Polytope of Type {8,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,20}*1600a
if this polytope has a name.
Group : SmallGroup(1600,6630)
Rank : 3
Schlafli Type : {8,20}
Number of vertices, edges, etc : 40, 400, 100
Order of s0s1s2 : 8
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
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 : {8,10}*800, {4,20}*800
4-fold quotients : {4,10}*400
8-fold quotients : {4,10}*200
25-fold quotients : {8,4}*64a
50-fold quotients : {4,4}*32, {8,2}*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 := ( 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);;
s1 := ( 1,401)( 2,409)( 3,412)( 4,420)( 5,423)( 6,413)( 7,416)( 8,424)
( 9,402)( 10,410)( 11,425)( 12,403)( 13,406)( 14,414)( 15,417)( 16,407)
( 17,415)( 18,418)( 19,421)( 20,404)( 21,419)( 22,422)( 23,405)( 24,408)
( 25,411)( 26,426)( 27,434)( 28,437)( 29,445)( 30,448)( 31,438)( 32,441)
( 33,449)( 34,427)( 35,435)( 36,450)( 37,428)( 38,431)( 39,439)( 40,442)
( 41,432)( 42,440)( 43,443)( 44,446)( 45,429)( 46,444)( 47,447)( 48,430)
( 49,433)( 50,436)( 51,451)( 52,459)( 53,462)( 54,470)( 55,473)( 56,463)
( 57,466)( 58,474)( 59,452)( 60,460)( 61,475)( 62,453)( 63,456)( 64,464)
( 65,467)( 66,457)( 67,465)( 68,468)( 69,471)( 70,454)( 71,469)( 72,472)
( 73,455)( 74,458)( 75,461)( 76,476)( 77,484)( 78,487)( 79,495)( 80,498)
( 81,488)( 82,491)( 83,499)( 84,477)( 85,485)( 86,500)( 87,478)( 88,481)
( 89,489)( 90,492)( 91,482)( 92,490)( 93,493)( 94,496)( 95,479)( 96,494)
( 97,497)( 98,480)( 99,483)(100,486)(101,526)(102,534)(103,537)(104,545)
(105,548)(106,538)(107,541)(108,549)(109,527)(110,535)(111,550)(112,528)
(113,531)(114,539)(115,542)(116,532)(117,540)(118,543)(119,546)(120,529)
(121,544)(122,547)(123,530)(124,533)(125,536)(126,501)(127,509)(128,512)
(129,520)(130,523)(131,513)(132,516)(133,524)(134,502)(135,510)(136,525)
(137,503)(138,506)(139,514)(140,517)(141,507)(142,515)(143,518)(144,521)
(145,504)(146,519)(147,522)(148,505)(149,508)(150,511)(151,576)(152,584)
(153,587)(154,595)(155,598)(156,588)(157,591)(158,599)(159,577)(160,585)
(161,600)(162,578)(163,581)(164,589)(165,592)(166,582)(167,590)(168,593)
(169,596)(170,579)(171,594)(172,597)(173,580)(174,583)(175,586)(176,551)
(177,559)(178,562)(179,570)(180,573)(181,563)(182,566)(183,574)(184,552)
(185,560)(186,575)(187,553)(188,556)(189,564)(190,567)(191,557)(192,565)
(193,568)(194,571)(195,554)(196,569)(197,572)(198,555)(199,558)(200,561)
(201,676)(202,684)(203,687)(204,695)(205,698)(206,688)(207,691)(208,699)
(209,677)(210,685)(211,700)(212,678)(213,681)(214,689)(215,692)(216,682)
(217,690)(218,693)(219,696)(220,679)(221,694)(222,697)(223,680)(224,683)
(225,686)(226,651)(227,659)(228,662)(229,670)(230,673)(231,663)(232,666)
(233,674)(234,652)(235,660)(236,675)(237,653)(238,656)(239,664)(240,667)
(241,657)(242,665)(243,668)(244,671)(245,654)(246,669)(247,672)(248,655)
(249,658)(250,661)(251,626)(252,634)(253,637)(254,645)(255,648)(256,638)
(257,641)(258,649)(259,627)(260,635)(261,650)(262,628)(263,631)(264,639)
(265,642)(266,632)(267,640)(268,643)(269,646)(270,629)(271,644)(272,647)
(273,630)(274,633)(275,636)(276,601)(277,609)(278,612)(279,620)(280,623)
