Polytope of Type {4,8,28}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,8,28}*1792d
Also Known As : {{4,8|2},{8,28|2}}. if this polytope has another name.
Group : SmallGroup(1792,201309)
Rank : 4
Schlafli Type : {4,8,28}
Number of vertices, edges, etc : 4, 16, 112, 28
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, {2,8,28}*896a, {4,8,14}*896a
4-fold quotients : {2,4,28}*448, {4,2,28}*448, {4,4,14}*448, {2,8,14}*448
7-fold quotients : {4,8,4}*256d
8-fold quotients : {2,2,28}*224, {2,4,14}*224, {4,2,14}*224
14-fold quotients : {4,4,4}*128, {2,8,4}*128a, {4,8,2}*128a
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, {2,8,2}*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 := ( 1,113)( 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 := ( 29, 36)( 30, 37)( 31, 38)( 32, 39)( 33, 40)( 34, 41)( 35, 42)( 43, 50)
( 44, 51)( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 85, 92)( 86, 93)
( 87, 94)( 88, 95)( 89, 96)( 90, 97)( 91, 98)( 99,106)(100,107)(101,108)
(102,109)(103,110)(104,111)(105,112)(113,169)(114,170)(115,171)(116,172)
(117,173)(118,174)(119,175)(120,176)(121,177)(122,178)(123,179)(124,180)
(125,181)(126,182)(127,183)(128,184)(129,185)(130,186)(131,187)(132,188)
(133,189)(134,190)(135,191)(136,192)(137,193)(138,194)(139,195)(140,196)
(141,204)(142,205)(143,206)(144,207)(145,208)(146,209)(147,210)(148,197)
(149,198)(150,199)(151,200)(152,201)(153,202)(154,203)(155,218)(156,219)
(157,220)(158,221)(159,222)(160,223)(161,224)(162,211)(163,212)(164,213)
(165,214)(166,215)(167,216)(168,217)(225,253)(226,254)(227,255)(228,256)
(229,257)(230,258)(231,259)(232,260)(233,261)(234,262)(235,263)(236,264)
(237,265)(238,266)(239,267)(240,268)(241,269)(242,270)(243,271)(244,272)
(245,273)(246,274)(247,275)(248,276)(249,277)(250,278)(251,279)(252,280)
(281,309)(282,310)(283,311)(284,312)(285,313)(286,314)(287,315)(288,316)
(289,317)(290,318)(291,319)(292,320)(293,321)(294,322)(295,323)(296,324)
(297,325)(298,326)(299,327)(300,328)(301,329)(302,330)(303,331)(304,332)
(305,333)(306,334)(307,335)(308,336)(337,421)(338,422)(339,423)(340,424)
(341,425)(342,426)(343,427)(344,428)(345,429)(346,430)(347,431)(348,432)
(349,433)(350,434)(351,435)(352,436)(353,437)(354,438)(355,439)(356,440)
(357,441)(358,442)(359,443)(360,444)(361,445)(362,446)(363,447)(364,448)
(365,393)(366,394)(367,395)(368,396)(369,397)(370,398)(371,399)(372,400)
(373,401)(374,402)(375,403)(376,404)(377,405)(378,406)(379,407)(380,408)
(381,409)(382,410)(383,411)(384,412)(385,413)(386,414)(387,415)(388,416)
(389,417)(390,418)(391,419)(392,420)(449,505)(450,506)(451,507)(452,508)
(453,509)(454,510)(455,511)(456,512)(457,513)(458,514)(459,515)(460,516)
(461,517)(462,518)(463,519)(464,520)(465,521)(466,522)(467,523)(468,524)
(469,525)(470,526)(471,527)(472,528)(473,529)(474,530)(475,531)(476,532)
(477,540)(478,541)(479,542)(480,543)(481,544)(482,545)(483,546)(484,533)
(485,534)(486,535)(487,536)(488,537)(489,538)(490,539)(491,554)(492,555)
(493,556)(494,557)(495,558)(496,559)(497,560)(498,547)(499,548)(500,549)
(501,550)(502,551)(503,552)(504,553)(589,596)(590,597)(591,598)(592,599)
(593,600)(594,601)(595,602)(603,610)(604,611)(605,612)(606,613)(607,614)
(608,615)(609,616)(645,652)(646,653)(647,654)(648,655)(649,656)(650,657)
(651,658)(659,666)(660,667)(661,668)(662,669)(663,670)(664,671)(665,672)
(673,757)(674,758)(675,759)(676,760)(677,761)(678,762)(679,763)(680,764)
(681,765)(682,766)(683,767)(684,768)(685,769)(686,770)(687,771)(688,772)
(689,773)(690,774)(691,775)(692,776)(693,777)(694,778)(695,779)(696,780)
(697,781)(698,782)(699,783)(700,784)(701,729)(702,730)(703,731)(704,732)
(705,733)(706,734)(707,735)(708,736)(709,737)(710,738)(711,739)(712,740)
(713,741)(714,742)(715,743)(716,744)(717,745)(718,746)(719,747)(720,748)
(721,749)(722,750)(723,751)(724,752)(725,753)(726,754)(727,755)(728,756)
(785,813)(786,814)(787,815)(788,816)(789,817)(790,818)(791,819)(792,820)
(793,821)(794,822)(795,823)(796,824)(797,825)(798,826)(799,827)(800,828)
(801,829)(802,830)(803,831)(804,832)(805,833)(806,834)(807,835)(808,836)
(809,837)(810,838)(811,839)(812,840)(841,869)(842,870)(843,871)(844,872)
(845,873)(846,874)(847,875)(848,876)(849,877)(850,878)(851,879)(852,880)
(853,881)(854,882)(855,883)(856,884)(857,885)(858,886)(859,887)(860,888)
(861,889)(862,890)(863,891)(864,892)(865,893)(866,894)(867,895)(868,896);;
s2 := ( 1,225)( 2,231)( 3,230)( 4,229)( 5,228)( 6,227)( 7,226)( 8,232)
( 9,238)( 10,237)( 11,236)( 12,235)( 13,234)( 14,233)( 15,239)( 16,245)
( 17,244)( 18,243)( 19,242)( 20,241)( 21,240)( 22,246)( 23,252)( 24,251)
( 25,250)( 26,249)( 27,248)( 28,247)( 29,260)( 30,266)( 31,265)( 32,264)
( 33,263)( 34,262)( 35,261)( 36,253)( 37,259)( 38,258)( 39,257)( 40,256)
( 41,255)( 42,254)( 43,274)( 44,280)( 45,279)( 46,278)( 47,277)( 48,276)
( 49,275)( 50,267)( 51,273)( 52,272)( 53,271)( 54,270)( 55,269)( 56,268)
( 57,281)( 58,287)( 59,286)( 60,285)( 61,284)( 62,283)( 63,282)( 64,288)
( 65,294)( 66,293)( 67,292)( 68,291)( 69,290)( 70,289)( 71,295)( 72,301)
( 73,300)( 74,299)( 75,298)( 76,297)( 77,296)( 78,302)( 79,308)( 80,307)
( 81,306)( 82,305)( 83,304)( 84,303)( 85,316)( 86,322)( 87,321)( 88,320)
( 89,319)( 90,318)( 91,317)( 92,309)( 93,315)( 94,314)( 95,313)( 96,312)
( 97,311)( 98,310)( 99,330)(100,336)(101,335)(102,334)(103,333)(104,332)
(105,331)(106,323)(107,329)(108,328)(109,327)(110,326)(111,325)(112,324)
(113,337)(114,343)(115,342)(116,341)(117,340)(118,339)(119,338)(120,344)
(121,350)(122,349)(123,348)(124,347)(125,346)(126,345)(127,351)(128,357)
(129,356)(130,355)(131,354)(132,353)(133,352)(134,358)(135,364)(136,363)
(137,362)(138,361)(139,360)(140,359)(141,372)(142,378)(143,377)(144,376)
(145,375)(146,374)(147,373)(148,365)(149,371)(150,370)(151,369)(152,368)
(153,367)(154,366)(155,386)(156,392)(157,391)(158,390)(159,389)(160,388)
(161,387)(162,379)(163,385)(164,384)(165,383)(166,382)(167,381)(168,380)
(169,393)(170,399)(171,398)(172,397)(173,396)(174,395)(175,394)(176,400)
(177,406)(178,405)(179,404)(180,403)(181,402)(182,401)(183,407)(184,413)
(185,412)(186,411)(187,410)(188,409)(189,408)(190,414)(191,420)(192,419)
(193,418)(194,417)(195,416)(196,415)(197,428)(198,434)(199,433)(200,432)
