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Polytope of Type {10,10,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,10,10}*2000a
if this polytope has a name.
Group : SmallGroup(2000,501)
Rank : 4
Schlafli Type : {10,10,10}
Number of vertices, edges, etc : 10, 50, 50, 10
Order of s0s1s2s3 : 10
Order of s0s1s2s3s2s1 : 10
Special Properties :
   Orientable
   Flat
   Self-Dual
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, {10,10,5}*1000a
   4-fold quotients : {5,10,5}*500
   5-fold quotients : {10,2,10}*400
   10-fold quotients : {5,2,10}*200, {10,2,5}*200
   20-fold quotients : {5,2,5}*100
   25-fold quotients : {2,2,10}*80, {10,2,2}*80
   50-fold quotients : {2,2,5}*40, {5,2,2}*40
   125-fold quotients : {2,2,2}*16
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 := (  1,276)(  2,280)(  3,279)(  4,278)(  5,277)(  6,282)(  7,281)(  8,285)
(  9,284)( 10,283)( 11,288)( 12,287)( 13,286)( 14,290)( 15,289)( 16,294)
( 17,293)( 18,292)( 19,291)( 20,295)( 21,300)( 22,299)( 23,298)( 24,297)
( 25,296)( 26,251)( 27,255)( 28,254)( 29,253)( 30,252)( 31,257)( 32,256)
( 33,260)( 34,259)( 35,258)( 36,263)( 37,262)( 38,261)( 39,265)( 40,264)
( 41,269)( 42,268)( 43,267)( 44,266)( 45,270)( 46,275)( 47,274)( 48,273)
( 49,272)( 50,271)( 51,351)( 52,355)( 53,354)( 54,353)( 55,352)( 56,357)
( 57,356)( 58,360)( 59,359)( 60,358)( 61,363)( 62,362)( 63,361)( 64,365)
( 65,364)( 66,369)( 67,368)( 68,367)( 69,366)( 70,370)( 71,375)( 72,374)
( 73,373)( 74,372)( 75,371)( 76,326)( 77,330)( 78,329)( 79,328)( 80,327)
( 81,332)( 82,331)( 83,335)( 84,334)( 85,333)( 86,338)( 87,337)( 88,336)
( 89,340)( 90,339)( 91,344)( 92,343)( 93,342)( 94,341)( 95,345)( 96,350)
( 97,349)( 98,348)( 99,347)(100,346)(101,301)(102,305)(103,304)(104,303)
(105,302)(106,307)(107,306)(108,310)(109,309)(110,308)(111,313)(112,312)
(113,311)(114,315)(115,314)(116,319)(117,318)(118,317)(119,316)(120,320)
(121,325)(122,324)(123,323)(124,322)(125,321)(126,401)(127,405)(128,404)
(129,403)(130,402)(131,407)(132,406)(133,410)(134,409)(135,408)(136,413)
(137,412)(138,411)(139,415)(140,414)(141,419)(142,418)(143,417)(144,416)
(145,420)(146,425)(147,424)(148,423)(149,422)(150,421)(151,376)(152,380)
(153,379)(154,378)(155,377)(156,382)(157,381)(158,385)(159,384)(160,383)
(161,388)(162,387)(163,386)(164,390)(165,389)(166,394)(167,393)(168,392)
(169,391)(170,395)(171,400)(172,399)(173,398)(174,397)(175,396)(176,476)
(177,480)(178,479)(179,478)(180,477)(181,482)(182,481)(183,485)(184,484)
(185,483)(186,488)(187,487)(188,486)(189,490)(190,489)(191,494)(192,493)
(193,492)(194,491)(195,495)(196,500)(197,499)(198,498)(199,497)(200,496)
(201,451)(202,455)(203,454)(204,453)(205,452)(206,457)(207,456)(208,460)
(209,459)(210,458)(211,463)(212,462)(213,461)(214,465)(215,464)(216,469)
(217,468)(218,467)(219,466)(220,470)(221,475)(222,474)(223,473)(224,472)
(225,471)(226,426)(227,430)(228,429)(229,428)(230,427)(231,432)(232,431)
(233,435)(234,434)(235,433)(236,438)(237,437)(238,436)(239,440)(240,439)
(241,444)(242,443)(243,442)(244,441)(245,445)(246,450)(247,449)(248,448)
(249,447)(250,446);;
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)
(251,256)(252,260)(253,259)(254,258)(255,257)(261,271)(262,275)(263,274)
(264,273)(265,272)(267,270)(268,269)(276,281)(277,285)(278,284)(279,283)
(280,282)(286,296)(287,300)(288,299)(289,298)(290,297)(292,295)(293,294)
(301,306)(302,310)(303,309)(304,308)(305,307)(311,321)(312,325)(313,324)
(314,323)(315,322)(317,320)(318,319)(326,331)(327,335)(328,334)(329,333)
(330,332)(336,346)(337,350)(338,349)(339,348)(340,347)(342,345)(343,344)
(351,356)(352,360)(353,359)(354,358)(355,357)(361,371)(362,375)(363,374)
(364,373)(365,372)(367,370)(368,369)(376,381)(377,385)(378,384)(379,383)
(380,382)(386,396)(387,400)(388,399)(389,398)(390,397)(392,395)(393,394)
(401,406)(402,410)(403,409)(404,408)(405,407)(411,421)(412,425)(413,424)
(414,423)(415,422)(417,420)(418,419)(426,431)(427,435)(428,434)(429,433)
(430,432)(436,446)(437,450)(438,449)(439,448)(440,447)(442,445)(443,444)
(451,456)(452,460)(453,459)(454,458)(455,457)(461,471)(462,475)(463,474)
(464,473)(465,472)(467,470)(468,469)(476,481)(477,485)(478,484)(479,483)
(480,482)(486,496)(487,500)(488,499)(489,498)(490,497)(492,495)(493,494);;
s3 := (  1,126)(  2,130)(  3,129)(  4,128)(  5,127)(  6,146)(  7,150)(  8,149)
(  9,148)( 10,147)( 11,141)( 12,145)( 13,144)( 14,143)( 15,142)( 16,136)
( 17,140)( 18,139)( 19,138)( 20,137)( 21,131)( 22,135)( 23,134)( 24,133)
( 25,132)( 26,151)( 27,155)( 28,154)( 29,153)( 30,152)( 31,171)( 32,175)
( 33,174)( 34,173)( 35,172)( 36,166)( 37,170)( 38,169)( 39,168)( 40,167)
( 41,161)( 42,165)( 43,164)( 44,163)( 45,162)( 46,156)( 47,160)( 48,159)
( 49,158)( 50,157)( 51,176)( 52,180)( 53,179)( 54,178)( 55,177)( 56,196)
( 57,200)( 58,199)( 59,198)( 60,197)( 61,191)( 62,195)( 63,194)( 64,193)
( 65,192)( 66,186)( 67,190)( 68,189)( 69,188)( 70,187)( 71,181)( 72,185)
( 73,184)( 74,183)( 75,182)( 76,201)( 77,205)( 78,204)( 79,203)( 80,202)
( 81,221)( 82,225)( 83,224)( 84,223)( 85,222)( 86,216)( 87,220)( 88,219)
( 89,218)( 90,217)( 91,211)( 92,215)( 93,214)( 94,213)( 95,212)( 96,206)
( 97,210)( 98,209)( 99,208)(100,207)(101,226)(102,230)(103,229)(104,228)
(105,227)(106,246)(107,250)(108,249)(109,248)(110,247)(111,241)(112,245)
(113,244)(114,243)(115,242)(116,236)(117,240)(118,239)(119,238)(120,237)
(121,231)(122,235)(123,234)(124,233)(125,232)(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);;
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*s2*s3*s2*s1*s0*s1*s0*s1*s2*s3*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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 ];;
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)!(  1,276)(  2,280)(  3,279)(  4,278)(  5,277)(  6,282)(  7,281)
(  8,285)(  9,284)( 10,283)( 11,288)( 12,287)( 13,286)( 14,290)( 15,289)
( 16,294)( 17,293)( 18,292)( 19,291)( 20,295)( 21,300)( 22,299)( 23,298)
( 24,297)( 25,296)( 26,251)( 27,255)( 28,254)( 29,253)( 30,252)( 31,257)
( 32,256)( 33,260)( 34,259)( 35,258)( 36,263)( 37,262)( 38,261)( 39,265)
( 40,264)( 41,269)( 42,268)( 43,267)( 44,266)( 45,270)( 46,275)( 47,274)
( 48,273)( 49,272)( 50,271)( 51,351)( 52,355)( 53,354)( 54,353)( 55,352)
( 56,357)( 57,356)( 58,360)( 59,359)( 60,358)( 61,363)( 62,362)( 63,361)
( 64,365)( 65,364)( 66,369)( 67,368)( 68,367)( 69,366)( 70,370)( 71,375)
( 72,374)( 73,373)( 74,372)( 75,371)( 76,326)( 77,330)( 78,329)( 79,328)
( 80,327)( 81,332)( 82,331)( 83,335)( 84,334)( 85,333)( 86,338)( 87,337)
( 88,336)( 89,340)( 90,339)( 91,344)( 92,343)( 93,342)( 94,341)( 95,345)
( 96,350)( 97,349)( 98,348)( 99,347)(100,346)(101,301)(102,305)(103,304)
(104,303)(105,302)(106,307)(107,306)(108,310)(109,309)(110,308)(111,313)
(112,312)(113,311)(114,315)(115,314)(116,319)(117,318)(118,317)(119,316)
(120,320)(121,325)(122,324)(123,323)(124,322)(125,321)(126,401)(127,405)
(128,404)(129,403)(130,402)(131,407)(132,406)(133,410)(134,409)(135,408)
(136,413)(137,412)(138,411)(139,415)(140,414)(141,419)(142,418)(143,417)
(144,416)(145,420)(146,425)(147,424)(148,423)(149,422)(150,421)(151,376)
