Polytope of Type {8,25}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,25}*1600b
if this polytope has a name.
Group : SmallGroup(1600,2008)
Rank : 3
Schlafli Type : {8,25}
Number of vertices, edges, etc : 32, 400, 100
Order of s₀s₁s₂ : 25
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
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 : {4,25}*800
   5-fold quotients : {8,5}*320b
   10-fold quotients : {4,5}*160
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, 
s0*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s0*s1, 
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