(281,613)(282,616)(283,624)(284,602)(285,610)(286,625)(287,603)(288,606)
(289,614)(290,617)(291,607)(292,615)(293,618)(294,621)(295,604)(296,619)
(297,622)(298,605)(299,608)(300,611)(301,751)(302,759)(303,762)(304,770)
(305,773)(306,763)(307,766)(308,774)(309,752)(310,760)(311,775)(312,753)
(313,756)(314,764)(315,767)(316,757)(317,765)(318,768)(319,771)(320,754)
(321,769)(322,772)(323,755)(324,758)(325,761)(326,776)(327,784)(328,787)
(329,795)(330,798)(331,788)(332,791)(333,799)(334,777)(335,785)(336,800)
(337,778)(338,781)(339,789)(340,792)(341,782)(342,790)(343,793)(344,796)
(345,779)(346,794)(347,797)(348,780)(349,783)(350,786)(351,701)(352,709)
(353,712)(354,720)(355,723)(356,713)(357,716)(358,724)(359,702)(360,710)
(361,725)(362,703)(363,706)(364,714)(365,717)(366,707)(367,715)(368,718)
(369,721)(370,704)(371,719)(372,722)(373,705)(374,708)(375,711)(376,726)
(377,734)(378,737)(379,745)(380,748)(381,738)(382,741)(383,749)(384,727)
(385,735)(386,750)(387,728)(388,731)(389,739)(390,742)(391,732)(392,740)
(393,743)(394,746)(395,729)(396,744)(397,747)(398,730)(399,733)(400,736);;
s2 := ( 1,307)( 2,306)( 3,310)( 4,309)( 5,308)( 6,302)( 7,301)( 8,305)
( 9,304)( 10,303)( 11,322)( 12,321)( 13,325)( 14,324)( 15,323)( 16,317)
( 17,316)( 18,320)( 19,319)( 20,318)( 21,312)( 22,311)( 23,315)( 24,314)
( 25,313)( 26,332)( 27,331)( 28,335)( 29,334)( 30,333)( 31,327)( 32,326)
( 33,330)( 34,329)( 35,328)( 36,347)( 37,346)( 38,350)( 39,349)( 40,348)
( 41,342)( 42,341)( 43,345)( 44,344)( 45,343)( 46,337)( 47,336)( 48,340)
( 49,339)( 50,338)( 51,357)( 52,356)( 53,360)( 54,359)( 55,358)( 56,352)
( 57,351)( 58,355)( 59,354)( 60,353)( 61,372)( 62,371)( 63,375)( 64,374)
( 65,373)( 66,367)( 67,366)( 68,370)( 69,369)( 70,368)( 71,362)( 72,361)
( 73,365)( 74,364)( 75,363)( 76,382)( 77,381)( 78,385)( 79,384)( 80,383)
( 81,377)( 82,376)( 83,380)( 84,379)( 85,378)( 86,397)( 87,396)( 88,400)
( 89,399)( 90,398)( 91,392)( 92,391)( 93,395)( 94,394)( 95,393)( 96,387)
( 97,386)( 98,390)( 99,389)(100,388)(101,232)(102,231)(103,235)(104,234)
(105,233)(106,227)(107,226)(108,230)(109,229)(110,228)(111,247)(112,246)
(113,250)(114,249)(115,248)(116,242)(117,241)(118,245)(119,244)(120,243)
(121,237)(122,236)(123,240)(124,239)(125,238)(126,207)(127,206)(128,210)
(129,209)(130,208)(131,202)(132,201)(133,205)(134,204)(135,203)(136,222)
(137,221)(138,225)(139,224)(140,223)(141,217)(142,216)(143,220)(144,219)
(145,218)(146,212)(147,211)(148,215)(149,214)(150,213)(151,282)(152,281)
(153,285)(154,284)(155,283)(156,277)(157,276)(158,280)(159,279)(160,278)
(161,297)(162,296)(163,300)(164,299)(165,298)(166,292)(167,291)(168,295)
(169,294)(170,293)(171,287)(172,286)(173,290)(174,289)(175,288)(176,257)
(177,256)(178,260)(179,259)(180,258)(181,252)(182,251)(183,255)(184,254)
(185,253)(186,272)(187,271)(188,275)(189,274)(190,273)(191,267)(192,266)
(193,270)(194,269)(195,268)(196,262)(197,261)(198,265)(199,264)(200,263)
(401,707)(402,706)(403,710)(404,709)(405,708)(406,702)(407,701)(408,705)
(409,704)(410,703)(411,722)(412,721)(413,725)(414,724)(415,723)(416,717)
(417,716)(418,720)(419,719)(420,718)(421,712)(422,711)(423,715)(424,714)
(425,713)(426,732)(427,731)(428,735)(429,734)(430,733)(431,727)(432,726)
(433,730)(434,729)(435,728)(436,747)(437,746)(438,750)(439,749)(440,748)
(441,742)(442,741)(443,745)(444,744)(445,743)(446,737)(447,736)(448,740)
(449,739)(450,738)(451,757)(452,756)(453,760)(454,759)(455,758)(456,752)
(457,751)(458,755)(459,754)(460,753)(461,772)(462,771)(463,775)(464,774)
(465,773)(466,767)(467,766)(468,770)(469,769)(470,768)(471,762)(472,761)
(473,765)(474,764)(475,763)(476,782)(477,781)(478,785)(479,784)(480,783)
(481,777)(482,776)(483,780)(484,779)(485,778)(486,797)(487,796)(488,800)
(489,799)(490,798)(491,792)(492,791)(493,795)(494,794)(495,793)(496,787)
(497,786)(498,790)(499,789)(500,788)(501,632)(502,631)(503,635)(504,634)
(505,633)(506,627)(507,626)(508,630)(509,629)(510,628)(511,647)(512,646)
(513,650)(514,649)(515,648)(516,642)(517,641)(518,645)(519,644)(520,643)
(521,637)(522,636)(523,640)(524,639)(525,638)(526,607)(527,606)(528,610)
(529,609)(530,608)(531,602)(532,601)(533,605)(534,604)(535,603)(536,622)
(537,621)(538,625)(539,624)(540,623)(541,617)(542,616)(543,620)(544,619)
(545,618)(546,612)(547,611)(548,615)(549,614)(550,613)(551,682)(552,681)
(553,685)(554,684)(555,683)(556,677)(557,676)(558,680)(559,679)(560,678)
(561,697)(562,696)(563,700)(564,699)(565,698)(566,692)(567,691)(568,695)
(569,694)(570,693)(571,687)(572,686)(573,690)(574,689)(575,688)(576,657)
(577,656)(578,660)(579,659)(580,658)(581,652)(582,651)(583,655)(584,654)
(585,653)(586,672)(587,671)(588,675)(589,674)(590,673)(591,667)(592,666)
(593,670)(594,669)(595,668)(596,662)(597,661)(598,665)(599,664)(600,663);;
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*s0*s1*s2*s0*s1*s2*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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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);
s1 := Sym(800)!( 1,401)( 2,409)( 3,412)( 4,420)( 5,423)( 6,413)( 7,416)
( 8,424)( 9,402)( 10,410)( 11,425)( 12,403)( 13,406)( 14,414)( 15,417)
( 16,407)( 17,415)( 18,418)( 19,421)( 20,404)( 21,419)( 22,422)( 23,405)
( 24,408)( 25,411)( 26,426)( 27,434)( 28,437)( 29,445)( 30,448)( 31,438)
( 32,441)( 33,449)( 34,427)( 35,435)( 36,450)( 37,428)( 38,431)( 39,439)
( 40,442)( 41,432)( 42,440)( 43,443)( 44,446)( 45,429)( 46,444)( 47,447)
( 48,430)( 49,433)( 50,436)( 51,451)( 52,459)( 53,462)( 54,470)( 55,473)
( 56,463)( 57,466)( 58,474)( 59,452)( 60,460)( 61,475)( 62,453)( 63,456)
( 64,464)( 65,467)( 66,457)( 67,465)( 68,468)( 69,471)( 70,454)( 71,469)
( 72,472)( 73,455)( 74,458)( 75,461)( 76,476)( 77,484)( 78,487)( 79,495)
( 80,498)( 81,488)( 82,491)( 83,499)( 84,477)( 85,485)( 86,500)( 87,478)
( 88,481)( 89,489)( 90,492)( 91,482)( 92,490)( 93,493)( 94,496)( 95,479)
( 96,494)( 97,497)( 98,480)( 99,483)(100,486)(101,526)(102,534)(103,537)
(104,545)(105,548)(106,538)(107,541)(108,549)(109,527)(110,535)(111,550)
(112,528)(113,531)(114,539)(115,542)(116,532)(117,540)(118,543)(119,546)
(120,529)(121,544)(122,547)(123,530)(124,533)(125,536)(126,501)(127,509)
(128,512)(129,520)(130,523)(131,513)(132,516)(133,524)(134,502)(135,510)
