Polytope of Type {5,10,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,10,20}*2000a
if this polytope has a name.
Group : SmallGroup(2000,372)
Rank : 4
Schlafli Type : {5,10,20}
Number of vertices, edges, etc : 5, 25, 100, 20
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 10
Special Properties :
Universal
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 : {5,10,10}*1000a
4-fold quotients : {5,10,5}*500
5-fold quotients : {5,2,20}*400
10-fold quotients : {5,2,10}*200
20-fold quotients : {5,2,5}*100
25-fold quotients : {5,2,4}*80
50-fold quotients : {5,2,2}*40
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)( 31,106)
( 32,110)( 33,109)( 34,108)( 35,107)( 36,111)( 37,115)( 38,114)( 39,113)
( 40,112)( 41,116)( 42,120)( 43,119)( 44,118)( 45,117)( 46,121)( 47,125)
( 48,124)( 49,123)( 50,122)( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)
( 56, 81)( 57, 85)( 58, 84)( 59, 83)( 60, 82)( 61, 86)( 62, 90)( 63, 89)
( 64, 88)( 65, 87)( 66, 91)( 67, 95)( 68, 94)( 69, 93)( 70, 92)( 71, 96)
( 72,100)( 73, 99)( 74, 98)( 75, 97)(127,130)(128,129)(132,135)(133,134)
(137,140)(138,139)(142,145)(143,144)(147,150)(148,149)(151,226)(152,230)
(153,229)(154,228)(155,227)(156,231)(157,235)(158,234)(159,233)(160,232)
(161,236)(162,240)(163,239)(164,238)(165,237)(166,241)(167,245)(168,244)
(169,243)(170,242)(171,246)(172,250)(173,249)(174,248)(175,247)(176,201)
(177,205)(178,204)(179,203)(180,202)(181,206)(182,210)(183,209)(184,208)
(185,207)(186,211)(187,215)(188,214)(189,213)(190,212)(191,216)(192,220)
(193,219)(194,218)(195,217)(196,221)(197,225)(198,224)(199,223)(200,222)
(252,255)(253,254)(257,260)(258,259)(262,265)(263,264)(267,270)(268,269)
(272,275)(273,274)(276,351)(277,355)(278,354)(279,353)(280,352)(281,356)
(282,360)(283,359)(284,358)(285,357)(286,361)(287,365)(288,364)(289,363)
(290,362)(291,366)(292,370)(293,369)(294,368)(295,367)(296,371)(297,375)
(298,374)(299,373)(300,372)(301,326)(302,330)(303,329)(304,328)(305,327)
(306,331)(307,335)(308,334)(309,333)(310,332)(311,336)(312,340)(313,339)
(314,338)(315,337)(316,341)(317,345)(318,344)(319,343)(320,342)(321,346)
(322,350)(323,349)(324,348)(325,347)(377,380)(378,379)(382,385)(383,384)
(387,390)(388,389)(392,395)(393,394)(397,400)(398,399)(401,476)(402,480)
(403,479)(404,478)(405,477)(406,481)(407,485)(408,484)(409,483)(410,482)
(411,486)(412,490)(413,489)(414,488)(415,487)(416,491)(417,495)(418,494)
(419,493)(420,492)(421,496)(422,500)(423,499)(424,498)(425,497)(426,451)
(427,455)(428,454)(429,453)(430,452)(431,456)(432,460)(433,459)(434,458)
(435,457)(436,461)(437,465)(438,464)(439,463)(440,462)(441,466)(442,470)
(443,469)(444,468)(445,467)(446,471)(447,475)(448,474)(449,473)(450,472);;
s1 := ( 1, 26)( 2, 30)( 3, 29)( 4, 28)( 5, 27)( 6, 32)( 7, 31)( 8, 35)
( 9, 34)( 10, 33)( 11, 38)( 12, 37)( 13, 36)( 14, 40)( 15, 39)( 16, 44)
( 17, 43)( 18, 42)( 19, 41)( 20, 45)( 21, 50)( 22, 49)( 23, 48)( 24, 47)
( 25, 46)( 51,101)( 52,105)( 53,104)( 54,103)( 55,102)( 56,107)( 57,106)
( 58,110)( 59,109)( 60,108)( 61,113)( 62,112)( 63,111)( 64,115)( 65,114)
( 66,119)( 67,118)( 68,117)( 69,116)( 70,120)( 71,125)( 72,124)( 73,123)
( 74,122)( 75,121)( 77, 80)( 78, 79)( 81, 82)( 83, 85)( 86, 88)( 89, 90)
( 91, 94)( 92, 93)( 96,100)( 97, 99)(126,151)(127,155)(128,154)(129,153)
(130,152)(131,157)(132,156)(133,160)(134,159)(135,158)(136,163)(137,162)
(138,161)(139,165)(140,164)(141,169)(142,168)(143,167)(144,166)(145,170)
(146,175)(147,174)(148,173)(149,172)(150,171)(176,226)(177,230)(178,229)
(179,228)(180,227)(181,232)(182,231)(183,235)(184,234)(185,233)(186,238)
(187,237)(188,236)(189,240)(190,239)(191,244)(192,243)(193,242)(194,241)
(195,245)(196,250)(197,249)(198,248)(199,247)(200,246)(202,205)(203,204)
(206,207)(208,210)(211,213)(214,215)(216,219)(217,218)(221,225)(222,224)
(251,276)(252,280)(253,279)(254,278)(255,277)(256,282)(257,281)(258,285)
(259,284)(260,283)(261,288)(262,287)(263,286)(264,290)(265,289)(266,294)
(267,293)(268,292)(269,291)(270,295)(271,300)(272,299)(273,298)(274,297)
(275,296)(301,351)(302,355)(303,354)(304,353)(305,352)(306,357)(307,356)
(308,360)(309,359)(310,358)(311,363)(312,362)(313,361)(314,365)(315,364)
(316,369)(317,368)(318,367)(319,366)(320,370)(321,375)(322,374)(323,373)
(324,372)(325,371)(327,330)(328,329)(331,332)(333,335)(336,338)(339,340)
(341,344)(342,343)(346,350)(347,349)(376,401)(377,405)(378,404)(379,403)
(380,402)(381,407)(382,406)(383,410)(384,409)(385,408)(386,413)(387,412)
(388,411)(389,415)(390,414)(391,419)(392,418)(393,417)(394,416)(395,420)
(396,425)(397,424)(398,423)(399,422)(400,421)(426,476)(427,480)(428,479)
(429,478)(430,477)(431,482)(432,481)(433,485)(434,484)(435,483)(436,488)
(437,487)(438,486)(439,490)(440,489)(441,494)(442,493)(443,492)(444,491)
(445,495)(446,500)(447,499)(448,498)(449,497)(450,496)(452,455)(453,454)
(456,457)(458,460)(461,463)(464,465)(466,469)(467,468)(471,475)(472,474);;
s2 := ( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 11, 21)( 12, 25)( 13, 24)
( 14, 23)( 15, 22)( 17, 20)( 18, 19)( 26, 31)( 27, 35)( 28, 34)( 29, 33)
( 30, 32)( 36, 46)( 37, 50)( 38, 49)( 39, 48)( 40, 47)( 42, 45)( 43, 44)
( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 71)( 62, 75)( 63, 74)
( 64, 73)( 65, 72)( 67, 70)( 68, 69)( 76, 81)( 77, 85)( 78, 84)( 79, 83)
( 80, 82)( 86, 96)( 87,100)( 88, 99)( 89, 98)( 90, 97)( 92, 95)( 93, 94)
(101,106)(102,110)(103,109)(104,108)(105,107)(111,121)(112,125)(113,124)
(114,123)(115,122)(117,120)(118,119)(126,131)(127,135)(128,134)(129,133)
(130,132)(136,146)(137,150)(138,149)(139,148)(140,147)(142,145)(143,144)
(151,156)(152,160)(153,159)(154,158)(155,157)(161,171)(162,175)(163,174)
(164,173)(165,172)(167,170)(168,169)(176,181)(177,185)(178,184)(179,183)
(180,182)(186,196)(187,200)(188,199)(189,198)(190,197)(192,195)(193,194)
(201,206)(202,210)(203,209)(204,208)(205,207)(211,221)(212,225)(213,224)
(214,223)(215,222)(217,220)(218,219)(226,231)(227,235)(228,234)(229,233)
(230,232)(236,246)(237,250)(238,249)(239,248)(240,247)(242,245)(243,244)
(251,381)(252,385)(253,384)(254,383)(255,382)(256,376)(257,380)(258,379)
(259,378)(260,377)(261,396)(262,400)(263,399)(264,398)(265,397)(266,391)
(267,395)(268,394)(269,393)(270,392)(271,386)(272,390)(273,389)(274,388)
(275,387)(276,406)(277,410)(278,409)(279,408)(280,407)(281,401)(282,405)
(283,404)(284,403)(285,402)(286,421)(287,425)(288,424)(289,423)(290,422)
(291,416)(292,420)(293,419)(294,418)(295,417)(296,411)(297,415)(298,414)
(299,413)(300,412)(301,431)(302,435)(303,434)(304,433)(305,432)(306,426)
(307,430)(308,429)(309,428)(310,427)(311,446)(312,450)(313,449)(314,448)
(315,447)(316,441)(317,445)(318,444)(319,443)(320,442)(321,436)(322,440)
(323,439)(324,438)(325,437)(326,456)(327,460)(328,459)(329,458)(330,457)
(331,451)(332,455)(333,454)(334,453)(335,452)(336,471)(337,475)(338,474)
(339,473)(340,472)(341,466)(342,470)(343,469)(344,468)(345,467)(346,461)
(347,465)(348,464)(349,463)(350,462)(351,481)(352,485)(353,484)(354,483)
(355,482)(356,476)(357,480)(358,479)(359,478)(360,477)(361,496)(362,500)
(363,499)(364,498)(365,497)(366,491)(367,495)(368,494)(369,493)(370,492)
(371,486)(372,490)(373,489)(374,488)(375,487);;
s3 := ( 1,251)( 2,255)( 3,254)( 4,253)( 5,252)( 6,271)( 7,275)( 8,274)
( 9,273)( 10,272)( 11,266)( 12,270)( 13,269)( 14,268)( 15,267)( 16,261)
( 17,265)( 18,264)( 19,263)( 20,262)( 21,256)( 22,260)( 23,259)( 24,258)
( 25,257)( 26,276)( 27,280)( 28,279)( 29,278)( 30,277)( 31,296)( 32,300)
( 33,299)( 34,298)( 35,297)( 36,291)( 37,295)( 38,294)( 39,293)( 40,292)
( 41,286)( 42,290)( 43,289)( 44,288)( 45,287)( 46,281)( 47,285)( 48,284)
( 49,283)( 50,282)( 51,301)( 52,305)( 53,304)( 54,303)( 55,302)( 56,321)
( 57,325)( 58,324)( 59,323)( 60,322)( 61,316)( 62,320)( 63,319)( 64,318)
( 65,317)( 66,311)( 67,315)( 68,314)( 69,313)( 70,312)( 71,306)( 72,310)
( 73,309)( 74,308)( 75,307)( 76,326)( 77,330)( 78,329)( 79,328)( 80,327)
( 81,346)( 82,350)( 83,349)( 84,348)( 85,347)( 86,341)( 87,345)( 88,344)
( 89,343)( 90,342)( 91,336)( 92,340)( 93,339)( 94,338)( 95,337)( 96,331)
( 97,335)( 98,334)( 99,333)(100,332)(101,351)(102,355)(103,354)(104,353)
(105,352)(106,371)(107,375)(108,374)(109,373)(110,372)(111,366)(112,370)
(113,369)(114,368)(115,367)(116,361)(117,365)(118,364)(119,363)(120,362)
(121,356)(122,360)(123,359)(124,358)(125,357)(126,376)(127,380)(128,379)
(129,378)(130,377)(131,396)(132,400)(133,399)(134,398)(135,397)(136,391)
(137,395)(138,394)(139,393)(140,392)(141,386)(142,390)(143,389)(144,388)
(145,387)(146,381)(147,385)(148,384)(149,383)(150,382)(151,401)(152,405)
(153,404)(154,403)(155,402)(156,421)(157,425)(158,424)(159,423)(160,422)
(161,416)(162,420)(163,419)(164,418)(165,417)(166,411)(167,415)(168,414)
(169,413)(170,412)(171,406)(172,410)(173,409)(174,408)(175,407)(176,426)
(177,430)(178,429)(179,428)(180,427)(181,446)(182,450)(183,449)(184,448)
(185,447)(186,441)(187,445)(188,444)(189,443)(190,442)(191,436)(192,440)
(193,439)(194,438)(195,437)(196,431)(197,435)(198,434)(199,433)(200,432)
(201,451)(202,455)(203,454)(204,453)(205,452)(206,471)(207,475)(208,474)
(209,473)(210,472)(211,466)(212,470)(213,469)(214,468)(215,467)(216,461)
(217,465)(218,464)(219,463)(220,462)(221,456)(222,460)(223,459)(224,458)
(225,457)(226,476)(227,480)(228,479)(229,478)(230,477)(231,496)(232,500)
(233,499)(234,498)(235,497)(236,491)(237,495)(238,494)(239,493)(240,492)
(241,486)(242,490)(243,489)(244,488)(245,487)(246,481)(247,485)(248,484)
(249,483)(250,482);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(500)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)
( 31,106)( 32,110)( 33,109)( 34,108)( 35,107)( 36,111)( 37,115)( 38,114)
( 39,113)( 40,112)( 41,116)( 42,120)( 43,119)( 44,118)( 45,117)( 46,121)
( 47,125)( 48,124)( 49,123)( 50,122)( 51, 76)( 52, 80)( 53, 79)( 54, 78)
( 55, 77)( 56, 81)( 57, 85)( 58, 84)( 59, 83)( 60, 82)( 61, 86)( 62, 90)
( 63, 89)( 64, 88)( 65, 87)( 66, 91)( 67, 95)( 68, 94)( 69, 93)( 70, 92)
( 71, 96)( 72,100)( 73, 99)( 74, 98)( 75, 97)(127,130)(128,129)(132,135)
(133,134)(137,140)(138,139)(142,145)(143,144)(147,150)(148,149)(151,226)
(152,230)(153,229)(154,228)(155,227)(156,231)(157,235)(158,234)(159,233)
(160,232)(161,236)(162,240)(163,239)(164,238)(165,237)(166,241)(167,245)
(168,244)(169,243)(170,242)(171,246)(172,250)(173,249)(174,248)(175,247)
(176,201)(177,205)(178,204)(179,203)(180,202)(181,206)(182,210)(183,209)
(184,208)(185,207)(186,211)(187,215)(188,214)(189,213)(190,212)(191,216)
(192,220)(193,219)(194,218)(195,217)(196,221)(197,225)(198,224)(199,223)
(200,222)(252,255)(253,254)(257,260)(258,259)(262,265)(263,264)(267,270)
(268,269)(272,275)(273,274)(276,351)(277,355)(278,354)(279,353)(280,352)
(281,356)(282,360)(283,359)(284,358)(285,357)(286,361)(287,365)(288,364)
(289,363)(290,362)(291,366)(292,370)(293,369)(294,368)(295,367)(296,371)
(297,375)(298,374)(299,373)(300,372)(301,326)(302,330)(303,329)(304,328)
(305,327)(306,331)(307,335)(308,334)(309,333)(310,332)(311,336)(312,340)
(313,339)(314,338)(315,337)(316,341)(317,345)(318,344)(319,343)(320,342)
(321,346)(322,350)(323,349)(324,348)(325,347)(377,380)(378,379)(382,385)
(383,384)(387,390)(388,389)(392,395)(393,394)(397,400)(398,399)(401,476)
(402,480)(403,479)(404,478)(405,477)(406,481)(407,485)(408,484)(409,483)
(410,482)(411,486)(412,490)(413,489)(414,488)(415,487)(416,491)(417,495)
(418,494)(419,493)(420,492)(421,496)(422,500)(423,499)(424,498)(425,497)
(426,451)(427,455)(428,454)(429,453)(430,452)(431,456)(432,460)(433,459)
(434,458)(435,457)(436,461)(437,465)(438,464)(439,463)(440,462)(441,466)
(442,470)(443,469)(444,468)(445,467)(446,471)(447,475)(448,474)(449,473)
(450,472);
s1 := Sym(500)!( 1, 26)( 2, 30)( 3, 29)( 4, 28)( 5, 27)( 6, 32)( 7, 31)
( 8, 35)( 9, 34)( 10, 33)( 11, 38)( 12, 37)( 13, 36)( 14, 40)( 15, 39)
( 16, 44)( 17, 43)( 18, 42)( 19, 41)( 20, 45)( 21, 50)( 22, 49)( 23, 48)
( 24, 47)( 25, 46)( 51,101)( 52,105)( 53,104)( 54,103)( 55,102)( 56,107)
( 57,106)( 58,110)( 59,109)( 60,108)( 61,113)( 62,112)( 63,111)( 64,115)
( 65,114)( 66,119)( 67,118)( 68,117)( 69,116)( 70,120)( 71,125)( 72,124)
( 73,123)( 74,122)( 75,121)( 77, 80)( 78, 79)( 81, 82)( 83, 85)( 86, 88)
( 89, 90)( 91, 94)( 92, 93)( 96,100)( 97, 99)(126,151)(127,155)(128,154)
(129,153)(130,152)(131,157)(132,156)(133,160)(134,159)(135,158)(136,163)
(137,162)(138,161)(139,165)(140,164)(141,169)(142,168)(143,167)(144,166)
(145,170)(146,175)(147,174)(148,173)(149,172)(150,171)(176,226)(177,230)
(178,229)(179,228)(180,227)(181,232)(182,231)(183,235)(184,234)(185,233)
(186,238)(187,237)(188,236)(189,240)(190,239)(191,244)(192,243)(193,242)
(194,241)(195,245)(196,250)(197,249)(198,248)(199,247)(200,246)(202,205)
(203,204)(206,207)(208,210)(211,213)(214,215)(216,219)(217,218)(221,225)
(222,224)(251,276)(252,280)(253,279)(254,278)(255,277)(256,282)(257,281)
(258,285)(259,284)(260,283)(261,288)(262,287)(263,286)(264,290)(265,289)
(266,294)(267,293)(268,292)(269,291)(270,295)(271,300)(272,299)(273,298)
(274,297)(275,296)(301,351)(302,355)(303,354)(304,353)(305,352)(306,357)
(307,356)(308,360)(309,359)(310,358)(311,363)(312,362)(313,361)(314,365)
(315,364)(316,369)(317,368)(318,367)(319,366)(320,370)(321,375)(322,374)
(323,373)(324,372)(325,371)(327,330)(328,329)(331,332)(333,335)(336,338)
(339,340)(341,344)(342,343)(346,350)(347,349)(376,401)(377,405)(378,404)
(379,403)(380,402)(381,407)(382,406)(383,410)(384,409)(385,408)(386,413)
(387,412)(388,411)(389,415)(390,414)(391,419)(392,418)(393,417)(394,416)
(395,420)(396,425)(397,424)(398,423)(399,422)(400,421)(426,476)(427,480)
(428,479)(429,478)(430,477)(431,482)(432,481)(433,485)(434,484)(435,483)
(436,488)(437,487)(438,486)(439,490)(440,489)(441,494)(442,493)(443,492)
(444,491)(445,495)(446,500)(447,499)(448,498)(449,497)(450,496)(452,455)
(453,454)(456,457)(458,460)(461,463)(464,465)(466,469)(467,468)(471,475)
(472,474);
s2 := Sym(500)!( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 11, 21)( 12, 25)
( 13, 24)( 14, 23)( 15, 22)( 17, 20)( 18, 19)( 26, 31)( 27, 35)( 28, 34)
( 29, 33)( 30, 32)( 36, 46)( 37, 50)( 38, 49)( 39, 48)( 40, 47)( 42, 45)
( 43, 44)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 71)( 62, 75)
( 63, 74)( 64, 73)( 65, 72)( 67, 70)( 68, 69)( 76, 81)( 77, 85)( 78, 84)
( 79, 83)( 80, 82)( 86, 96)( 87,100)( 88, 99)( 89, 98)( 90, 97)( 92, 95)
( 93, 94)(101,106)(102,110)(103,109)(104,108)(105,107)(111,121)(112,125)
(113,124)(114,123)(115,122)(117,120)(118,119)(126,131)(127,135)(128,134)
(129,133)(130,132)(136,146)(137,150)(138,149)(139,148)(140,147)(142,145)
(143,144)(151,156)(152,160)(153,159)(154,158)(155,157)(161,171)(162,175)
(163,174)(164,173)(165,172)(167,170)(168,169)(176,181)(177,185)(178,184)
(179,183)(180,182)(186,196)(187,200)(188,199)(189,198)(190,197)(192,195)
(193,194)(201,206)(202,210)(203,209)(204,208)(205,207)(211,221)(212,225)
(213,224)(214,223)(215,222)(217,220)(218,219)(226,231)(227,235)(228,234)
(229,233)(230,232)(236,246)(237,250)(238,249)(239,248)(240,247)(242,245)
(243,244)(251,381)(252,385)(253,384)(254,383)(255,382)(256,376)(257,380)
(258,379)(259,378)(260,377)(261,396)(262,400)(263,399)(264,398)(265,397)
(266,391)(267,395)(268,394)(269,393)(270,392)(271,386)(272,390)(273,389)
(274,388)(275,387)(276,406)(277,410)(278,409)(279,408)(280,407)(281,401)
(282,405)(283,404)(284,403)(285,402)(286,421)(287,425)(288,424)(289,423)
(290,422)(291,416)(292,420)(293,419)(294,418)(295,417)(296,411)(297,415)
(298,414)(299,413)(300,412)(301,431)(302,435)(303,434)(304,433)(305,432)
(306,426)(307,430)(308,429)(309,428)(310,427)(311,446)(312,450)(313,449)
(314,448)(315,447)(316,441)(317,445)(318,444)(319,443)(320,442)(321,436)
(322,440)(323,439)(324,438)(325,437)(326,456)(327,460)(328,459)(329,458)
(330,457)(331,451)(332,455)(333,454)(334,453)(335,452)(336,471)(337,475)
(338,474)(339,473)(340,472)(341,466)(342,470)(343,469)(344,468)(345,467)
(346,461)(347,465)(348,464)(349,463)(350,462)(351,481)(352,485)(353,484)
(354,483)(355,482)(356,476)(357,480)(358,479)(359,478)(360,477)(361,496)
(362,500)(363,499)(364,498)(365,497)(366,491)(367,495)(368,494)(369,493)
(370,492)(371,486)(372,490)(373,489)(374,488)(375,487);
s3 := Sym(500)!( 1,251)( 2,255)( 3,254)( 4,253)( 5,252)( 6,271)( 7,275)
( 8,274)( 9,273)( 10,272)( 11,266)( 12,270)( 13,269)( 14,268)( 15,267)
( 16,261)( 17,265)( 18,264)( 19,263)( 20,262)( 21,256)( 22,260)( 23,259)
( 24,258)( 25,257)( 26,276)( 27,280)( 28,279)( 29,278)( 30,277)( 31,296)
( 32,300)( 33,299)( 34,298)( 35,297)( 36,291)( 37,295)( 38,294)( 39,293)
( 40,292)( 41,286)( 42,290)( 43,289)( 44,288)( 45,287)( 46,281)( 47,285)
( 48,284)( 49,283)( 50,282)( 51,301)( 52,305)( 53,304)( 54,303)( 55,302)
( 56,321)( 57,325)( 58,324)( 59,323)( 60,322)( 61,316)( 62,320)( 63,319)
( 64,318)( 65,317)( 66,311)( 67,315)( 68,314)( 69,313)( 70,312)( 71,306)
( 72,310)( 73,309)( 74,308)( 75,307)( 76,326)( 77,330)( 78,329)( 79,328)
( 80,327)( 81,346)( 82,350)( 83,349)( 84,348)( 85,347)( 86,341)( 87,345)
( 88,344)( 89,343)( 90,342)( 91,336)( 92,340)( 93,339)( 94,338)( 95,337)
( 96,331)( 97,335)( 98,334)( 99,333)(100,332)(101,351)(102,355)(103,354)
(104,353)(105,352)(106,371)(107,375)(108,374)(109,373)(110,372)(111,366)
(112,370)(113,369)(114,368)(115,367)(116,361)(117,365)(118,364)(119,363)
(120,362)(121,356)(122,360)(123,359)(124,358)(125,357)(126,376)(127,380)
(128,379)(129,378)(130,377)(131,396)(132,400)(133,399)(134,398)(135,397)
(136,391)(137,395)(138,394)(139,393)(140,392)(141,386)(142,390)(143,389)
(144,388)(145,387)(146,381)(147,385)(148,384)(149,383)(150,382)(151,401)
(152,405)(153,404)(154,403)(155,402)(156,421)(157,425)(158,424)(159,423)
(160,422)(161,416)(162,420)(163,419)(164,418)(165,417)(166,411)(167,415)
(168,414)(169,413)(170,412)(171,406)(172,410)(173,409)(174,408)(175,407)
(176,426)(177,430)(178,429)(179,428)(180,427)(181,446)(182,450)(183,449)
(184,448)(185,447)(186,441)(187,445)(188,444)(189,443)(190,442)(191,436)
(192,440)(193,439)(194,438)(195,437)(196,431)(197,435)(198,434)(199,433)
(200,432)(201,451)(202,455)(203,454)(204,453)(205,452)(206,471)(207,475)
(208,474)(209,473)(210,472)(211,466)(212,470)(213,469)(214,468)(215,467)
(216,461)(217,465)(218,464)(219,463)(220,462)(221,456)(222,460)(223,459)
(224,458)(225,457)(226,476)(227,480)(228,479)(229,478)(230,477)(231,496)
(232,500)(233,499)(234,498)(235,497)(236,491)(237,495)(238,494)(239,493)
(240,492)(241,486)(242,490)(243,489)(244,488)(245,487)(246,481)(247,485)
(248,484)(249,483)(250,482);
poly := sub<Sym(500)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope