Polytope of Type {150,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {150,4}*1200c
if this polytope has a name.
Group : SmallGroup(1200,198)
Rank : 3
Schlafli Type : {150,4}
Number of vertices, edges, etc : 150, 300, 4
Order of s0s1s2 : 75
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat
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
5-fold quotients : {30,4}*240c
10-fold quotients : {15,4}*120
25-fold quotients : {6,4}*48b
50-fold quotients : {3,4}*24
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 := ( 1,421)( 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);;
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*s2*s1*s0*s2*s1*s0*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 ];;
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)!( 1,421)( 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);
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*s2*s1*s0*s2*s1*s0*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 >;
References : None.
to this polytope