(544,656)
(545,657)(546,658)(547,659)(548,660)(549,661)(550,662)(551,663)(552,664)
(553,665)(554,666)(555,667)(556,668)(557,669)(558,670)(559,671)(560,672)
(673,785)(674,786)(675,787)(676,788)(677,789)(678,790)(679,791)(680,792)
(681,793)(682,794)(683,795)(684,796)(685,797)(686,798)(687,799)(688,800)
(689,801)(690,802)(691,803)(692,804)(693,805)(694,806)(695,807)(696,808)
(697,809)(698,810)(699,811)(700,812)(701,813)(702,814)(703,815)(704,816)
(705,817)(706,818)(707,819)(708,820)(709,821)(710,822)(711,823)(712,824)
(713,825)(714,826)(715,827)(716,828)(717,829)(718,830)(719,831)(720,832)
(721,833)(722,834)(723,835)(724,836)(725,837)(726,838)(727,839)(728,840)
(729,841)(730,842)(731,843)(732,844)(733,845)(734,846)(735,847)(736,848)
(737,849)(738,850)(739,851)(740,852)(741,853)(742,854)(743,855)(744,856)
(745,857)(746,858)(747,859)(748,860)(749,861)(750,862)(751,863)(752,864)
(753,865)(754,866)(755,867)(756,868)(757,869)(758,870)(759,871)(760,872)
(761,873)(762,874)(763,875)(764,876)(765,877)(766,878)(767,879)(768,880)
(769,881)(770,882)(771,883)(772,884)(773,885)(774,886)(775,887)(776,888)
(777,889)(778,890)(779,891)(780,892)(781,893)(782,894)(783,895)(784,896);;
s1 := ( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 16, 21)( 17, 20)
( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 29, 36)( 30, 42)( 31, 41)( 32, 40)
( 33, 39)( 34, 38)( 35, 37)( 43, 50)( 44, 56)( 45, 55)( 46, 54)( 47, 53)
( 48, 52)( 49, 51)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)
( 72, 77)( 73, 76)( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 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)
(141,204)(142,210)(143,209)(144,208)(145,207)(146,206)(147,205)(148,197)
(149,203)(150,202)(151,201)(152,200)(153,199)(154,198)(155,218)(156,224)
(157,223)(158,222)(159,221)(160,220)(161,219)(162,211)(163,217)(164,216)
(165,215)(166,214)(167,213)(168,212)(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)
(281,309)(282,315)(283,314)(284,313)(285,312)(286,311)(287,310)(288,316)
(289,322)(290,321)(291,320)(292,319)(293,318)(294,317)(295,323)(296,329)
(297,328)(298,327)(299,326)(300,325)(301,324)(302,330)(303,336)(304,335)
(305,334)(306,333)(307,332)(308,331)(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)
(477,540)(478,546)(479,545)(480,544)(481,543)(482,542)(483,541)(484,533)
(485,539)(486,538)(487,537)(488,536)(489,535)(490,534)(491,554)(492,560)
(493,559)(494,558)(495,557)(496,556)(497,555)(498,547)(499,553)(500,552)
(501,551)(502,550)(503,549)(504,548)(562,567)(563,566)(564,565)(569,574)
(570,573)(571,572)(576,581)(577,580)(578,579)(583,588)(584,587)(585,586)
(589,596)(590,602)(591,601)(592,600)(593,599)(594,598)(595,597)(603,610)
(604,616)(605,615)(606,614)(607,613)(608,612)(609,611)(618,623)(619,622)
(620,621)(625,630)(626,629)(627,628)(632,637)(633,636)(634,635)(639,644)
(640,643)(641,642)(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)(841,869)(842,875)(843,874)(844,873)
(845,872)(846,871)(847,870)(848,876)(849,882)(850,881)(851,880)(852,879)
(853,878)(854,877)(855,883)(856,889)(857,888)(858,887)(859,886)(860,885)
(861,884)(862,890)(863,896)(864,895)(865,894)(866,893)(867,892)(868,891);;
s2 := ( 1,226)( 2,225)( 3,231)( 4,230)( 5,229)( 6,228)( 7,227)( 8,233)
( 9,232)( 10,238)( 11,237)( 12,236)( 13,235)( 14,234)( 15,240)( 16,239)
( 17,245)( 18,244)( 19,243)( 20,242)( 21,241)( 22,247)( 23,246)( 24,252)
( 25,251)( 26,250)( 27,249)( 28,248)( 29,261)( 30,260)( 31,266)( 32,265)
( 33,264)( 34,263)( 35,262)( 36,254)( 37,253)( 38,259)( 39,258)( 40,257)
( 41,256)( 42,255)( 43,275)( 44,274)( 45,280)( 46,279)( 47,278)( 48,277)
( 49,276)( 50,268)( 51,267)( 52,273)( 53,272)( 54,271)( 55,270)( 56,269)
( 57,282)( 58,281)( 59,287)( 60,286)( 61,285)( 62,284)( 63,283)( 64,289)
( 65,288)( 66,294)( 67,293)( 68,292)( 69,291)( 70,290)( 71,296)( 72,295)
( 73,301)( 74,300)( 75,299)( 76,298)( 77,297)( 78,303)( 79,302)( 80,308)
( 81,307)( 82,306)( 83,305)( 84,304)( 85,317)( 86,316)( 87,322)( 88,321)
( 89,320)( 90,319)( 91,318)( 92,310)( 93,309)( 94,315)( 95,314)( 96,313)
( 97,312)( 98,311)( 99,331)(100,330)(101,336)(102,335)(103,334)(104,333)
(105,332)(106,324)(107,323)(108,329)(109,328)(110,327)(111,326)(112,325)
(113,338)(114,337)(115,343)(116,342)(117,341)(118,340)(119,339)(120,345)
(121,344)(122,350)(123,349)(124,348)(125,347)(126,346)(127,352)(128,351)
(129,357)(130,356)(131,355)(132,354)(133,353)(134,359)(135,358)(136,364)
(137,363)(138,362)(139,361)(140,360)(141,373)(142,372)(143,378)(144,377)
(145,376)(146,375)(147,374)(148,366)(149,365)(150,371)(151,370)(152,369)
(153,368)(154,367)(155,387)(156,386)(157,392)(158,391)(159,390)(160,389)
(161,388)(162,380)(163,379)(164,385)(165,384)(166,383)(167,382)(168,381)
(169,394)(170,393)(171,399)(172,398)(173,397)(174,396)(175,395)(176,401)
(177,400)(178,406)(179,405)(180,404)(181,403)(182,402)(183,408)(184,407)
(185,413)(186,412)(187,411)(188,410)(189,409)(190,415)(191,414)(192,420)
(193,419)(194,418)(195,417)(196,416)(197,429)(198,428)(199,434)(200,433)
(201,432)(202,431)(203,430)(204,422)(205,421)(206,427)(207,426)(208,425)
(209,424)(210,423)(211,443)(212,442)(213,448)(214,447)(215,446)(216,445)
(217,444)(218,436)(219,435)(220,441)(221,440)(222,439)(223,438)(224,437)
(449,674)(450,673)(451,679)(452,678)(453,677)(454,676)(455,675)(456,681)
(457,680)(458,686)(459,685)(460,684)(461,683)(462,682)(463,688)(464,687)
(465,693)(466,692)(467,691)(468,690)(469,689)(470,695)(471,694)(472,700)
(473,699)(474,698)(475,697)(476,696)(477,709)(478,708)(479,714)(480,713)
(481,712)(482,711)(483,710)(484,702)(485,701)(486,707)(487,706)(488,705)
(489,704)(490,703)(491,723)(492,722)(493,728)(494,727)(495,726)(496,725)
(497,724)(498,716)(499,715)(500,721)(501,720)(502,719)(503,718)(504,717)
(505,730)(506,729)(507,735)(508,734)(509,733)(510,732)(511,731)(512,737)
(513,736)(514,742)(515,741)(516,740)(517,739)(518,738)(519,744)(520,743)
(521,749)(522,748)(523,747)(524,746)(525,745)(526,751)(527,750)(528,756)
(529,755)(530,754)(531,753)(532,752)(533,765)(534,764)(535,770)(536,769)
(537,768)(538,767)(539,766)(540,758)(541,757)(542,763)(543,762)(544,761)
(545,760)(546,759)(547,779)(548,778)(549,784)(550,783)(551,782)(552,781)
(553,780)(554,772)(555,771)(556,777)(557,776)(558,775)(559,774)(560,773)
(561,786)(562,785)(563,791)(564,790)(565,789)(566,788)(567,787)(568,793)
(569,792)(570,798)(571,797)(572,796)(573,795)(574,794)(575,800)(576,799)
(577,805)(578,804)(579,803)(580,802)(581,801)(582,807)(583,806)(584,812)
(585,811)(586,810)(587,809)(588,808)(589,821)(590,820)(591,826)(592,825)
(593,824)(594,823)(595,822)(596,814)(597,813)(598,819)(599,818)(600,817)
(601,816)(602,815)(603,835)(604,834)(605,840)(606,839)(607,838)(608,837)
(609,836)(610,828)(611,827)(612,833)(613,832)(614,831)(615,830)(616,829)
(617,842)(618,841)(619,847)(620,846)(621,845)(622,844)(623,843)(624,849)
(625,848)(626,854)(627,853)(628,852)(629,851)(630,850)(631,856)(632,855)
(633,861)(634,860)(635,859)(636,858)(637,857)(638,863)(639,862)(640,868)
(641,867)(642,866)(643,865)(644,864)(645,877)(646,876)(647,882)(648,881)
(649,880)(650,879)(651,878)(652,870)(653,869)(654,875)(655,874)(656,873)
(657,872)(658,871)(659,891)(660,890)(661,896)(662,895)(663,894)(664,893)
(665,892)(666,884)(667,883)(668,889)(669,888)(670,887)(671,886)(672,885);;
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*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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(896)!( 1,113)( 2,114)( 3,115)( 4,116)( 5,117)( 6,118)( 7,119)
( 8,120)( 9,121)( 10,122)( 11,123)( 12,124)( 13,125)( 14,126)( 15,127)
( 16,128)( 17,129)( 18,130)( 19,131)( 20,132)( 21,133)( 22,134)( 23,135)
( 24,136)( 25,137)( 26,138)( 27,139)( 28,140)( 29,141)( 30,142)( 31,143)
( 32,144)( 33,145)( 34,146)( 35,147)( 36,148)( 37,149)( 38,150)( 39,151)
( 40,152)( 41,153)( 42,154)( 43,155)( 44,156)( 45,157)( 46,158)( 47,159)
( 48,160)( 49,161)( 50,162)( 51,163)( 52,164)( 53,165)( 54,166)( 55,167)
( 56,168)( 57,169)( 58,170)( 59,171)( 60,172)( 61,173)( 62,174)( 63,175)
( 64,176)( 65,177)( 66,178)( 67,179)( 68,180)( 69,181)( 70,182)( 71,183)
( 72,184)( 73,185)( 74,186)( 75,187)( 76,188)( 77,189)( 78,190)( 79,191)
( 80,192)( 81,193)( 82,194)( 83,195)( 84,196)( 85,197)( 86,198)( 87,199)
( 88,200)( 89,201)( 90,202)( 91,203)( 92,204)( 93,205)( 94,206)( 95,207)
( 96,208)( 97,209)( 98,210)( 99,211)(100,212)(101,213)(102,214)(103,215)
(104,216)(105,217)(106,218)(107,219)(108,220)(109,221)(110,222)(111,223)
(112,224)(225,337)(226,338)(227,339)(228,340)(229,341)(230,342)(231,343)
(232,344)(233,345)(234,346)(235,347)(236,348)(237,349)(238,350)(239,351)
(240,352)(241,353)(242,354)(243,355)(244,356)(245,357)(246,358)(247,359)
(248,360)(249,361)(250,362)(251,363)(252,364)(253,365)(254,366)(255,367)
(256,368)(257,369)(258,370)(259,371)(260,372)(261,373)(262,374)(263,375)
(264,376)(265,377)(266,378)(267,379)(268,380)(269,381)(270,382)(271,383)
(272,384)(273,385)(274,386)(275,387)(276,388)(277,389)(278,390)(279,391)
(280,392)(281,393)(282,394)(283,395)(284,396)(285,397)(286,398)(287,399)
(288,400)(289,401)(290,402)(291,403)(292,404)(293,405)(294,406)(295,407)
(296,408)(297,409)(298,410)(299,411)(300,412)(301,413)(302,414)(303,415)
(304,416)(305,417)(306,418)(307,419)(308,420)(309,421)(310,422)(311,423)
(312,424)(313,425)(314,426)(315,427)(316,428)(317,429)(318,430)(319,431)
(320,432)(321,433)(322,434)(323,435)(324,436)(325,437)(326,438)(327,439)
(328,440)(329,441)(330,442)(331,443)(332,444)(333,445)(334,446)(335,447)
(336,448)(449,561)(450,562)(451,563)(452,564)(453,565)(454,566)(455,567)
(456,568)(457,569)(458,570)(459,571)(460,572)(461,573)(462,574)(463,575)
(464,576)(465,577)(466,578)(467,579)(468,580)(469,581)(470,582)(471,583)
(472,584)(473,585)(474,586)(475,587)(476,588)(477,589)(478,590)(479,591)
(480,592)(481,593)(482,594)(483,595)(484,596)(485,597)(486,598)(487,599)
(488,600)(489,601)(490,602)(491,603)(492,604)(493,605)(494,606)(495,607)
(496,608)(497,609)(498,610)(499,611)(500,612)(501,613)(502,614)(503,615)
(504,616)(505,617)(506,618)(507,619)(508,620)(509,621)(510,622)(511,623)
(512,624)(513,625)(514,626)(515,627)(516,628)(517,629)(518,630)(519,631)
(520,632)(521,633)(522,634)(523,635)(524,636)(525,637)(526,638)(527,639)
(528,640)(529,641)(530,642)(531,643)(532,644)(533,645)(534,646)(535,647)
(536,648)(537,649)(538,650)(539,651)(540,652)(541,653)(542,654)(543,655)
(544,656)(545,657)(546,658)(547,659)(548,660)(549,661)(550,662)(551,663)
(552,664)(553,665)(554,666)(555,667)(556,668)(557,669)(558,670)(559,671)
(560,672)(673,785)(674,786)(675,787)(676,788)(677,789)(678,790)(679,791)
(680,792)(681,793)(682,794)(683,795)(684,796)(685,797)(686,798)(687,799)
(688,800)(689,801)(690,802)(691,803)(692,804)(693,805)(694,806)(695,807)
(696,808)(697,809)(698,810)(699,811)(700,812)(701,813)(702,814)(703,815)
(704,816)(705,817)(706,818)(707,819)(708,820)(709,821)(710,822)(711,823)
(712,824)(713,825)(714,826)(715,827)(716,828)(717,829)(718,830)(719,831)
(720,832)(721,833)(722,834)(723,835)(724,836)(725,837)(726,838)(727,839)
(728,840)(729,841)(730,842)(731,843)(732,844)(733,845)(734,846)(735,847)
(736,848)(737,849)(738,850)(739,851)(740,852)(741,853)(742,854)(743,855)
(744,856)(745,857)(746,858)(747,859)(748,860)(749,861)(750,862)(751,863)
(752,864)(753,865)(754,866)(755,867)(756,868)(757,869)(758,870)(759,871)
(760,872)(761,873)(762,874)(763,875)(764,876)(765,877)(766,878)(767,879)
(768,880)(769,881)(770,882)(771,883)(772,884)(773,885)(774,886)(775,887)
(776,888)(777,889)(778,890)(779,891)(780,892)(781,893)(782,894)(783,895)
(784,896);
s1 := 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)( 29, 36)( 30, 42)( 31, 41)
( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 43, 50)( 44, 56)( 45, 55)( 46, 54)
( 47, 53)( 48, 52)( 49, 51)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)
( 67, 68)( 72, 77)( 73, 76)( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 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)(141,204)(142,210)(143,209)(144,208)(145,207)(146,206)(147,205)
(148,197)(149,203)(150,202)(151,201)(152,200)(153,199)(154,198)(155,218)
(156,224)(157,223)(158,222)(159,221)(160,220)(161,219)(162,211)(163,217)
(164,216)(165,215)(166,214)(167,213)(168,212)(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)(281,309)(282,315)(283,314)(284,313)(285,312)(286,311)(287,310)
(288,316)(289,322)(290,321)(291,320)(292,319)(293,318)(294,317)(295,323)
(296,329)(297,328)(298,327)(299,326)(300,325)(301,324)(302,330)(303,336)
(304,335)(305,334)(306,333)(307,332)(308,331)(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)(477,540)(478,546)(479,545)(480,544)(481,543)(482,542)(483,541)
(484,533)(485,539)(486,538)(487,537)(488,536)(489,535)(490,534)(491,554)
(492,560)(493,559)(494,558)(495,557)(496,556)(497,555)(498,547)(499,553)
(500,552)(501,551)(502,550)(503,549)(504,548)(562,567)(563,566)(564,565)
(569,574)(570,573)(571,572)(576,581)(577,580)(578,579)(583,588)(584,587)
(585,586)(589,596)(590,602)(591,601)(592,600)(593,599)(594,598)(595,597)
(603,610)(604,616)(605,615)(606,614)(607,613)(608,612)(609,611)(618,623)
(619,622)(620,621)(625,630)(626,629)(627,628)(632,637)(633,636)(634,635)
(639,644)(640,643)(641,642)(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)(841,869)(842,875)(843,874)
(844,873)(845,872)(846,871)(847,870)(848,876)(849,882)(850,881)(851,880)
(852,879)(853,878)(854,877)(855,883)(856,889)(857,888)(858,887)(859,886)
(860,885)(861,884)(862,890)(863,896)(864,895)(865,894)(866,893)(867,892)
(868,891);
s2 := Sym(896)!( 1,226)( 2,225)( 3,231)( 4,230)( 5,229)( 6,228)( 7,227)
( 8,233)( 9,232)( 10,238)( 11,237)( 12,236)( 13,235)( 14,234)( 15,240)
( 16,239)( 17,245)( 18,244)( 19,243)( 20,242)( 21,241)( 22,247)( 23,246)
( 24,252)( 25,251)( 26,250)( 27,249)( 28,248)( 29,261)( 30,260)( 31,266)
( 32,265)( 33,264)( 34,263)( 35,262)( 36,254)( 37,253)( 38,259)( 39,258)
( 40,257)( 41,256)( 42,255)( 43,275)( 44,274)( 45,280)( 46,279)( 47,278)
( 48,277)( 49,276)( 50,268)( 51,267)( 52,273)( 53,272)( 54,271)( 55,270)
( 56,269)( 57,282)( 58,281)( 59,287)( 60,286)( 61,285)( 62,284)( 63,283)
( 64,289)( 65,288)( 66,294)( 67,293)( 68,292)( 69,291)( 70,290)( 71,296)
( 72,295)( 73,301)( 74,300)( 75,299)( 76,298)( 77,297)( 78,303)( 79,302)
( 80,308)( 81,307)( 82,306)( 83,305)( 84,304)( 85,317)( 86,316)( 87,322)
( 88,321)( 89,320)( 90,319)( 91,318)( 92,310)( 93,309)( 94,315)( 95,314)
( 96,313)( 97,312)( 98,311)( 99,331)(100,330)(101,336)(102,335)(103,334)
(104,333)(105,332)(106,324)(107,323)(108,329)(109,328)(110,327)(111,326)
(112,325)(113,338)(114,337)(115,343)(116,342)(117,341)(118,340)(119,339)
(120,345)(121,344)(122,350)(123,349)(124,348)(125,347)(126,346)(127,352)
(128,351)(129,357)(130,356)(131,355)(132,354)(133,353)(134,359)(135,358)
(136,364)(137,363)(138,362)(139,361)(140,360)(141,373)(142,372)(143,378)
(144,377)(145,376)(146,375)(147,374)(148,366)(149,365)(150,371)(151,370)
(152,369)(153,368)(154,367)(155,387)(156,386)(157,392)(158,391)(159,390)
(160,389)(161,388)(162,380)(163,379)(164,385)(165,384)(166,383)(167,382)
(168,381)(169,394)(170,393)(171,399)(172,398)(173,397)(174,396)(175,395)
(176,401)(177,400)(178,406)(179,405)(180,404)(181,403)(182,402)(183,408)
(184,407)(185,413)(186,412)(187,411)(188,410)(189,409)(190,415)(191,414)
(192,420)(193,419)(194,418)(195,417)(196,416)(197,429)(198,428)(199,434)
(200,433)(201,432)(202,431)(203,430)(204,422)(205,421)(206,427)(207,426)
(208,425)(209,424)(210,423)(211,443)(212,442)(213,448)(214,447)(215,446)
(216,445)(217,444)(218,436)(219,435)(220,441)(221,440)(222,439)(223,438)
(224,437)(449,674)(450,673)(451,679)(452,678)(453,677)(454,676)(455,675)
(456,681)(457,680)(458,686)(459,685)(460,684)(461,683)(462,682)(463,688)
(464,687)(465,693)(466,692)(467,691)(468,690)(469,689)(470,695)(471,694)
(472,700)(473,699)(474,698)(475,697)(476,696)(477,709)(478,708)(479,714)
(480,713)(481,712)(482,711)(483,710)(484,702)(485,701)(486,707)(487,706)
(488,705)(489,704)(490,703)(491,723)(492,722)(493,728)(494,727)(495,726)
(496,725)(497,724)(498,716)(499,715)(500,721)(501,720)(502,719)(503,718)
(504,717)(505,730)(506,729)(507,735)(508,734)(509,733)(510,732)(511,731)
(512,737)(513,736)(514,742)(515,741)(516,740)(517,739)(518,738)(519,744)
(520,743)(521,749)(522,748)(523,747)(524,746)(525,745)(526,751)(527,750)
(528,756)(529,755)(530,754)(531,753)(532,752)(533,765)(534,764)(535,770)
(536,769)(537,768)(538,767)(539,766)(540,758)(541,757)(542,763)(543,762)
(544,761)(545,760)(546,759)(547,779)(548,778)(549,784)(550,783)(551,782)
(552,781)(553,780)(554,772)(555,771)(556,777)(557,776)(558,775)(559,774)
(560,773)(561,786)(562,785)(563,791)(564,790)(565,789)(566,788)(567,787)
(568,793)(569,792)(570,798)(571,797)(572,796)(573,795)(574,794)(575,800)
(576,799)(577,805)(578,804)(579,803)(580,802)(581,801)(582,807)(583,806)
(584,812)(585,811)(586,810)(587,809)(588,808)(589,821)(590,820)(591,826)
(592,825)(593,824)(594,823)(595,822)(596,814)(597,813)(598,819)(599,818)
(600,817)(601,816)(602,815)(603,835)(604,834)(605,840)(606,839)(607,838)
(608,837)(609,836)(610,828)(611,827)(612,833)(613,832)(614,831)(615,830)
(616,829)(617,842)(618,841)(619,847)(620,846)(621,845)(622,844)(623,843)
(624,849)(625,848)(626,854)(627,853)(628,852)(629,851)(630,850)(631,856)
(632,855)(633,861)(634,860)(635,859)(636,858)(637,857)(638,863)(639,862)
(640,868)(641,867)(642,866)(643,865)(644,864)(645,877)(646,876)(647,882)
(648,881)(649,880)(650,879)(651,878)(652,870)(653,869)(654,875)(655,874)
(656,873)(657,872)(658,871)(659,891)(660,890)(661,896)(662,895)(663,894)
(664,893)(665,892)(666,884)(667,883)(668,889)(669,888)(670,887)(671,886)
(672,885);
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*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*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope