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