(201,431)(202,430)(203,429)(204,421)(205,427)(206,426)(207,425)(208,424)
(209,423)(210,422)(211,442)(212,448)(213,447)(214,446)(215,445)(216,444)
(217,443)(218,435)(219,441)(220,440)(221,439)(222,438)(223,437)(224,436)
(449,673)(450,679)(451,678)(452,677)(453,676)(454,675)(455,674)(456,680)
(457,686)(458,685)(459,684)(460,683)(461,682)(462,681)(463,687)(464,693)
(465,692)(466,691)(467,690)(468,689)(469,688)(470,694)(471,700)(472,699)
(473,698)(474,697)(475,696)(476,695)(477,708)(478,714)(479,713)(480,712)
(481,711)(482,710)(483,709)(484,701)(485,707)(486,706)(487,705)(488,704)
(489,703)(490,702)(491,722)(492,728)(493,727)(494,726)(495,725)(496,724)
(497,723)(498,715)(499,721)(500,720)(501,719)(502,718)(503,717)(504,716)
(505,729)(506,735)(507,734)(508,733)(509,732)(510,731)(511,730)(512,736)
(513,742)(514,741)(515,740)(516,739)(517,738)(518,737)(519,743)(520,749)
(521,748)(522,747)(523,746)(524,745)(525,744)(526,750)(527,756)(528,755)
(529,754)(530,753)(531,752)(532,751)(533,764)(534,770)(535,769)(536,768)
(537,767)(538,766)(539,765)(540,757)(541,763)(542,762)(543,761)(544,760)
(545,759)(546,758)(547,778)(548,784)(549,783)(550,782)(551,781)(552,780)
(553,779)(554,771)(555,777)(556,776)(557,775)(558,774)(559,773)(560,772)
(561,785)(562,791)(563,790)(564,789)(565,788)(566,787)(567,786)(568,792)
(569,798)(570,797)(571,796)(572,795)(573,794)(574,793)(575,799)(576,805)
(577,804)(578,803)(579,802)(580,801)(581,800)(582,806)(583,812)(584,811)
(585,810)(586,809)(587,808)(588,807)(589,820)(590,826)(591,825)(592,824)
(593,823)(594,822)(595,821)(596,813)(597,819)(598,818)(599,817)(600,816)
(601,815)(602,814)(603,834)(604,840)(605,839)(606,838)(607,837)(608,836)
(609,835)(610,827)(611,833)(612,832)(613,831)(614,830)(615,829)(616,828)
(617,841)(618,847)(619,846)(620,845)(621,844)(622,843)(623,842)(624,848)
(625,854)(626,853)(627,852)(628,851)(629,850)(630,849)(631,855)(632,861)
(633,860)(634,859)(635,858)(636,857)(637,856)(638,862)(639,868)(640,867)
(641,866)(642,865)(643,864)(644,863)(645,876)(646,882)(647,881)(648,880)
(649,879)(650,878)(651,877)(652,869)(653,875)(654,874)(655,873)(656,872)
(657,871)(658,870)(659,890)(660,896)(661,895)(662,894)(663,893)(664,892)
(665,891)(666,883)(667,889)(668,888)(669,887)(670,886)(671,885)(672,884);;
s3 := ( 1,562)( 2,561)( 3,567)( 4,566)( 5,565)( 6,564)( 7,563)( 8,569)
( 9,568)( 10,574)( 11,573)( 12,572)( 13,571)( 14,570)( 15,576)( 16,575)
( 17,581)( 18,580)( 19,579)( 20,578)( 21,577)( 22,583)( 23,582)( 24,588)
( 25,587)( 26,586)( 27,585)( 28,584)( 29,590)( 30,589)( 31,595)( 32,594)
( 33,593)( 34,592)( 35,591)( 36,597)( 37,596)( 38,602)( 39,601)( 40,600)
( 41,599)( 42,598)( 43,604)( 44,603)( 45,609)( 46,608)( 47,607)( 48,606)
( 49,605)( 50,611)( 51,610)( 52,616)( 53,615)( 54,614)( 55,613)( 56,612)
( 57,618)( 58,617)( 59,623)( 60,622)( 61,621)( 62,620)( 63,619)( 64,625)
( 65,624)( 66,630)( 67,629)( 68,628)( 69,627)( 70,626)( 71,632)( 72,631)
( 73,637)( 74,636)( 75,635)( 76,634)( 77,633)( 78,639)( 79,638)( 80,644)
( 81,643)( 82,642)( 83,641)( 84,640)( 85,646)( 86,645)( 87,651)( 88,650)