(136,525)(137,503)(138,506)(139,514)(140,517)(141,507)(142,515)(143,518)
(144,521)(145,504)(146,519)(147,522)(148,505)(149,508)(150,511)(151,576)
(152,584)(153,587)(154,595)(155,598)(156,588)(157,591)(158,599)(159,577)
(160,585)(161,600)(162,578)(163,581)(164,589)(165,592)(166,582)(167,590)
(168,593)(169,596)(170,579)(171,594)(172,597)(173,580)(174,583)(175,586)
(176,551)(177,559)(178,562)(179,570)(180,573)(181,563)(182,566)(183,574)
(184,552)(185,560)(186,575)(187,553)(188,556)(189,564)(190,567)(191,557)
(192,565)(193,568)(194,571)(195,554)(196,569)(197,572)(198,555)(199,558)
(200,561)(201,676)(202,684)(203,687)(204,695)(205,698)(206,688)(207,691)
(208,699)(209,677)(210,685)(211,700)(212,678)(213,681)(214,689)(215,692)
(216,682)(217,690)(218,693)(219,696)(220,679)(221,694)(222,697)(223,680)
(224,683)(225,686)(226,651)(227,659)(228,662)(229,670)(230,673)(231,663)
(232,666)(233,674)(234,652)(235,660)(236,675)(237,653)(238,656)(239,664)
(240,667)(241,657)(242,665)(243,668)(244,671)(245,654)(246,669)(247,672)
(248,655)(249,658)(250,661)(251,626)(252,634)(253,637)(254,645)(255,648)
(256,638)(257,641)(258,649)(259,627)(260,635)(261,650)(262,628)(263,631)
(264,639)(265,642)(266,632)(267,640)(268,643)(269,646)(270,629)(271,644)
(272,647)(273,630)(274,633)(275,636)(276,601)(277,609)(278,612)(279,620)
(280,623)(281,613)(282,616)(283,624)(284,602)(285,610)(286,625)(287,603)
(288,606)(289,614)(290,617)(291,607)(292,615)(293,618)(294,621)(295,604)
(296,619)(297,622)(298,605)(299,608)(300,611)(301,751)(302,759)(303,762)
(304,770)(305,773)(306,763)(307,766)(308,774)(309,752)(310,760)(311,775)
(312,753)(313,756)(314,764)(315,767)(316,757)(317,765)(318,768)(319,771)
(320,754)(321,769)(322,772)(323,755)(324,758)(325,761)(326,776)(327,784)
(328,787)(329,795)(330,798)(331,788)(332,791)(333,799)(334,777)(335,785)
(336,800)(337,778)(338,781)(339,789)(340,792)(341,782)(342,790)(343,793)
(344,796)(345,779)(346,794)(347,797)(348,780)(349,783)(350,786)(351,701)
(352,709)(353,712)(354,720)(355,723)(356,713)(357,716)(358,724)(359,702)
(360,710)(361,725)(362,703)(363,706)(364,714)(365,717)(366,707)(367,715)
(368,718)(369,721)(370,704)(371,719)(372,722)(373,705)(374,708)(375,711)
(376,726)(377,734)(378,737)(379,745)(380,748)(381,738)(382,741)(383,749)
(384,727)(385,735)(386,750)(387,728)(388,731)(389,739)(390,742)(391,732)
(392,740)(393,743)(394,746)(395,729)(396,744)(397,747)(398,730)(399,733)
(400,736);
s2 := Sym(800)!( 1,307)( 2,306)( 3,310)( 4,309)( 5,308)( 6,302)( 7,301)
( 8,305)( 9,304)( 10,303)( 11,322)( 12,321)( 13,325)( 14,324)( 15,323)
( 16,317)( 17,316)( 18,320)( 19,319)( 20,318)( 21,312)( 22,311)( 23,315)
( 24,314)( 25,313)( 26,332)( 27,331)( 28,335)( 29,334)( 30,333)( 31,327)
( 32,326)( 33,330)( 34,329)( 35,328)( 36,347)( 37,346)( 38,350)( 39,349)
( 40,348)( 41,342)( 42,341)( 43,345)( 44,344)( 45,343)( 46,337)( 47,336)
( 48,340)( 49,339)( 50,338)( 51,357)( 52,356)( 53,360)( 54,359)( 55,358)
( 56,352)( 57,351)( 58,355)( 59,354)( 60,353)( 61,372)( 62,371)( 63,375)
( 64,374)( 65,373)( 66,367)( 67,366)( 68,370)( 69,369)( 70,368)( 71,362)
( 72,361)( 73,365)( 74,364)( 75,363)( 76,382)( 77,381)( 78,385)( 79,384)
( 80,383)( 81,377)( 82,376)( 83,380)( 84,379)( 85,378)( 86,397)( 87,396)
( 88,400)( 89,399)( 90,398)( 91,392)( 92,391)( 93,395)( 94,394)( 95,393)
( 96,387)( 97,386)( 98,390)( 99,389)(100,388)(101,232)(102,231)(103,235)
(104,234)(105,233)(106,227)(107,226)(108,230)(109,229)(110,228)(111,247)
(112,246)(113,250)(114,249)(115,248)(116,242)(117,241)(118,245)(119,244)
(120,243)(121,237)(122,236)(123,240)(124,239)(125,238)(126,207)(127,206)
(128,210)(129,209)(130,208)(131,202)(132,201)(133,205)(134,204)(135,203)
(136,222)(137,221)(138,225)(139,224)(140,223)(141,217)(142,216)(143,220)
(144,219)(145,218)(146,212)(147,211)(148,215)(149,214)(150,213)(151,282)
(152,281)(153,285)(154,284)(155,283)(156,277)(157,276)(158,280)(159,279)
(160,278)(161,297)(162,296)(163,300)(164,299)(165,298)(166,292)(167,291)
(168,295)(169,294)(170,293)(171,287)(172,286)(173,290)(174,289)(175,288)
(176,257)(177,256)(178,260)(179,259)(180,258)(181,252)(182,251)(183,255)
(184,254)(185,253)(186,272)(187,271)(188,275)(189,274)(190,273)(191,267)
(192,266)(193,270)(194,269)(195,268)(196,262)(197,261)(198,265)(199,264)
(200,263)(401,707)(402,706)(403,710)(404,709)(405,708)(406,702)(407,701)
(408,705)(409,704)(410,703)(411,722)(412,721)(413,725)(414,724)(415,723)
(416,717)(417,716)(418,720)(419,719)(420,718)(421,712)(422,711)(423,715)
(424,714)(425,713)(426,732)(427,731)(428,735)(429,734)(430,733)(431,727)
(432,726)(433,730)(434,729)(435,728)(436,747)(437,746)(438,750)(439,749)
(440,748)(441,742)(442,741)(443,745)(444,744)(445,743)(446,737)(447,736)
(448,740)(449,739)(450,738)(451,757)(452,756)(453,760)(454,759)(455,758)
(456,752)(457,751)(458,755)(459,754)(460,753)(461,772)(462,771)(463,775)
(464,774)(465,773)(466,767)(467,766)(468,770)(469,769)(470,768)(471,762)
(472,761)(473,765)(474,764)(475,763)(476,782)(477,781)(478,785)(479,784)
(480,783)(481,777)(482,776)(483,780)(484,779)(485,778)(486,797)(487,796)
(488,800)(489,799)(490,798)(491,792)(492,791)(493,795)(494,794)(495,793)
(496,787)(497,786)(498,790)(499,789)(500,788)(501,632)(502,631)(503,635)
(504,634)(505,633)(506,627)(507,626)(508,630)(509,629)(510,628)(511,647)
(512,646)(513,650)(514,649)(515,648)(516,642)(517,641)(518,645)(519,644)
(520,643)(521,637)(522,636)(523,640)(524,639)(525,638)(526,607)(527,606)
(528,610)(529,609)(530,608)(531,602)(532,601)(533,605)(534,604)(535,603)
(536,622)(537,621)(538,625)(539,624)(540,623)(541,617)(542,616)(543,620)
(544,619)(545,618)(546,612)(547,611)(548,615)(549,614)(550,613)(551,682)
(552,681)(553,685)(554,684)(555,683)(556,677)(557,676)(558,680)(559,679)
(560,678)(561,697)(562,696)(563,700)(564,699)(565,698)(566,692)(567,691)
(568,695)(569,694)(570,693)(571,687)(572,686)(573,690)(574,689)(575,688)
(576,657)(577,656)(578,660)(579,659)(580,658)(581,652)(582,651)(583,655)
(584,654)(585,653)(586,672)(587,671)(588,675)(589,674)(590,673)(591,667)
(592,666)(593,670)(594,669)(595,668)(596,662)(597,661)(598,665)(599,664)
(600,663);
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*s0*s1*s2*s0*s1*s2*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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;
References : None.
to this polytope