Questions?
See the FAQ
or other info.

Polytope of Type {4,4,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,16}*512b
if this polytope has a name.
Group : SmallGroup(512,406950)
Rank : 4
Schlafli Type : {4,4,16}
Number of vertices, edges, etc : 4, 8, 32, 16
Order of s0s1s2s3 : 16
Order of s0s1s2s3s2s1 : 2
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 : {4,4,8}*256a, {2,4,16}*256b
   4-fold quotients : {4,4,4}*128, {2,4,8}*128a, {4,2,8}*128
   8-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64, {2,2,8}*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 := (  1,161)(  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);;
s1 := (  1, 65)(  2, 66)(  3, 67)(  4, 68)(  5, 69)(  6, 70)(  7, 71)(  8, 72)
(  9, 73)( 10, 74)( 11, 75)( 12, 76)( 13, 77)( 14, 78)( 15, 79)( 16, 80)
( 17, 82)( 18, 81)( 19, 84)( 20, 83)( 21, 86)( 22, 85)( 23, 88)( 24, 87)
( 25, 90)( 26, 89)( 27, 92)( 28, 91)( 29, 94)( 30, 93)( 31, 96)( 32, 95)
( 33, 97)( 34, 98)( 35, 99)( 36,100)( 37,101)( 38,102)( 39,103)( 40,104)
( 41,105)( 42,106)( 43,107)( 44,108)( 45,109)( 46,110)( 47,111)( 48,112)
( 49,114)( 50,113)( 51,116)( 52,115)( 53,118)( 54,117)( 55,120)( 56,119)
( 57,122)( 58,121)( 59,124)( 60,123)( 61,126)( 62,125)( 63,128)( 64,127)
(129,193)(130,194)(131,195)(132,196)(133,197)(134,198)(135,199)(136,200)
(137,201)(138,202)(139,203)(140,204)(141,205)(142,206)(143,207)(144,208)
(145,210)(146,209)(147,212)(148,211)(149,214)(150,213)(151,216)(152,215)
(153,218)(154,217)(155,220)(156,219)(157,222)(158,221)(159,224)(160,223)
(161,225)(162,226)(163,227)(164,228)(165,229)(166,230)(167,231)(168,232)
(169,233)(170,234)(171,235)(172,236)(173,237)(174,238)(175,239)(176,240)
(177,242)(178,241)(179,244)(180,243)(181,246)(182,245)(183,248)(184,247)
(185,250)(186,249)(187,252)(188,251)(189,254)(190,253)(191,256)(192,255)
(257,321)(258,322)(259,323)(260,324)(261,325)(262,326)(263,327)(264,328)
(265,329)(266,330)(267,331)(268,332)(269,333)(270,334)(271,335)(272,336)
(273,338)(274,337)(275,340)(276,339)(277,342)(278,341)(279,344)(280,343)
(281,346)(282,345)(283,348)(284,347)(285,350)(286,349)(287,352)(288,351)
(289,353)(290,354)(291,355)(292,356)(293,357)(294,358)(295,359)(296,360)
(297,361)(298,362)(299,363)(300,364)(301,365)(302,366)(303,367)(304,368)
(305,370)(306,369)(307,372)(308,371)(309,374)(310,373)(311,376)(312,375)
(313,378)(314,377)(315,380)(316,379)(317,382)(318,381)(319,384)(320,383)
(385,449)(386,450)(387,451)(388,452)(389,453)(390,454)(391,455)(392,456)
(393,457)(394,458)(395,459)(396,460)(397,461)(398,462)(399,463)(400,464)
(401,466)(402,465)(403,468)(404,467)(405,470)(406,469)(407,472)(408,471)
(409,474)(410,473)(411,476)(412,475)(413,478)(414,477)(415,480)(416,479)
(417,481)(418,482)(419,483)(420,484)(421,485)(422,486)(423,487)(424,488)
(425,489)(426,490)(427,491)(428,492)(429,493)(430,494)(431,495)(432,496)
(433,498)(434,497)(435,500)(436,499)(437,502)(438,501)(439,504)(440,503)
(441,506)(442,505)(443,508)(444,507)(445,510)(446,509)(447,512)(448,511);;
s2 := (  1,257)(  2,258)(  3,260)(  4,259)(  5,261)(  6,262)(  7,264)(  8,263)
(  9,265)( 10,266)( 11,268)( 12,267)( 13,269)( 14,270)( 15,272)( 16,271)
( 17,275)( 18,276)( 19,273)( 20,274)( 21,279)( 22,280)( 23,277)( 24,278)
( 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)
( 41,313)( 42,314)( 43,316)( 44,315)( 45,317)( 46,318)( 47,320)( 48,319)
( 49,289)( 50,290)( 51,292)( 52,291)( 53,293)( 54,294)( 55,296)( 56,295)
( 57,297)( 58,298)( 59,300)( 60,299)( 61,301)( 62,302)( 63,304)( 64,303)
( 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)
( 81,347)( 82,348)( 83,345)( 84,346)( 85,351)( 86,352)( 87,349)( 88,350)
( 89,339)( 90,340)( 91,337)( 92,338)( 93,343)( 94,344)( 95,341)( 96,342)
( 97,378)( 98,377)( 99,379)(100,380)(101,382)(102,381)(103,383)(104,384)
(105,370)(106,369)(107,371)(108,372)(109,374)(110,373)(111,375)(112,376)
(113,362)(114,361)(115,363)(116,364)(117,366)(118,365)(119,367)(120,368)
(121,354)(122,353)(123,355)(124,356)(125,358)(126,357)(127,359)(128,360)
(129,401)(130,402)(131,404)(132,403)(133,405)(134,406)(135,408)(136,407)
(137,409)(138,410)(139,412)(140,411)(141,413)(142,414)(143,416)(144,415)
(145,385)(146,386)(147,388)(148,387)(149,389)(150,390)(151,392)(152,391)
(153,393)(154,394)(155,396)(156,395)(157,397)(158,398)(159,400)(160,399)
(161,417)(162,418)(163,420)(164,419)(165,421)(166,422)(167,424)(168,423)
(169,425)(170,426)(171,428)(172,427)(173,429)(174,430)(175,432)(176,431)
(177,435)(178,436)(179,433)(180,434)(181,439)(182,440)(183,437)(184,438)
(185,443)(186,444)(187,441)(188,442)(189,447)(190,448)(191,445)(192,446)
(193,474)(194,473)(195,475)(196,476)(197,478)(198,477)(199,479)(200,480)
(201,466)(202,465)(203,467)(204,468)(205,470)(206,469)(207,471)(208,472)
(209,458)(210,457)(211,459)(212,460)(213,462)(214,461)(215,463)(216,464)
(217,450)(218,449)(219,451)(220,452)(221,454)(222,453)(223,455)(224,456)
(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)
(241,507)(242,508)(243,505)(244,506)(245,511)(246,512)(247,509)(248,510)
(249,499)(250,500)(251,497)(252,498)(253,503)(254,504)(255,501)(256,502);;
s3 := (  1, 33)(  2, 34)(  3, 36)(  4, 35)(  5, 37)(  6, 38)(  7, 40)(  8, 39)
(  9, 42)( 10, 41)( 11, 43)( 12, 44)( 13, 46)( 14, 45)( 15, 47)( 16, 48)
( 17, 51)( 18, 52)( 19, 49)( 20, 50)( 21, 55)( 22, 56)( 23, 53)( 24, 54)
( 25, 60)( 26, 59)( 27, 58)( 28, 57)( 29, 64)( 30, 63)( 31, 62)( 32, 61)
( 65, 97)( 66, 98)( 67,100)( 68, 99)( 69,101)( 70,102)( 71,104)( 72,103)
( 73,106)( 74,105)( 75,107)( 76,108)( 77,110)( 78,109)( 79,111)( 80,112)
( 81,115)( 82,116)( 83,113)( 84,114)( 85,119)( 86,120)( 87,117)( 88,118)
( 89,124)( 90,123)( 91,122)( 92,121)( 93,128)( 94,127)( 95,126)( 96,125)
(129,161)(130,162)(131,164)(132,163)(133,165)(134,166)(135,168)(136,167)
(137,170)(138,169)(139,171)(140,172)(141,174)(142,173)(143,175)(144,176)
(145,179)(146,180)(147,177)(148,178)(149,183)(150,184)(151,181)(152,182)
(153,188)(154,187)(155,186)(156,185)(157,192)(158,191)(159,190)(160,189)
(193,225)(194,226)(195,228)(196,227)(197,229)(198,230)(199,232)(200,231)
(201,234)(202,233)(203,235)(204,236)(205,238)(206,237)(207,239)(208,240)
(209,243)(210,244)(211,241)(212,242)(213,247)(214,248)(215,245)(216,246)
(217,252)(218,251)(219,250)(220,249)(221,256)(222,255)(223,254)(224,253)
(257,289)(258,290)(259,292)(260,291)(261,293)(262,294)(263,296)(264,295)
(265,298)(266,297)(267,299)(268,300)(269,302)(270,301)(271,303)(272,304)
(273,307)(274,308)(275,305)(276,306)(277,311)(278,312)(279,309)(280,310)
(281,316)(282,315)(283,314)(284,313)(285,320)(286,319)(287,318)(288,317)
(321,353)(322,354)(323,356)(324,355)(325,357)(326,358)(327,360)(328,359)
(329,362)(330,361)(331,363)(332,364)(333,366)(334,365)(335,367)(336,368)
(337,371)(338,372)(339,369)(340,370)(341,375)(342,376)(343,373)(344,374)
(345,380)(346,379)(347,378)(348,377)(349,384)(350,383)(351,382)(352,381)
(385,417)(386,418)(387,420)(388,419)(389,421)(390,422)(391,424)(392,423)
(393,426)(394,425)(395,427)(396,428)(397,430)(398,429)(399,431)(400,432)
(401,435)(402,436)(403,433)(404,434)(405,439)(406,440)(407,437)(408,438)
(409,444)(410,443)(411,442)(412,441)(413,448)(414,447)(415,446)(416,445)
(449,481)(450,482)(451,484)(452,483)(453,485)(454,486)(455,488)(456,487)
(457,490)(458,489)(459,491)(460,492)(461,494)(462,493)(463,495)(464,496)
(465,499)(466,500)(467,497)(468,498)(469,503)(470,504)(471,501)(472,502)
(473,508)(474,507)(475,506)(476,505)(477,512)(478,511)(479,510)(480,509);;
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*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2, 
s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := 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);
s1 := Sym(512)!(  1, 65)(  2, 66)(  3, 67)(  4, 68)(  5, 69)(  6, 70)(  7, 71)
(  8, 72)(  9, 73)( 10, 74)( 11, 75)( 12, 76)( 13, 77)( 14, 78)( 15, 79)
( 16, 80)( 17, 82)( 18, 81)( 19, 84)( 20, 83)( 21, 86)( 22, 85)( 23, 88)
( 24, 87)( 25, 90)( 26, 89)( 27, 92)( 28, 91)( 29, 94)( 30, 93)( 31, 96)
( 32, 95)( 33, 97)( 34, 98)( 35, 99)( 36,100)( 37,101)( 38,102)( 39,103)
( 40,104)( 41,105)( 42,106)( 43,107)( 44,108)( 45,109)( 46,110)( 47,111)
( 48,112)( 49,114)( 50,113)( 51,116)( 52,115)( 53,118)( 54,117)( 55,120)
( 56,119)( 57,122)( 58,121)( 59,124)( 60,123)( 61,126)( 62,125)( 63,128)
( 64,127)(129,193)(130,194)(131,195)(132,196)(133,197)(134,198)(135,199)
