Polytope of Type {20,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,8}*1600a
if this polytope has a name.
Group : SmallGroup(1600,6630)
Rank : 3
Schlafli Type : {20,8}
Number of vertices, edges, etc : 100, 400, 40
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {10,8}*800, {20,4}*800
   4-fold quotients : {10,4}*400
   8-fold quotients : {10,4}*200
   25-fold quotients : {4,8}*64a
   50-fold quotients : {4,4}*32, {2,8}*32
   100-fold quotients : {2,4}*16, {4,2}*16
   200-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope