Polytope of Type {4,150}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,150}*1200b
if this polytope has a name.
Group : SmallGroup(1200,198)
Rank : 3
Schlafli Type : {4,150}
Number of vertices, edges, etc : 4, 300, 150
Order of s₀s₁s₂ : 150
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,75}*600
   5-fold quotients : {4,30}*240b
   10-fold quotients : {4,15}*120
   25-fold quotients : {4,6}*48c
   50-fold quotients : {4,3}*24
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);;
s1 := (  3,  4)(  5, 17)(  6, 18)(  7, 20)(  8, 19)(  9, 13)( 10, 14)( 11, 16)
( 12, 15)( 21, 97)( 22, 98)( 23,100)( 24, 99)( 25, 93)( 26, 94)( 27, 96)
( 28, 95)( 29, 89)( 30, 90)( 31, 92)( 32, 91)( 33, 85)( 34, 86)( 35, 88)
( 36, 87)( 37, 81)( 38, 82)( 39, 84)( 40, 83)( 41, 77)( 42, 78)( 43, 80)
( 44, 79)( 45, 73)( 46, 74)( 47, 76)( 48, 75)( 49, 69)( 50, 70)( 51, 72)
( 52, 71)( 53, 65)( 54, 66)( 55, 68)( 56, 67)( 57, 61)( 58, 62)( 59, 64)
( 60, 63)(101,201)(102,202)(103,204)(104,203)(105,217)(106,218)(107,220)
(108,219)(109,213)(110,214)(111,216)(112,215)(113,209)(114,210)(115,212)
(116,211)(117,205)(118,206)(119,208)(120,207)(121,297)(122,298)(123,300)
(124,299)(125,293)(126,294)(127,296)(128,295)(129,289)(130,290)(131,292)
(132,291)(133,285)(134,286)(135,288)(136,287)(137,281)(138,282)(139,284)
(140,283)(141,277)(142,278)(143,280)(144,279)(145,273)(146,274)(147,276)
(148,275)(149,269)(150,270)(151,272)(152,271)(153,265)(154,266)(155,268)
(156,267)(157,261)(158,262)(159,264)(160,263)(161,257)(162,258)(163,260)
(164,259)(165,253)(166,254)(167,256)(168,255)(169,249)(170,250)(171,252)
(172,251)(173,245)(174,246)(175,248)(176,247)(177,241)(178,242)(179,244)
(180,243)(181,237)(182,238)(183,240)(184,239)(185,233)(186,234)(187,236)
(188,235)(189,229)(190,230)(191,232)(192,231)(193,225)(194,226)(195,228)
(196,227)(197,221)(198,222)(199,224)(200,223)(303,304)(305,317)(306,318)
(307,320)(308,319)(309,313)(310,314)(311,316)(312,315)(321,397)(322,398)
(323,400)(324,399)(325,393)(326,394)(327,396)(328,395)(329,389)(330,390)
(331,392)(332,391)(333,385)(334,386)(335,388)(336,387)(337,381)(338,382)
(339,384)(340,383)(341,377)(342,378)(343,380)(344,379)(345,373)(346,374)
(347,376)(348,375)(349,369)(350,370)(351,372)(352,371)(353,365)(354,366)
(355,368)(356,367)(357,361)(358,362)(359,364)(360,363)(401,501)(402,502)
(403,504)(404,503)(405,517)(406,518)(407,520)(408,519)(409,513)(410,514)
(411,516)(412,515)(413,509)(414,510)(415,512)(416,511)(417,505)(418,506)
(419,508)(420,507)(421,597)(422,598)(423,600)(424,599)(425,593)(426,594)
(427,596)(428,595)(429,589)(430,590)(431,592)(432,591)(433,585)(434,586)
(435,588)(436,587)(437,581)(438,582)(439,584)(440,583)(441,577)(442,578)
(443,580)(444,579)(445,573)(446,574)(447,576)(448,575)(449,569)(450,570)
(451,572)(452,571)(453,565)(454,566)(455,568)(456,567)(457,561)(458,562)
(459,564)(460,563)(461,557)(462,558)(463,560)(464,559)(465,553)(466,554)
(467,556)(468,555)(469,549)(470,550)(471,552)(472,551)(473,545)(474,546)
(475,548)(476,547)(477,541)(478,542)(479,544)(480,543)(481,537)(482,538)
(483,540)(484,539)(485,533)(486,534)(487,536)(488,535)(489,529)(490,530)
(491,532)(492,531)(493,525)(494,526)(495,528)(496,527)(497,521)(498,522)
(499,524)(500,523);;
s2 := (  1,421)(  2,424)(  3,423)(  4,422)(  5,437)(  6,440)(  7,439)(  8,438)
(  9,433)( 10,436)( 11,435)( 12,434)( 13,429)( 14,432)( 15,431)( 16,430)
( 17,425)( 18,428)( 19,427)( 20,426)( 21,401)( 22,404)( 23,403)( 24,402)
( 25,417)( 26,420)( 27,419)( 28,418)( 29,413)( 30,416)( 31,415)( 32,414)
( 33,409)( 34,412)( 35,411)( 36,410)( 37,405)( 38,408)( 39,407)( 40,406)
( 41,497)( 42,500)( 43,499)( 44,498)( 45,493)( 46,496)( 47,495)( 48,494)
( 49,489)( 50,492)( 51,491)( 52,490)( 53,485)( 54,488)( 55,487)( 56,486)
( 57,481)( 58,484)( 59,483)( 60,482)( 61,477)( 62,480)( 63,479)( 64,478)
( 65,473)( 66,476)( 67,475)( 68,474)( 69,469)( 70,472)( 71,471)( 72,470)
( 73,465)( 74,468)( 75,467)( 76,466)( 77,461)( 78,464)( 79,463)( 80,462)
( 81,457)( 82,460)( 83,459)( 84,458)( 85,453)( 86,456)( 87,455)( 88,454)
( 89,449)( 90,452)( 91,451)( 92,450)( 93,445)( 94,448)( 95,447)( 96,446)
( 97,441)( 98,444)( 99,443)(100,442)(101,321)(102,324)(103,323)(104,322)
(105,337)(106,340)(107,339)(108,338)(109,333)(110,336)(111,335)(112,334)
(113,329)(114,332)(115,331)(116,330)(117,325)(118,328)(119,327)(120,326)
(121,301)(122,304)(123,303)(124,302)(125,317)(126,320)(127,319)(128,318)
(129,313)(130,316)(131,315)(132,314)(133,309)(134,312)(135,311)(136,310)
(137,305)(138,308)(139,307)(140,306)(141,397)(142,400)(143,399)(144,398)
(145,393)(146,396)(147,395)(148,394)(149,389)(150,392)(151,391)(152,390)
(153,385)(154,388)(155,387)(156,386)(157,381)(158,384)(159,383)(160,382)
(161,377)(162,380)(163,379)(164,378)(165,373)(166,376)(167,375)(168,374)
(169,369)(170,372)(171,371)(172,370)(173,365)(174,368)(175,367)(176,366)
(177,361)(178,364)(179,363)(180,362)(181,357)(182,360)(183,359)(184,358)
(185,353)(186,356)(187,355)(188,354)(189,349)(190,352)(191,351)(192,350)
(193,345)(194,348)(195,347)(196,346)(197,341)(198,344)(199,343)(200,342)
(201,521)(202,524)(203,523)(204,522)(205,537)(206,540)(207,539)(208,538)
(209,533)(210,536)(211,535)(212,534)(213,529)(214,532)(215,531)(216,530)
(217,525)(218,528)(219,527)(220,526)(221,501)(222,504)(223,503)(224,502)
(225,517)(226,520)(227,519)(228,518)(229,513)(230,516)(231,515)(232,514)
(233,509)(234,512)(235,511)(236,510)(237,505)(238,508)(239,507)(240,506)
(241,597)(242,600)(243,599)(244,598)(245,593)(246,596)(247,595)(248,594)
(249,589)(250,592)(251,591)(252,590)(253,585)(254,588)(255,587)(256,586)
(257,581)(258,584)(259,583)(260,582)(261,577)(262,580)(263,579)(264,578)
(265,573)(266,576)(267,575)(268,574)(269,569)(270,572)(271,571)(272,570)
(273,565)(274,568)(275,567)(276,566)(277,561)(278,564)(279,563)(280,562)
(281,557)(282,560)(283,559)(284,558)(285,553)(286,556)(287,555)(288,554)
(289,549)(290,552)(291,551)(292,550)(293,545)(294,548)(295,547)(296,546)
(297,541)(298,544)(299,543)(300,542);;
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*s2*s1*s0*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*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*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*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*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*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(600)!(  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);
s1 := Sym(600)!(  3,  4)(  5, 17)(  6, 18)(  7, 20)(  8, 19)(  9, 13)( 10, 14)
( 11, 16)( 12, 15)( 21, 97)( 22, 98)( 23,100)( 24, 99)( 25, 93)( 26, 94)
( 27, 96)( 28, 95)( 29, 89)( 30, 90)( 31, 92)( 32, 91)( 33, 85)( 34, 86)
( 35, 88)( 36, 87)( 37, 81)( 38, 82)( 39, 84)( 40, 83)( 41, 77)( 42, 78)
( 43, 80)( 44, 79)( 45, 73)( 46, 74)( 47, 76)( 48, 75)( 49, 69)( 50, 70)
( 51, 72)( 52, 71)( 53, 65)( 54, 66)( 55, 68)( 56, 67)( 57, 61)( 58, 62)
( 59, 64)( 60, 63)(101,201)(102,202)(103,204)(104,203)(105,217)(106,218)
(107,220)(108,219)(109,213)(110,214)(111,216)(112,215)(113,209)(114,210)
(115,212)(116,211)(117,205)(118,206)(119,208)(120,207)(121,297)(122,298)
(123,300)(124,299)(125,293)(126,294)(127,296)(128,295)(129,289)(130,290)
(131,292)(132,291)(133,285)(134,286)(135,288)(136,287)(137,281)(138,282)
(139,284)(140,283)(141,277)(142,278)(143,280)(144,279)(145,273)(146,274)
(147,276)(148,275)(149,269)(150,270)(151,272)(152,271)(153,265)(154,266)
(155,268)(156,267)(157,261)(158,262)(159,264)(160,263)(161,257)(162,258)
(163,260)(164,259)(165,253)(166,254)(167,256)(168,255)(169,249)(170,250)
(171,252)(172,251)(173,245)(174,246)(175,248)(176,247)(177,241)(178,242)
(179,244)(180,243)(181,237)(182,238)(183,240)(184,239)(185,233)(186,234)
(187,236)(188,235)(189,229)(190,230)(191,232)(192,231)(193,225)(194,226)
(195,228)(196,227)(197,221)(198,222)(199,224)(200,223)(303,304)(305,317)
(306,318)(307,320)(308,319)(309,313)(310,314)(311,316)(312,315)(321,397)
(322,398)(323,400)(324,399)(325,393)(326,394)(327,396)(328,395)(329,389)
(330,390)(331,392)(332,391)(333,385)(334,386)(335,388)(336,387)(337,381)
(338,382)(339,384)(340,383)(341,377)(342,378)(343,380)(344,379)(345,373)
(346,374)(347,376)(348,375)(349,369)(350,370)(351,372)(352,371)(353,365)
(354,366)(355,368)(356,367)(357,361)(358,362)(359,364)(360,363)(401,501)
(402,502)(403,504)(404,503)(405,517)(406,518)(407,520)(408,519)(409,513)
(410,514)(411,516)(412,515)(413,509)(414,510)(415,512)(416,511)(417,505)
(418,506)(419,508)(420,507)(421,597)(422,598)(423,600)(424,599)(425,593)
(426,594)(427,596)(428,595)(429,589)(430,590)(431,592)(432,591)(433,585)
(434,586)(435,588)(436,587)(437,581)(438,582)(439,584)(440,583)(441,577)
(442,578)(443,580)(444,579)(445,573)(446,574)(447,576)(448,575)(449,569)
(450,570)(451,572)(452,571)(453,565)(454,566)(455,568)(456,567)(457,561)
(458,562)(459,564)(460,563)(461,557)(462,558)(463,560)(464,559)(465,553)
(466,554)(467,556)(468,555)(469,549)(470,550)(471,552)(472,551)(473,545)
(474,546)(475,548)(476,547)(477,541)(478,542)(479,544)(480,543)(481,537)
(482,538)(483,540)(484,539)(485,533)(486,534)(487,536)(488,535)(489,529)
(490,530)(491,532)(492,531)(493,525)(494,526)(495,528)(496,527)(497,521)
(498,522)(499,524)(500,523);
s2 := Sym(600)!(  1,421)(  2,424)(  3,423)(  4,422)(  5,437)(  6,440)(  7,439)