(152,380)(153,379)(154,378)(155,377)(156,382)(157,381)(158,385)(159,384)
(160,383)(161,388)(162,387)(163,386)(164,390)(165,389)(166,394)(167,393)
(168,392)(169,391)(170,395)(171,400)(172,399)(173,398)(174,397)(175,396)
(176,476)(177,480)(178,479)(179,478)(180,477)(181,482)(182,481)(183,485)
(184,484)(185,483)(186,488)(187,487)(188,486)(189,490)(190,489)(191,494)
(192,493)(193,492)(194,491)(195,495)(196,500)(197,499)(198,498)(199,497)
(200,496)(201,451)(202,455)(203,454)(204,453)(205,452)(206,457)(207,456)
(208,460)(209,459)(210,458)(211,463)(212,462)(213,461)(214,465)(215,464)
(216,469)(217,468)(218,467)(219,466)(220,470)(221,475)(222,474)(223,473)
(224,472)(225,471)(226,426)(227,430)(228,429)(229,428)(230,427)(231,432)
(232,431)(233,435)(234,434)(235,433)(236,438)(237,437)(238,436)(239,440)
(240,439)(241,444)(242,443)(243,442)(244,441)(245,445)(246,450)(247,449)
(248,448)(249,447)(250,446);
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)(251,256)(252,260)(253,259)(254,258)(255,257)(261,271)(262,275)
(263,274)(264,273)(265,272)(267,270)(268,269)(276,281)(277,285)(278,284)
(279,283)(280,282)(286,296)(287,300)(288,299)(289,298)(290,297)(292,295)
(293,294)(301,306)(302,310)(303,309)(304,308)(305,307)(311,321)(312,325)
(313,324)(314,323)(315,322)(317,320)(318,319)(326,331)(327,335)(328,334)
(329,333)(330,332)(336,346)(337,350)(338,349)(339,348)(340,347)(342,345)
(343,344)(351,356)(352,360)(353,359)(354,358)(355,357)(361,371)(362,375)
(363,374)(364,373)(365,372)(367,370)(368,369)(376,381)(377,385)(378,384)
(379,383)(380,382)(386,396)(387,400)(388,399)(389,398)(390,397)(392,395)
(393,394)(401,406)(402,410)(403,409)(404,408)(405,407)(411,421)(412,425)
(413,424)(414,423)(415,422)(417,420)(418,419)(426,431)(427,435)(428,434)
(429,433)(430,432)(436,446)(437,450)(438,449)(439,448)(440,447)(442,445)
(443,444)(451,456)(452,460)(453,459)(454,458)(455,457)(461,471)(462,475)
(463,474)(464,473)(465,472)(467,470)(468,469)(476,481)(477,485)(478,484)
(479,483)(480,482)(486,496)(487,500)(488,499)(489,498)(490,497)(492,495)
(493,494);
s3 := Sym(500)!(  1,126)(  2,130)(  3,129)(  4,128)(  5,127)(  6,146)(  7,150)
(  8,149)(  9,148)( 10,147)( 11,141)( 12,145)( 13,144)( 14,143)( 15,142)
( 16,136)( 17,140)( 18,139)( 19,138)( 20,137)( 21,131)( 22,135)( 23,134)
( 24,133)( 25,132)( 26,151)( 27,155)( 28,154)( 29,153)( 30,152)( 31,171)
( 32,175)( 33,174)( 34,173)( 35,172)( 36,166)( 37,170)( 38,169)( 39,168)
( 40,167)( 41,161)( 42,165)( 43,164)( 44,163)( 45,162)( 46,156)( 47,160)
( 48,159)( 49,158)( 50,157)( 51,176)( 52,180)( 53,179)( 54,178)( 55,177)
( 56,196)( 57,200)( 58,199)( 59,198)( 60,197)( 61,191)( 62,195)( 63,194)
( 64,193)( 65,192)( 66,186)( 67,190)( 68,189)( 69,188)( 70,187)( 71,181)
( 72,185)( 73,184)( 74,183)( 75,182)( 76,201)( 77,205)( 78,204)( 79,203)
( 80,202)( 81,221)( 82,225)( 83,224)( 84,223)( 85,222)( 86,216)( 87,220)
( 88,219)( 89,218)( 90,217)( 91,211)( 92,215)( 93,214)( 94,213)( 95,212)
( 96,206)( 97,210)( 98,209)( 99,208)(100,207)(101,226)(102,230)(103,229)
(104,228)(105,227)(106,246)(107,250)(108,249)(109,248)(110,247)(111,241)
(112,245)(113,244)(114,243)(115,242)(116,236)(117,240)(118,239)(119,238)
(120,237)(121,231)(122,235)(123,234)(124,233)(125,232)(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);
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*s2*s3*s2*s1*s0*s1*s0*s1*s2*s3*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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 >; 
 
References : None.
to this polytope