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Polytope of Type {4,16,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,16,4}*512a
Also Known As : {{4,16|2},{16,4|2}}. if this polytope has another name.
Group : SmallGroup(512,407087)
Rank : 4
Schlafli Type : {4,16,4}
Number of vertices, edges, etc : 4, 32, 32, 4
Order of s0s1s2s3 : 16
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   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 : {4,8,4}*256d, {2,16,4}*256a, {4,16,2}*256a
   4-fold quotients : {4,4,4}*128, {2,8,4}*128a, {4,8,2}*128a, {2,16,2}*128
   8-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64, {2,8,2}*64
   16-fold quotients : {2,2,4}*32, {2,4,2}*32, {4,2,2}*32
   32-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1, 33)(  2, 34)(  3, 35)(  4, 36)(  5, 37)(  6, 38)(  7, 39)(  8, 40)
(  9, 41)( 10, 42)( 11, 43)( 12, 44)( 13, 45)( 14, 46)( 15, 47)( 16, 48)
( 17, 49)( 18, 50)( 19, 51)( 20, 52)( 21, 53)( 22, 54)( 23, 55)( 24, 56)
( 25, 57)( 26, 58)( 27, 59)( 28, 60)( 29, 61)( 30, 62)( 31, 63)( 32, 64)
( 65, 97)( 66, 98)( 67, 99)( 68,100)( 69,101)( 70,102)( 71,103)( 72,104)
( 73,105)( 74,106)( 75,107)( 76,108)( 77,109)( 78,110)( 79,111)( 80,112)
( 81,113)( 82,114)( 83,115)( 84,116)( 85,117)( 86,118)( 87,119)( 88,120)
( 89,121)( 90,122)( 91,123)( 92,124)( 93,125)( 94,126)( 95,127)( 96,128)
(129,161)(130,162)(131,163)(132,164)(133,165)(134,166)(135,167)(136,168)
(137,169)(138,170)(139,171)(140,172)(141,173)(142,174)(143,175)(144,176)
(145,177)(146,178)(147,179)(148,180)(149,181)(150,182)(151,183)(152,184)
(153,185)(154,186)(155,187)(156,188)(157,189)(158,190)(159,191)(160,192)
(193,225)(194,226)(195,227)(196,228)(197,229)(198,230)(199,231)(200,232)
(201,233)(202,234)(203,235)(204,236)(205,237)(206,238)(207,239)(208,240)
(209,241)(210,242)(211,243)(212,244)(213,245)(214,246)(215,247)(216,248)
(217,249)(218,250)(219,251)(220,252)(221,253)(222,254)(223,255)(224,256)
(257,289)(258,290)(259,291)(260,292)(261,293)(262,294)(263,295)(264,296)
(265,297)(266,298)(267,299)(268,300)(269,301)(270,302)(271,303)(272,304)
(273,305)(274,306)(275,307)(276,308)(277,309)(278,310)(279,311)(280,312)
(281,313)(282,314)(283,315)(284,316)(285,317)(286,318)(287,319)(288,320)
(321,353)(322,354)(323,355)(324,356)(325,357)(326,358)(327,359)(328,360)
(329,361)(330,362)(331,363)(332,364)(333,365)(334,366)(335,367)(336,368)
(337,369)(338,370)(339,371)(340,372)(341,373)(342,374)(343,375)(344,376)
(345,377)(346,378)(347,379)(348,380)(349,381)(350,382)(351,383)(352,384)
(385,417)(386,418)(387,419)(388,420)(389,421)(390,422)(391,423)(392,424)
(393,425)(394,426)(395,427)(396,428)(397,429)(398,430)(399,431)(400,432)
(401,433)(402,434)(403,435)(404,436)(405,437)(406,438)(407,439)(408,440)
(409,441)(410,442)(411,443)(412,444)(413,445)(414,446)(415,447)(416,448)
(449,481)(450,482)(451,483)(452,484)(453,485)(454,486)(455,487)(456,488)
(457,489)(458,490)(459,491)(460,492)(461,493)(462,494)(463,495)(464,496)
(465,497)(466,498)(467,499)(468,500)(469,501)(470,502)(471,503)(472,504)
(473,505)(474,506)(475,507)(476,508)(477,509)(478,510)(479,511)(480,512);;
s1 := (  1,257)(  2,258)(  3,260)(  4,259)(  5,261)(  6,262)(  7,264)(  8,263)
(  9,267)( 10,268)( 11,265)( 12,266)( 13,271)( 14,272)( 15,269)( 16,270)
( 17,273)( 18,274)( 19,276)( 20,275)( 21,277)( 22,278)( 23,280)( 24,279)
( 25,283)( 26,284)( 27,281)( 28,282)( 29,287)( 30,288)( 31,285)( 32,286)
( 33,305)( 34,306)( 35,308)( 36,307)( 37,309)( 38,310)( 39,312)( 40,311)
( 41,315)( 42,316)( 43,313)( 44,314)( 45,319)( 46,320)( 47,317)( 48,318)
( 49,289)( 50,290)( 51,292)( 52,291)( 53,293)( 54,294)( 55,296)( 56,295)
( 57,299)( 58,300)( 59,297)( 60,298)( 61,303)( 62,304)( 63,301)( 64,302)
( 65,329)( 66,330)( 67,332)( 68,331)( 69,333)( 70,334)( 71,336)( 72,335)
( 73,321)( 74,322)( 75,324)( 76,323)( 77,325)( 78,326)( 79,328)( 80,327)
( 81,345)( 82,346)( 83,348)( 84,347)( 85,349)( 86,350)( 87,352)( 88,351)
( 89,337)( 90,338)( 91,340)( 92,339)( 93,341)( 94,342)( 95,344)( 96,343)
( 97,377)( 98,378)( 99,380)(100,379)(101,381)(102,382)(103,384)(104,383)
(105,369)(106,370)(107,372)(108,371)(109,373)(110,374)(111,376)(112,375)
(113,361)(114,362)(115,364)(116,363)(117,365)(118,366)(119,368)(120,367)
(121,353)(122,354)(123,356)(124,355)(125,357)(126,358)(127,360)(128,359)
(129,401)(130,402)(131,404)(132,403)(133,405)(134,406)(135,408)(136,407)
(137,411)(138,412)(139,409)(140,410)(141,415)(142,416)(143,413)(144,414)
(145,385)(146,386)(147,388)(148,387)(149,389)(150,390)(151,392)(152,391)
(153,395)(154,396)(155,393)(156,394)(157,399)(158,400)(159,397)(160,398)
(161,417)(162,418)(163,420)(164,419)(165,421)(166,422)(167,424)(168,423)
(169,427)(170,428)(171,425)(172,426)(173,431)(174,432)(175,429)(176,430)
(177,433)(178,434)(179,436)(180,435)(181,437)(182,438)(183,440)(184,439)
(185,443)(186,444)(187,441)(188,442)(189,447)(190,448)(191,445)(192,446)
(193,473)(194,474)(195,476)(196,475)(197,477)(198,478)(199,480)(200,479)
(201,465)(202,466)(203,468)(204,467)(205,469)(206,470)(207,472)(208,471)
(209,457)(210,458)(211,460)(212,459)(213,461)(214,462)(215,464)(216,463)
(217,449)(218,450)(219,452)(220,451)(221,453)(222,454)(223,456)(224,455)
(225,489)(226,490)(227,492)(228,491)(229,493)(230,494)(231,496)(232,495)
(233,481)(234,482)(235,484)(236,483)(237,485)(238,486)(239,488)(240,487)
(241,505)(242,506)(243,508)(244,507)(245,509)(246,510)(247,512)(248,511)
(249,497)(250,498)(251,500)(252,499)(253,501)(254,502)(255,504)(256,503);;
s2 := (  1, 65)(  2, 66)(  3, 68)(  4, 67)(  5, 69)(  6, 70)(  7, 72)(  8, 71)
(  9, 75)( 10, 76)( 11, 73)( 12, 74)( 13, 79)( 14, 80)( 15, 77)( 16, 78)
( 17, 81)( 18, 82)( 19, 84)( 20, 83)( 21, 85)( 22, 86)( 23, 88)( 24, 87)
( 25, 91)( 26, 92)( 27, 89)( 28, 90)( 29, 95)( 30, 96)( 31, 93)( 32, 94)
( 33, 97)( 34, 98)( 35,100)( 36, 99)( 37,101)( 38,102)( 39,104)( 40,103)
( 41,107)( 42,108)( 43,105)( 44,106)( 45,111)( 46,112)( 47,109)( 48,110)
( 49,113)( 50,114)( 51,116)( 52,115)( 53,117)( 54,118)( 55,120)( 56,119)
( 57,123)( 58,124)( 59,121)( 60,122)( 61,127)( 62,128)( 63,125)( 64,126)
(129,193)(130,194)(131,196)(132,195)(133,197)(134,198)(135,200)(136,199)
(137,203)(138,204)(139,201)(140,202)(141,207)(142,208)(143,205)(144,206)
(145,209)(146,210)(147,212)(148,211)(149,213)(150,214)(151,216)(152,215)
(153,219)(154,220)(155,217)(156,218)(157,223)(158,224)(159,221)(160,222)
(161,225)(162,226)(163,228)(164,227)(165,229)(166,230)(167,232)(168,231)
(169,235)(170,236)(171,233)(172,234)(173,239)(174,240)(175,237)(176,238)
(177,241)(178,242)(179,244)(180,243)(181,245)(182,246)(183,248)(184,247)
(185,251)(186,252)(187,249)(188,250)(189,255)(190,256)(191,253)(192,254)
(257,321)(258,322)(259,324)(260,323)(261,325)(262,326)(263,328)(264,327)
(265,331)(266,332)(267,329)(268,330)(269,335)(270,336)(271,333)(272,334)
(273,337)(274,338)(275,340)(276,339)(277,341)(278,342)(279,344)(280,343)
(281,347)(282,348)(283,345)(284,346)(285,351)(286,352)(287,349)(288,350)
(289,353)(290,354)(291,356)(292,355)(293,357)(294,358)(295,360)(296,359)
(297,363)(298,364)(299,361)(300,362)(301,367)(302,368)(303,365)(304,366)
(305,369)(306,370)(307,372)(308,371)(309,373)(310,374)(311,376)(312,375)
(313,379)(314,380)(315,377)(316,378)(317,383)(318,384)(319,381)(320,382)
(385,449)(386,450)(387,452)(388,451)(389,453)(390,454)(391,456)(392,455)
(393,459)(394,460)(395,457)(396,458)(397,463)(398,464)(399,461)(400,462)
(401,465)(402,466)(403,468)(404,467)(405,469)(406,470)(407,472)(408,471)
(409,475)(410,476)(411,473)(412,474)(413,479)(414,480)(415,477)(416,478)
(417,481)(418,482)(419,484)(420,483)(421,485)(422,486)(423,488)(424,487)
(425,491)(426,492)(427,489)(428,490)(429,495)(430,496)(431,493)(432,494)
(433,497)(434,498)(435,500)(436,499)(437,501)(438,502)(439,504)(440,503)
(441,507)(442,508)(443,505)(444,506)(445,511)(446,512)(447,509)(448,510);;
s3 := (  1,161)(  2,162)(  3,163)(  4,164)(  5,165)(  6,166)(  7,167)(  8,168)
(  9,169)( 10,170)( 11,171)( 12,172)( 13,173)( 14,174)( 15,175)( 16,176)
( 17,177)( 18,178)( 19,179)( 20,180)( 21,181)( 22,182)( 23,183)( 24,184)
( 25,185)( 26,186)( 27,187)( 28,188)( 29,189)( 30,190)( 31,191)( 32,192)
( 33,129)( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,135)( 40,136)
( 41,137)( 42,138)( 43,139)( 44,140)( 45,141)( 46,142)( 47,143)( 48,144)
( 49,145)( 50,146)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)
( 57,153)( 58,154)( 59,155)( 60,156)( 61,157)( 62,158)( 63,159)( 64,160)
( 65,229)( 66,230)( 67,231)( 68,232)( 69,225)( 70,226)( 71,227)( 72,228)
( 73,237)( 74,238)( 75,239)( 76,240)( 77,233)( 78,234)( 79,235)( 80,236)
( 81,245)( 82,246)( 83,247)( 84,248)( 85,241)( 86,242)( 87,243)( 88,244)
( 89,253)( 90,254)( 91,255)( 92,256)( 93,249)( 94,250)( 95,251)( 96,252)
( 97,197)( 98,198)( 99,199)(100,200)(101,193)(102,194)(103,195)(104,196)
(105,205)(106,206)(107,207)(108,208)(109,201)(110,202)(111,203)(112,204)
(113,213)(114,214)(115,215)(116,216)(117,209)(118,210)(119,211)(120,212)
(121,221)(122,222)(123,223)(124,224)(125,217)(126,218)(127,219)(128,220)
(257,417)(258,418)(259,419)(260,420)(261,421)(262,422)(263,423)(264,424)
(265,425)(266,426)(267,427)(268,428)(269,429)(270,430)(271,431)(272,432)
(273,433)(274,434)(275,435)(276,436)(277,437)(278,438)(279,439)(280,440)
(281,441)(282,442)(283,443)(284,444)(285,445)(286,446)(287,447)(288,448)
(289,385)(290,386)(291,387)(292,388)(293,389)(294,390)(295,391)(296,392)
(297,393)(298,394)(299,395)(300,396)(301,397)(302,398)(303,399)(304,400)
(305,401)(306,402)(307,403)(308,404)(309,405)(310,406)(311,407)(312,408)
(313,409)(314,410)(315,411)(316,412)(317,413)(318,414)(319,415)(320,416)
(321,485)(322,486)(323,487)(324,488)(325,481)(326,482)(327,483)(328,484)
(329,493)(330,494)(331,495)(332,496)(333,489)(334,490)(335,491)(336,492)
(337,501)(338,502)(339,503)(340,504)(341,497)(342,498)(343,499)(344,500)
(345,509)(346,510)(347,511)(348,512)(349,505)(350,506)(351,507)(352,508)
(353,453)(354,454)(355,455)(356,456)(357,449)(358,450)(359,451)(360,452)
(361,461)(362,462)(363,463)(364,464)(365,457)(366,458)(367,459)(368,460)
(369,469)(370,470)(371,471)(372,472)(373,465)(374,466)(375,467)(376,468)
(377,477)(378,478)(379,479)(380,480)(381,473)(382,474)(383,475)(384,476);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(512)!(  1, 33)(  2, 34)(  3, 35)(  4, 36)(  5, 37)(  6, 38)(  7, 39)
(  8, 40)(  9, 41)( 10, 42)( 11, 43)( 12, 44)( 13, 45)( 14, 46)( 15, 47)
( 16, 48)( 17, 49)( 18, 50)( 19, 51)( 20, 52)( 21, 53)( 22, 54)( 23, 55)
( 24, 56)( 25, 57)( 26, 58)( 27, 59)( 28, 60)( 29, 61)( 30, 62)( 31, 63)
( 32, 64)( 65, 97)( 66, 98)( 67, 99)( 68,100)( 69,101)( 70,102)( 71,103)
( 72,104)( 73,105)( 74,106)( 75,107)( 76,108)( 77,109)( 78,110)( 79,111)
( 80,112)( 81,113)( 82,114)( 83,115)( 84,116)( 85,117)( 86,118)( 87,119)
( 88,120)( 89,121)( 90,122)( 91,123)( 92,124)( 93,125)( 94,126)( 95,127)
( 96,128)(129,161)(130,162)(131,163)(132,164)(133,165)(134,166)(135,167)
(136,168)(137,169)(138,170)(139,171)(140,172)(141,173)(142,174)(143,175)
(144,176)(145,177)(146,178)(147,179)(148,180)(149,181)(150,182)(151,183)
(152,184)(153,185)(154,186)(155,187)(156,188)(157,189)(158,190)(159,191)
(160,192)(193,225)(194,226)(195,227)(196,228)(197,229)(198,230)(199,231)
(200,232)(201,233)(202,234)(203,235)(204,236)(205,237)(206,238)(207,239)
(208,240)(209,241)(210,242)(211,243)(212,244)(213,245)(214,246)(215,247)
(216,248)(217,249)(218,250)(219,251)(220,252)(221,253)(222,254)(223,255)
(224,256)(257,289)(258,290)(259,291)(260,292)(261,293)(262,294)(263,295)
(264,296)(265,297)(266,298)(267,299)(268,300)(269,301)(270,302)(271,303)
(272,304)(273,305)(274,306)(275,307)(276,308)(277,309)(278,310)(279,311)
(280,312)(281,313)(282,314)(283,315)(284,316)(285,317)(286,318)(287,319)
(288,320)(321,353)(322,354)(323,355)(324,356)(325,357)(326,358)(327,359)
(328,360)(329,361)(330,362)(331,363)(332,364)(333,365)(334,366)(335,367)
(336,368)(337,369)(338,370)(339,371)(340,372)(341,373)(342,374)(343,375)
(344,376)(345,377)(346,378)(347,379)(348,380)(349,381)(350,382)(351,383)
(352,384)(385,417)(386,418)(387,419)(388,420)(389,421)(390,422)(391,423)
(392,424)(393,425)(394,426)(395,427)(396,428)(397,429)(398,430)(399,431)
(400,432)(401,433)(402,434)(403,435)(404,436)(405,437)(406,438)(407,439)
(408,440)(409,441)(410,442)(411,443)(412,444)(413,445)(414,446)(415,447)
(416,448)(449,481)(450,482)(451,483)(452,484)(453,485)(454,486)(455,487)
(456,488)(457,489)(458,490)(459,491)(460,492)(461,493)(462,494)(463,495)
(464,496)(465,497)(466,498)(467,499)(468,500)(469,501)(470,502)(471,503)
(472,504)(473,505)(474,506)(475,507)(476,508)(477,509)(478,510)(479,511)
(480,512);
s1 := Sym(512)!(  1,257)(  2,258)(  3,260)(  4,259)(  5,261)(  6,262)(  7,264)
(  8,263)(  9,267)( 10,268)( 11,265)( 12,266)( 13,271)( 14,272)( 15,269)
( 16,270)( 17,273)( 18,274)( 19,276)( 20,275)( 21,277)( 22,278)( 23,280)
( 24,279)( 25,283)( 26,284)( 27,281)( 28,282)( 29,287)( 30,288)( 31,285)
( 32,286)( 33,305)( 34,306)( 35,308)( 36,307)( 37,309)( 38,310)( 39,312)
( 40,311)( 41,315)( 42,316)( 43,313)( 44,314)( 45,319)( 46,320)( 47,317)
( 48,318)( 49,289)( 50,290)( 51,292)( 52,291)( 53,293)( 54,294)( 55,296)
( 56,295)( 57,299)( 58,300)( 59,297)( 60,298)( 61,303)( 62,304)( 63,301)
( 64,302)( 65,329)( 66,330)( 67,332)( 68,331)( 69,333)( 70,334)( 71,336)
( 72,335)( 73,321)( 74,322)( 75,324)( 76,323)( 77,325)( 78,326)( 79,328)
( 80,327)( 81,345)( 82,346)( 83,348)( 84,347)( 85,349)( 86,350)( 87,352)
( 88,351)( 89,337)( 90,338)( 91,340)( 92,339)( 93,341)( 94,342)( 95,344)
( 96,343)( 97,377)( 98,378)( 99,380)(100,379)(101,381)(102,382)(103,384)
(104,383)(105,369)(106,370)(107,372)(108,371)(109,373)(110,374)(111,376)
(112,375)(113,361)(114,362)(115,364)(116,363)(117,365)(118,366)(119,368)
(120,367)(121,353)(122,354)(123,356)(124,355)(125,357)(126,358)(127,360)
(128,359)(129,401)(130,402)(131,404)(132,403)(133,405)(134,406)(135,408)
(136,407)(137,411)(138,412)(139,409)(140,410)(141,415)(142,416)(143,413)
(144,414)(145,385)(146,386)(147,388)(148,387)(149,389)(150,390)(151,392)
(152,391)(153,395)(154,396)(155,393)(156,394)(157,399)(158,400)(159,397)
(160,398)(161,417)(162,418)(163,420)(164,419)(165,421)(166,422)(167,424)
(168,423)(169,427)(170,428)(171,425)(172,426)(173,431)(174,432)(175,429)
(176,430)(177,433)(178,434)(179,436)(180,435)(181,437)(182,438)(183,440)
(184,439)(185,443)(186,444)(187,441)(188,442)(189,447)(190,448)(191,445)
(192,446)(193,473)(194,474)(195,476)(196,475)(197,477)(198,478)(199,480)
(200,479)(201,465)(202,466)(203,468)(204,467)(205,469)(206,470)(207,472)
(208,471)(209,457)(210,458)(211,460)(212,459)(213,461)(214,462)(215,464)
(216,463)(217,449)(218,450)(219,452)(220,451)(221,453)(222,454)(223,456)
(224,455)(225,489)(226,490)(227,492)(228,491)(229,493)(230,494)(231,496)
(232,495)(233,481)(234,482)(235,484)(236,483)(237,485)(238,486)(239,488)
(240,487)(241,505)(242,506)(243,508)(244,507)(245,509)(246,510)(247,512)
(248,511)(249,497)(250,498)(251,500)(252,499)(253,501)(254,502)(255,504)
(256,503);
s2 := Sym(512)!(  1, 65)(  2, 66)(  3, 68)(  4, 67)(  5, 69)(  6, 70)(  7, 72)
(  8, 71)(  9, 75)( 10, 76)( 11, 73)( 12, 74)( 13, 79)( 14, 80)( 15, 77)
( 16, 78)( 17, 81)( 18, 82)( 19, 84)( 20, 83)( 21, 85)( 22, 86)( 23, 88)
( 24, 87)( 25, 91)( 26, 92)( 27, 89)( 28, 90)( 29, 95)( 30, 96)( 31, 93)
( 32, 94)( 33, 97)( 34, 98)( 35,100)( 36, 99)( 37,101)( 38,102)( 39,104)
( 40,103)( 41,107)( 42,108)( 43,105)( 44,106)( 45,111)( 46,112)( 47,109)
( 48,110)( 49,113)( 50,114)( 51,116)( 52,115)( 53,117)( 54,118)( 55,120)
( 56,119)( 57,123)( 58,124)( 59,121)( 60,122)( 61,127)( 62,128)( 63,125)
( 64,126)(129,193)(130,194)(131,196)(132,195)(133,197)(134,198)(135,200)
(136,199)(137,203)(138,204)(139,201)(140,202)(141,207)(142,208)(143,205)
(144,206)(145,209)(146,210)(147,212)(148,211)(149,213)(150,214)(151,216)
(152,215)(153,219)(154,220)(155,217)(156,218)(157,223)(158,224)(159,221)
(160,222)(161,225)(162,226)(163,228)(164,227)(165,229)(166,230)(167,232)
(168,231)(169,235)(170,236)(171,233)(172,234)(173,239)(174,240)(175,237)
(176,238)(177,241)(178,242)(179,244)(180,243)(181,245)(182,246)(183,248)
(184,247)(185,251)(186,252)(187,249)(188,250)(189,255)(190,256)(191,253)
(192,254)(257,321)(258,322)(259,324)(260,323)(261,325)(262,326)(263,328)
(264,327)(265,331)(266,332)(267,329)(268,330)(269,335)(270,336)(271,333)
(272,334)(273,337)(274,338)(275,340)(276,339)(277,341)(278,342)(279,344)
(280,343)(281,347)(282,348)(283,345)(284,346)(285,351)(286,352)(287,349)
(288,350)(289,353)(290,354)(291,356)(292,355)(293,357)(294,358)(295,360)
(296,359)(297,363)(298,364)(299,361)(300,362)(301,367)(302,368)(303,365)
(304,366)(305,369)(306,370)(307,372)(308,371)(309,373)(310,374)(311,376)
(312,375)(313,379)(314,380)(315,377)(316,378)(317,383)(318,384)(319,381)
(320,382)(385,449)(386,450)(387,452)(388,451)(389,453)(390,454)(391,456)
(392,455)(393,459)(394,460)(395,457)(396,458)(397,463)(398,464)(399,461)
(400,462)(401,465)(402,466)(403,468)(404,467)(405,469)(406,470)(407,472)
(408,471)(409,475)(410,476)(411,473)(412,474)(413,479)(414,480)(415,477)
(416,478)(417,481)(418,482)(419,484)(420,483)(421,485)(422,486)(423,488)
(424,487)(425,491)(426,492)(427,489)(428,490)(429,495)(430,496)(431,493)
(432,494)(433,497)(434,498)(435,500)(436,499)(437,501)(438,502)(439,504)
(440,503)(441,507)(442,508)(443,505)(444,506)(445,511)(446,512)(447,509)
(448,510);
s3 := Sym(512)!(  1,161)(  2,162)(  3,163)(  4,164)(  5,165)(  6,166)(  7,167)
(  8,168)(  9,169)( 10,170)( 11,171)( 12,172)( 13,173)( 14,174)( 15,175)
( 16,176)( 17,177)( 18,178)( 19,179)( 20,180)( 21,181)( 22,182)( 23,183)
( 24,184)( 25,185)( 26,186)( 27,187)( 28,188)( 29,189)( 30,190)( 31,191)
( 32,192)( 33,129)( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,135)
( 40,136)( 41,137)( 42,138)( 43,139)( 44,140)( 45,141)( 46,142)( 47,143)
( 48,144)( 49,145)( 50,146)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)
( 56,152)( 57,153)( 58,154)( 59,155)( 60,156)( 61,157)( 62,158)( 63,159)
( 64,160)( 65,229)( 66,230)( 67,231)( 68,232)( 69,225)( 70,226)( 71,227)
( 72,228)( 73,237)( 74,238)( 75,239)( 76,240)( 77,233)( 78,234)( 79,235)
( 80,236)( 81,245)( 82,246)( 83,247)( 84,248)( 85,241)( 86,242)( 87,243)
( 88,244)( 89,253)( 90,254)( 91,255)( 92,256)( 93,249)( 94,250)( 95,251)
( 96,252)( 97,197)( 98,198)( 99,199)(100,200)(101,193)(102,194)(103,195)
(104,196)(105,205)(106,206)(107,207)(108,208)(109,201)(110,202)(111,203)
(112,204)(113,213)(114,214)(115,215)(116,216)(117,209)(118,210)(119,211)
(120,212)(121,221)(122,222)(123,223)(124,224)(125,217)(126,218)(127,219)
(128,220)(257,417)(258,418)(259,419)(260,420)(261,421)(262,422)(263,423)
(264,424)(265,425)(266,426)(267,427)(268,428)(269,429)(270,430)(271,431)
(272,432)(273,433)(274,434)(275,435)(276,436)(277,437)(278,438)(279,439)
(280,440)(281,441)(282,442)(283,443)(284,444)(285,445)(286,446)(287,447)
(288,448)(289,385)(290,386)(291,387)(292,388)(293,389)(294,390)(295,391)
(296,392)(297,393)(298,394)(299,395)(300,396)(301,397)(302,398)(303,399)
(304,400)(305,401)(306,402)(307,403)(308,404)(309,405)(310,406)(311,407)
(312,408)(313,409)(314,410)(315,411)(316,412)(317,413)(318,414)(319,415)
(320,416)(321,485)(322,486)(323,487)(324,488)(325,481)(326,482)(327,483)
(328,484)(329,493)(330,494)(331,495)(332,496)(333,489)(334,490)(335,491)
(336,492)(337,501)(338,502)(339,503)(340,504)(341,497)(342,498)(343,499)
(344,500)(345,509)(346,510)(347,511)(348,512)(349,505)(350,506)(351,507)
(352,508)(353,453)(354,454)(355,455)(356,456)(357,449)(358,450)(359,451)
(360,452)(361,461)(362,462)(363,463)(364,464)(365,457)(366,458)(367,459)
(368,460)(369,469)(370,470)(371,471)(372,472)(373,465)(374,466)(375,467)
(376,468)(377,477)(378,478)(379,479)(380,480)(381,473)(382,474)(383,475)
(384,476);
poly := sub<Sym(512)|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, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
to this polytope