( 89,649)( 90,648)( 91,647)( 92,653)( 93,652)( 94,658)( 95,657)( 96,656)
( 97,655)( 98,654)( 99,660)(100,659)(101,665)(102,664)(103,663)(104,662)
(105,661)(106,667)(107,666)(108,672)(109,671)(110,670)(111,669)(112,668)
(113,450)(114,449)(115,455)(116,454)(117,453)(118,452)(119,451)(120,457)
(121,456)(122,462)(123,461)(124,460)(125,459)(126,458)(127,464)(128,463)
(129,469)(130,468)(131,467)(132,466)(133,465)(134,471)(135,470)(136,476)
(137,475)(138,474)(139,473)(140,472)(141,478)(142,477)(143,483)(144,482)
(145,481)(146,480)(147,479)(148,485)(149,484)(150,490)(151,489)(152,488)
(153,487)(154,486)(155,492)(156,491)(157,497)(158,496)(159,495)(160,494)
(161,493)(162,499)(163,498)(164,504)(165,503)(166,502)(167,501)(168,500)
(169,506)(170,505)(171,511)(172,510)(173,509)(174,508)(175,507)(176,513)
(177,512)(178,518)(179,517)(180,516)(181,515)(182,514)(183,520)(184,519)
(185,525)(186,524)(187,523)(188,522)(189,521)(190,527)(191,526)(192,532)
(193,531)(194,530)(195,529)(196,528)(197,534)(198,533)(199,539)(200,538)
(201,537)(202,536)(203,535)(204,541)(205,540)(206,546)(207,545)(208,544)
(209,543)(210,542)(211,548)(212,547)(213,553)(214,552)(215,551)(216,550)
(217,549)(218,555)(219,554)(220,560)(221,559)(222,558)(223,557)(224,556)
(225,800)(226,799)(227,805)(228,804)(229,803)(230,802)(231,801)(232,807)
(233,806)(234,812)(235,811)(236,810)(237,809)(238,808)(239,786)(240,785)
(241,791)(242,790)(243,789)(244,788)(245,787)(246,793)(247,792)(248,798)
(249,797)(250,796)(251,795)(252,794)(253,828)(254,827)(255,833)(256,832)
(257,831)(258,830)(259,829)(260,835)(261,834)(262,840)(263,839)(264,838)
(265,837)(266,836)(267,814)(268,813)(269,819)(270,818)(271,817)(272,816)
(273,815)(274,821)(275,820)(276,826)(277,825)(278,824)(279,823)(280,822)
(281,856)(282,855)(283,861)(284,860)(285,859)(286,858)(287,857)(288,863)
(289,862)(290,868)(291,867)(292,866)(293,865)(294,864)(295,842)(296,841)
(297,847)(298,846)(299,845)(300,844)(301,843)(302,849)(303,848)(304,854)
(305,853)(306,852)(307,851)(308,850)(309,884)(310,883)(311,889)(312,888)
(313,887)(314,886)(315,885)(316,891)(317,890)(318,896)(319,895)(320,894)
(321,893)(322,892)(323,870)(324,869)(325,875)(326,874)(327,873)(328,872)
(329,871)(330,877)(331,876)(332,882)(333,881)(334,880)(335,879)(336,878)
(337,688)(338,687)(339,693)(340,692)(341,691)(342,690)(343,689)(344,695)
(345,694)(346,700)(347,699)(348,698)(349,697)(350,696)(351,674)(352,673)
(353,679)(354,678)(355,677)(356,676)(357,675)(358,681)(359,680)(360,686)
(361,685)(362,684)(363,683)(364,682)(365,716)(366,715)(367,721)(368,720)
(369,719)(370,718)(371,717)(372,723)(373,722)(374,728)(375,727)(376,726)
(377,725)(378,724)(379,702)(380,701)(381,707)(382,706)(383,705)(384,704)
(385,703)(386,709)(387,708)(388,714)(389,713)(390,712)(391,711)(392,710)
(393,744)(394,743)(395,749)(396,748)(397,747)(398,746)(399,745)(400,751)
(401,750)(402,756)(403,755)(404,754)(405,753)(406,752)(407,730)(408,729)
(409,735)(410,734)(411,733)(412,732)(413,731)(414,737)(415,736)(416,742)
(417,741)(418,740)(419,739)(420,738)(421,772)(422,771)(423,777)(424,776)
(425,775)(426,774)(427,773)(428,779)(429,778)(430,784)(431,783)(432,782)
(433,781)(434,780)(435,758)(436,757)(437,763)(438,762)(439,761)(440,760)
(441,759)(442,765)(443,764)(444,770)(445,769)(446,768)(447,767)(448,766);;
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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 ];;
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)!( 29, 36)( 30, 37)( 31, 38)( 32, 39)( 33, 40)( 34, 41)( 35, 42)
( 43, 50)( 44, 51)( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 85, 92)
( 86, 93)( 87, 94)( 88, 95)( 89, 96)( 90, 97)( 91, 98)( 99,106)(100,107)
(101,108)(102,109)(103,110)(104,111)(105,112)(113,169)(114,170)(115,171)
(116,172)(117,173)(118,174)(119,175)(120,176)(121,177)(122,178)(123,179)
(124,180)(125,181)(126,182)(127,183)(128,184)(129,185)(130,186)(131,187)
(132,188)(133,189)(134,190)(135,191)(136,192)(137,193)(138,194)(139,195)
(140,196)(141,204)(142,205)(143,206)(144,207)(145,208)(146,209)(147,210)
(148,197)(149,198)(150,199)(151,200)(152,201)(153,202)(154,203)(155,218)
(156,219)(157,220)(158,221)(159,222)(160,223)(161,224)(162,211)(163,212)
(164,213)(165,214)(166,215)(167,216)(168,217)(225,253)(226,254)(227,255)
(228,256)(229,257)(230,258)(231,259)(232,260)(233,261)(234,262)(235,263)
(236,264)(237,265)(238,266)(239,267)(240,268)(241,269)(242,270)(243,271)
(244,272)(245,273)(246,274)(247,275)(248,276)(249,277)(250,278)(251,279)
(252,280)(281,309)(282,310)(283,311)(284,312)(285,313)(286,314)(287,315)
(288,316)(289,317)(290,318)(291,319)(292,320)(293,321)(294,322)(295,323)
(296,324)(297,325)(298,326)(299,327)(300,328)(301,329)(302,330)(303,331)
(304,332)(305,333)(306,334)(307,335)(308,336)(337,421)(338,422)(339,423)
(340,424)(341,425)(342,426)(343,427)(344,428)(345,429)(346,430)(347,431)
(348,432)(349,433)(350,434)(351,435)(352,436)(353,437)(354,438)(355,439)
(356,440)(357,441)(358,442)(359,443)(360,444)(361,445)(362,446)(363,447)
(364,448)(365,393)(366,394)(367,395)(368,396)(369,397)(370,398)(371,399)
(372,400)(373,401)(374,402)(375,403)(376,404)(377,405)(378,406)(379,407)
(380,408)(381,409)(382,410)(383,411)(384,412)(385,413)(386,414)(387,415)
(388,416)(389,417)(390,418)(391,419)(392,420)(449,505)(450,506)(451,507)
(452,508)(453,509)(454,510)(455,511)(456,512)(457,513)(458,514)(459,515)
(460,516)(461,517)(462,518)(463,519)(464,520)(465,521)(466,522)(467,523)
(468,524)(469,525)(470,526)(471,527)(472,528)(473,529)(474,530)(475,531)
(476,532)(477,540)(478,541)(479,542)(480,543)(481,544)(482,545)(483,546)
(484,533)(485,534)(486,535)(487,536)(488,537)(489,538)(490,539)(491,554)
(492,555)(493,556)(494,557)(495,558)(496,559)(497,560)(498,547)(499,548)
(500,549)(501,550)(502,551)(503,552)(504,553)(589,596)(590,597)(591,598)
(592,599)(593,600)(594,601)(595,602)(603,610)(604,611)(605,612)(606,613)
(607,614)(608,615)(609,616)(645,652)(646,653)(647,654)(648,655)(649,656)
(650,657)(651,658)(659,666)(660,667)(661,668)(662,669)(663,670)(664,671)
(665,672)(673,757)(674,758)(675,759)(676,760)(677,761)(678,762)(679,763)
(680,764)(681,765)(682,766)(683,767)(684,768)(685,769)(686,770)(687,771)
(688,772)(689,773)(690,774)(691,775)(692,776)(693,777)(694,778)(695,779)
(696,780)(697,781)(698,782)(699,783)(700,784)(701,729)(702,730)(703,731)
(704,732)(705,733)(706,734)(707,735)(708,736)(709,737)(710,738)(711,739)
(712,740)(713,741)(714,742)(715,743)(716,744)(717,745)(718,746)(719,747)
(720,748)(721,749)(722,750)(723,751)(724,752)(725,753)(726,754)(727,755)
(728,756)(785,813)(786,814)(787,815)(788,816)(789,817)(790,818)(791,819)
(792,820)(793,821)(794,822)(795,823)(796,824)(797,825)(798,826)(799,827)
(800,828)(801,829)(802,830)(803,831)(804,832)(805,833)(806,834)(807,835)
(808,836)(809,837)(810,838)(811,839)(812,840)(841,869)(842,870)(843,871)
(844,872)(845,873)(846,874)(847,875)(848,876)(849,877)(850,878)(851,879)
(852,880)(853,881)(854,882)(855,883)(856,884)(857,885)(858,886)(859,887)
(860,888)(861,889)(862,890)(863,891)(864,892)(865,893)(866,894)(867,895)
(868,896);
s2 := Sym(896)!( 1,225)( 2,231)( 3,230)( 4,229)( 5,228)( 6,227)( 7,226)
( 8,232)( 9,238)( 10,237)( 11,236)( 12,235)( 13,234)( 14,233)( 15,239)
( 16,245)( 17,244)( 18,243)( 19,242)( 20,241)( 21,240)( 22,246)( 23,252)
( 24,251)( 25,250)( 26,249)( 27,248)( 28,247)( 29,260)( 30,266)( 31,265)
( 32,264)( 33,263)( 34,262)( 35,261)( 36,253)( 37,259)( 38,258)( 39,257)
( 40,256)( 41,255)( 42,254)( 43,274)( 44,280)( 45,279)( 46,278)( 47,277)
( 48,276)( 49,275)( 50,267)( 51,273)( 52,272)( 53,271)( 54,270)( 55,269)
( 56,268)( 57,281)( 58,287)( 59,286)( 60,285)( 61,284)( 62,283)( 63,282)
( 64,288)( 65,294)( 66,293)( 67,292)( 68,291)( 69,290)( 70,289)( 71,295)
( 72,301)( 73,300)( 74,299)( 75,298)( 76,297)( 77,296)( 78,302)( 79,308)
( 80,307)( 81,306)( 82,305)( 83,304)( 84,303)( 85,316)( 86,322)( 87,321)
( 88,320)( 89,319)( 90,318)( 91,317)( 92,309)( 93,315)( 94,314)( 95,313)
( 96,312)( 97,311)( 98,310)( 99,330)(100,336)(101,335)(102,334)(103,333)
(104,332)(105,331)(106,323)(107,329)(108,328)(109,327)(110,326)(111,325)
(112,324)(113,337)(114,343)(115,342)(116,341)(117,340)(118,339)(119,338)
(120,344)(121,350)(122,349)(123,348)(124,347)(125,346)(126,345)(127,351)
(128,357)(129,356)(130,355)(131,354)(132,353)(133,352)(134,358)(135,364)
(136,363)(137,362)(138,361)(139,360)(140,359)(141,372)(142,378)(143,377)
(144,376)(145,375)(146,374)(147,373)(148,365)(149,371)(150,370)(151,369)
(152,368)(153,367)(154,366)(155,386)(156,392)(157,391)(158,390)(159,389)
(160,388)(161,387)(162,379)(163,385)(164,384)(165,383)(166,382)(167,381)
(168,380)(169,393)(170,399)(171,398)(172,397)(173,396)(174,395)(175,394)
(176,400)(177,406)(178,405)(179,404)(180,403)(181,402)(182,401)(183,407)
(184,413)(185,412)(186,411)(187,410)(188,409)(189,408)(190,414)(191,420)
(192,419)(193,418)(194,417)(195,416)(196,415)(197,428)(198,434)(199,433)
(200,432)(201,431)(202,430)(203,429)(204,421)(205,427)(206,426)(207,425)
(208,424)(209,423)(210,422)(211,442)(212,448)(213,447)(214,446)(215,445)
(216,444)(217,443)(218,435)(219,441)(220,440)(221,439)(222,438)(223,437)
(224,436)(449,673)(450,679)(451,678)(452,677)(453,676)(454,675)(455,674)
(456,680)(457,686)(458,685)(459,684)(460,683)(461,682)(462,681)(463,687)
(464,693)(465,692)(466,691)(467,690)(468,689)(469,688)(470,694)(471,700)
(472,699)(473,698)(474,697)(475,696)(476,695)(477,708)(478,714)(479,713)
(480,712)(481,711)(482,710)(483,709)(484,701)(485,707)(486,706)(487,705)
(488,704)(489,703)(490,702)(491,722)(492,728)(493,727)(494,726)(495,725)
(496,724)(497,723)(498,715)(499,721)(500,720)(501,719)(502,718)(503,717)
(504,716)(505,729)(506,735)(507,734)(508,733)(509,732)(510,731)(511,730)
(512,736)(513,742)(514,741)(515,740)(516,739)(517,738)(518,737)(519,743)
(520,749)(521,748)(522,747)(523,746)(524,745)(525,744)(526,750)(527,756)
(528,755)(529,754)(530,753)(531,752)(532,751)(533,764)(534,770)(535,769)
(536,768)(537,767)(538,766)(539,765)(540,757)(541,763)(542,762)(543,761)
(544,760)(545,759)(546,758)(547,778)(548,784)(549,783)(550,782)(551,781)
(552,780)(553,779)(554,771)(555,777)(556,776)(557,775)(558,774)(559,773)
(560,772)(561,785)(562,791)(563,790)(564,789)(565,788)(566,787)(567,786)
(568,792)(569,798)(570,797)(571,796)(572,795)(573,794)(574,793)(575,799)
(576,805)(577,804)(578,803)(579,802)(580,801)(581,800)(582,806)(583,812)
(584,811)(585,810)(586,809)(587,808)(588,807)(589,820)(590,826)(591,825)
(592,824)(593,823)(594,822)(595,821)(596,813)(597,819)(598,818)(599,817)
(600,816)(601,815)(602,814)(603,834)(604,840)(605,839)(606,838)(607,837)
(608,836)(609,835)(610,827)(611,833)(612,832)(613,831)(614,830)(615,829)
(616,828)(617,841)(618,847)(619,846)(620,845)(621,844)(622,843)(623,842)
(624,848)(625,854)(626,853)(627,852)(628,851)(629,850)(630,849)(631,855)
(632,861)(633,860)(634,859)(635,858)(636,857)(637,856)(638,862)(639,868)
(640,867)(641,866)(642,865)(643,864)(644,863)(645,876)(646,882)(647,881)
(648,880)(649,879)(650,878)(651,877)(652,869)(653,875)(654,874)(655,873)
(656,872)(657,871)(658,870)(659,890)(660,896)(661,895)(662,894)(663,893)
(664,892)(665,891)(666,883)(667,889)(668,888)(669,887)(670,886)(671,885)
(672,884);
s3 := Sym(896)!( 1,562)( 2,561)( 3,567)( 4,566)( 5,565)( 6,564)( 7,563)
( 8,569)( 9,568)( 10,574)( 11,573)( 12,572)( 13,571)( 14,570)( 15,576)
( 16,575)( 17,581)( 18,580)( 19,579)( 20,578)( 21,577)( 22,583)( 23,582)
( 24,588)( 25,587)( 26,586)( 27,585)( 28,584)( 29,590)( 30,589)( 31,595)
( 32,594)( 33,593)( 34,592)( 35,591)( 36,597)( 37,596)( 38,602)( 39,601)
( 40,600)( 41,599)( 42,598)( 43,604)( 44,603)( 45,609)( 46,608)( 47,607)
( 48,606)( 49,605)( 50,611)( 51,610)( 52,616)( 53,615)( 54,614)( 55,613)
( 56,612)( 57,618)( 58,617)( 59,623)( 60,622)( 61,621)( 62,620)( 63,619)
( 64,625)( 65,624)( 66,630)( 67,629)( 68,628)( 69,627)( 70,626)( 71,632)
( 72,631)( 73,637)( 74,636)( 75,635)( 76,634)( 77,633)( 78,639)( 79,638)
( 80,644)( 81,643)( 82,642)( 83,641)( 84,640)( 85,646)( 86,645)( 87,651)
( 88,650)( 89,649)( 90,648)( 91,647)( 92,653)( 93,652)( 94,658)( 95,657)
( 96,656)( 97,655)( 98,654)( 99,660)(100,659)(101,665)(102,664)(103,663)
(104,662)(105,661)(106,667)(107,666)(108,672)(109,671)(110,670)(111,669)
(112,668)(113,450)(114,449)(115,455)(116,454)(117,453)(118,452)(119,451)
(120,457)(121,456)(122,462)(123,461)(124,460)(125,459)(126,458)(127,464)
(128,463)(129,469)(130,468)(131,467)(132,466)(133,465)(134,471)(135,470)
(136,476)(137,475)(138,474)(139,473)(140,472)(141,478)(142,477)(143,483)
(144,482)(145,481)(146,480)(147,479)(148,485)(149,484)(150,490)(151,489)
(152,488)(153,487)(154,486)(155,492)(156,491)(157,497)(158,496)(159,495)
(160,494)(161,493)(162,499)(163,498)(164,504)(165,503)(166,502)(167,501)
(168,500)(169,506)(170,505)(171,511)(172,510)(173,509)(174,508)(175,507)
(176,513)(177,512)(178,518)(179,517)(180,516)(181,515)(182,514)(183,520)
(184,519)(185,525)(186,524)(187,523)(188,522)(189,521)(190,527)(191,526)
(192,532)(193,531)(194,530)(195,529)(196,528)(197,534)(198,533)(199,539)
(200,538)(201,537)(202,536)(203,535)(204,541)(205,540)(206,546)(207,545)
(208,544)(209,543)(210,542)(211,548)(212,547)(213,553)(214,552)(215,551)
(216,550)(217,549)(218,555)(219,554)(220,560)(221,559)(222,558)(223,557)
(224,556)(225,800)(226,799)(227,805)(228,804)(229,803)(230,802)(231,801)
(232,807)(233,806)(234,812)(235,811)(236,810)(237,809)(238,808)(239,786)
(240,785)(241,791)(242,790)(243,789)(244,788)(245,787)(246,793)(247,792)
(248,798)(249,797)(250,796)(251,795)(252,794)(253,828)(254,827)(255,833)
(256,832)(257,831)(258,830)(259,829)(260,835)(261,834)(262,840)(263,839)
(264,838)(265,837)(266,836)(267,814)(268,813)(269,819)(270,818)(271,817)
(272,816)(273,815)(274,821)(275,820)(276,826)(277,825)(278,824)(279,823)
(280,822)(281,856)(282,855)(283,861)(284,860)(285,859)(286,858)(287,857)
(288,863)(289,862)(290,868)(291,867)(292,866)(293,865)(294,864)(295,842)
(296,841)(297,847)(298,846)(299,845)(300,844)(301,843)(302,849)(303,848)
(304,854)(305,853)(306,852)(307,851)(308,850)(309,884)(310,883)(311,889)
(312,888)(313,887)(314,886)(315,885)(316,891)(317,890)(318,896)(319,895)
(320,894)(321,893)(322,892)(323,870)(324,869)(325,875)(326,874)(327,873)
(328,872)(329,871)(330,877)(331,876)(332,882)(333,881)(334,880)(335,879)
(336,878)(337,688)(338,687)(339,693)(340,692)(341,691)(342,690)(343,689)
(344,695)(345,694)(346,700)(347,699)(348,698)(349,697)(350,696)(351,674)
(352,673)(353,679)(354,678)(355,677)(356,676)(357,675)(358,681)(359,680)
(360,686)(361,685)(362,684)(363,683)(364,682)(365,716)(366,715)(367,721)
(368,720)(369,719)(370,718)(371,717)(372,723)(373,722)(374,728)(375,727)
(376,726)(377,725)(378,724)(379,702)(380,701)(381,707)(382,706)(383,705)
(384,704)(385,703)(386,709)(387,708)(388,714)(389,713)(390,712)(391,711)
(392,710)(393,744)(394,743)(395,749)(396,748)(397,747)(398,746)(399,745)
(400,751)(401,750)(402,756)(403,755)(404,754)(405,753)(406,752)(407,730)
(408,729)(409,735)(410,734)(411,733)(412,732)(413,731)(414,737)(415,736)
(416,742)(417,741)(418,740)(419,739)(420,738)(421,772)(422,771)(423,777)
(424,776)(425,775)(426,774)(427,773)(428,779)(429,778)(430,784)(431,783)
(432,782)(433,781)(434,780)(435,758)(436,757)(437,763)(438,762)(439,761)
(440,760)(441,759)(442,765)(443,764)(444,770)(445,769)(446,768)(447,767)
(448,766);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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 >;
References : None.
to this polytope