(  8,438)(  9,433)( 10,436)( 11,435)( 12,434)( 13,429)( 14,432)( 15,431)
( 16,430)( 17,425)( 18,428)( 19,427)( 20,426)( 21,401)( 22,404)( 23,403)
( 24,402)( 25,417)( 26,420)( 27,419)( 28,418)( 29,413)( 30,416)( 31,415)
( 32,414)( 33,409)( 34,412)( 35,411)( 36,410)( 37,405)( 38,408)( 39,407)
( 40,406)( 41,497)( 42,500)( 43,499)( 44,498)( 45,493)( 46,496)( 47,495)
( 48,494)( 49,489)( 50,492)( 51,491)( 52,490)( 53,485)( 54,488)( 55,487)
( 56,486)( 57,481)( 58,484)( 59,483)( 60,482)( 61,477)( 62,480)( 63,479)
( 64,478)( 65,473)( 66,476)( 67,475)( 68,474)( 69,469)( 70,472)( 71,471)
( 72,470)( 73,465)( 74,468)( 75,467)( 76,466)( 77,461)( 78,464)( 79,463)
( 80,462)( 81,457)( 82,460)( 83,459)( 84,458)( 85,453)( 86,456)( 87,455)
( 88,454)( 89,449)( 90,452)( 91,451)( 92,450)( 93,445)( 94,448)( 95,447)
( 96,446)( 97,441)( 98,444)( 99,443)(100,442)(101,321)(102,324)(103,323)
(104,322)(105,337)(106,340)(107,339)(108,338)(109,333)(110,336)(111,335)
(112,334)(113,329)(114,332)(115,331)(116,330)(117,325)(118,328)(119,327)
(120,326)(121,301)(122,304)(123,303)(124,302)(125,317)(126,320)(127,319)
(128,318)(129,313)(130,316)(131,315)(132,314)(133,309)(134,312)(135,311)
(136,310)(137,305)(138,308)(139,307)(140,306)(141,397)(142,400)(143,399)
(144,398)(145,393)(146,396)(147,395)(148,394)(149,389)(150,392)(151,391)
(152,390)(153,385)(154,388)(155,387)(156,386)(157,381)(158,384)(159,383)
(160,382)(161,377)(162,380)(163,379)(164,378)(165,373)(166,376)(167,375)
(168,374)(169,369)(170,372)(171,371)(172,370)(173,365)(174,368)(175,367)
(176,366)(177,361)(178,364)(179,363)(180,362)(181,357)(182,360)(183,359)
(184,358)(185,353)(186,356)(187,355)(188,354)(189,349)(190,352)(191,351)
(192,350)(193,345)(194,348)(195,347)(196,346)(197,341)(198,344)(199,343)
(200,342)(201,521)(202,524)(203,523)(204,522)(205,537)(206,540)(207,539)
(208,538)(209,533)(210,536)(211,535)(212,534)(213,529)(214,532)(215,531)
(216,530)(217,525)(218,528)(219,527)(220,526)(221,501)(222,504)(223,503)
(224,502)(225,517)(226,520)(227,519)(228,518)(229,513)(230,516)(231,515)
(232,514)(233,509)(234,512)(235,511)(236,510)(237,505)(238,508)(239,507)
(240,506)(241,597)(242,600)(243,599)(244,598)(245,593)(246,596)(247,595)
(248,594)(249,589)(250,592)(251,591)(252,590)(253,585)(254,588)(255,587)
(256,586)(257,581)(258,584)(259,583)(260,582)(261,577)(262,580)(263,579)
(264,578)(265,573)(266,576)(267,575)(268,574)(269,569)(270,572)(271,571)
(272,570)(273,565)(274,568)(275,567)(276,566)(277,561)(278,564)(279,563)
(280,562)(281,557)(282,560)(283,559)(284,558)(285,553)(286,556)(287,555)
(288,554)(289,549)(290,552)(291,551)(292,550)(293,545)(294,548)(295,547)
(296,546)(297,541)(298,544)(299,543)(300,542);
poly := sub<Sym(600)|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*s2*s1*s0*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*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*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*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*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*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