Polytope of Type {25,8}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope