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