(136,200)(137,201)(138,202)(139,203)(140,204)(141,205)(142,206)(143,207)
(144,208)(145,210)(146,209)(147,212)(148,211)(149,214)(150,213)(151,216)
(152,215)(153,218)(154,217)(155,220)(156,219)(157,222)(158,221)(159,224)
(160,223)(161,225)(162,226)(163,227)(164,228)(165,229)(166,230)(167,231)
(168,232)(169,233)(170,234)(171,235)(172,236)(173,237)(174,238)(175,239)
(176,240)(177,242)(178,241)(179,244)(180,243)(181,246)(182,245)(183,248)
(184,247)(185,250)(186,249)(187,252)(188,251)(189,254)(190,253)(191,256)
(192,255)(257,321)(258,322)(259,323)(260,324)(261,325)(262,326)(263,327)
(264,328)(265,329)(266,330)(267,331)(268,332)(269,333)(270,334)(271,335)
(272,336)(273,338)(274,337)(275,340)(276,339)(277,342)(278,341)(279,344)
(280,343)(281,346)(282,345)(283,348)(284,347)(285,350)(286,349)(287,352)
(288,351)(289,353)(290,354)(291,355)(292,356)(293,357)(294,358)(295,359)
(296,360)(297,361)(298,362)(299,363)(300,364)(301,365)(302,366)(303,367)
(304,368)(305,370)(306,369)(307,372)(308,371)(309,374)(310,373)(311,376)
(312,375)(313,378)(314,377)(315,380)(316,379)(317,382)(318,381)(319,384)
(320,383)(385,449)(386,450)(387,451)(388,452)(389,453)(390,454)(391,455)
(392,456)(393,457)(394,458)(395,459)(396,460)(397,461)(398,462)(399,463)
(400,464)(401,466)(402,465)(403,468)(404,467)(405,470)(406,469)(407,472)
(408,471)(409,474)(410,473)(411,476)(412,475)(413,478)(414,477)(415,480)
(416,479)(417,481)(418,482)(419,483)(420,484)(421,485)(422,486)(423,487)
(424,488)(425,489)(426,490)(427,491)(428,492)(429,493)(430,494)(431,495)
(432,496)(433,498)(434,497)(435,500)(436,499)(437,502)(438,501)(439,504)
(440,503)(441,506)(442,505)(443,508)(444,507)(445,510)(446,509)(447,512)
(448,511);
s2 := Sym(512)!(  1,257)(  2,258)(  3,260)(  4,259)(  5,261)(  6,262)(  7,264)
(  8,263)(  9,265)( 10,266)( 11,268)( 12,267)( 13,269)( 14,270)( 15,272)
( 16,271)( 17,275)( 18,276)( 19,273)( 20,274)( 21,279)( 22,280)( 23,277)
( 24,278)( 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)( 41,313)( 42,314)( 43,316)( 44,315)( 45,317)( 46,318)( 47,320)
( 48,319)( 49,289)( 50,290)( 51,292)( 52,291)( 53,293)( 54,294)( 55,296)
( 56,295)( 57,297)( 58,298)( 59,300)( 60,299)( 61,301)( 62,302)( 63,304)
( 64,303)( 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)( 81,347)( 82,348)( 83,345)( 84,346)( 85,351)( 86,352)( 87,349)
( 88,350)( 89,339)( 90,340)( 91,337)( 92,338)( 93,343)( 94,344)( 95,341)
( 96,342)( 97,378)( 98,377)( 99,379)(100,380)(101,382)(102,381)(103,383)
(104,384)(105,370)(106,369)(107,371)(108,372)(109,374)(110,373)(111,375)
(112,376)(113,362)(114,361)(115,363)(116,364)(117,366)(118,365)(119,367)
(120,368)(121,354)(122,353)(123,355)(124,356)(125,358)(126,357)(127,359)
(128,360)(129,401)(130,402)(131,404)(132,403)(133,405)(134,406)(135,408)
(136,407)(137,409)(138,410)(139,412)(140,411)(141,413)(142,414)(143,416)
(144,415)(145,385)(146,386)(147,388)(148,387)(149,389)(150,390)(151,392)
(152,391)(153,393)(154,394)(155,396)(156,395)(157,397)(158,398)(159,400)
(160,399)(161,417)(162,418)(163,420)(164,419)(165,421)(166,422)(167,424)
(168,423)(169,425)(170,426)(171,428)(172,427)(173,429)(174,430)(175,432)
(176,431)(177,435)(178,436)(179,433)(180,434)(181,439)(182,440)(183,437)
(184,438)(185,443)(186,444)(187,441)(188,442)(189,447)(190,448)(191,445)
(192,446)(193,474)(194,473)(195,475)(196,476)(197,478)(198,477)(199,479)
(200,480)(201,466)(202,465)(203,467)(204,468)(205,470)(206,469)(207,471)
(208,472)(209,458)(210,457)(211,459)(212,460)(213,462)(214,461)(215,463)
(216,464)(217,450)(218,449)(219,451)(220,452)(221,454)(222,453)(223,455)
(224,456)(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)(241,507)(242,508)(243,505)(244,506)(245,511)(246,512)(247,509)
(248,510)(249,499)(250,500)(251,497)(252,498)(253,503)(254,504)(255,501)
(256,502);
s3 := Sym(512)!(  1, 33)(  2, 34)(  3, 36)(  4, 35)(  5, 37)(  6, 38)(  7, 40)
(  8, 39)(  9, 42)( 10, 41)( 11, 43)( 12, 44)( 13, 46)( 14, 45)( 15, 47)
( 16, 48)( 17, 51)( 18, 52)( 19, 49)( 20, 50)( 21, 55)( 22, 56)( 23, 53)
( 24, 54)( 25, 60)( 26, 59)( 27, 58)( 28, 57)( 29, 64)( 30, 63)( 31, 62)
( 32, 61)( 65, 97)( 66, 98)( 67,100)( 68, 99)( 69,101)( 70,102)( 71,104)
( 72,103)( 73,106)( 74,105)( 75,107)( 76,108)( 77,110)( 78,109)( 79,111)
( 80,112)( 81,115)( 82,116)( 83,113)( 84,114)( 85,119)( 86,120)( 87,117)
( 88,118)( 89,124)( 90,123)( 91,122)( 92,121)( 93,128)( 94,127)( 95,126)
( 96,125)(129,161)(130,162)(131,164)(132,163)(133,165)(134,166)(135,168)
(136,167)(137,170)(138,169)(139,171)(140,172)(141,174)(142,173)(143,175)
(144,176)(145,179)(146,180)(147,177)(148,178)(149,183)(150,184)(151,181)
(152,182)(153,188)(154,187)(155,186)(156,185)(157,192)(158,191)(159,190)
(160,189)(193,225)(194,226)(195,228)(196,227)(197,229)(198,230)(199,232)
(200,231)(201,234)(202,233)(203,235)(204,236)(205,238)(206,237)(207,239)
(208,240)(209,243)(210,244)(211,241)(212,242)(213,247)(214,248)(215,245)
(216,246)(217,252)(218,251)(219,250)(220,249)(221,256)(222,255)(223,254)
(224,253)(257,289)(258,290)(259,292)(260,291)(261,293)(262,294)(263,296)
(264,295)(265,298)(266,297)(267,299)(268,300)(269,302)(270,301)(271,303)
(272,304)(273,307)(274,308)(275,305)(276,306)(277,311)(278,312)(279,309)
(280,310)(281,316)(282,315)(283,314)(284,313)(285,320)(286,319)(287,318)
(288,317)(321,353)(322,354)(323,356)(324,355)(325,357)(326,358)(327,360)
(328,359)(329,362)(330,361)(331,363)(332,364)(333,366)(334,365)(335,367)
(336,368)(337,371)(338,372)(339,369)(340,370)(341,375)(342,376)(343,373)
(344,374)(345,380)(346,379)(347,378)(348,377)(349,384)(350,383)(351,382)
(352,381)(385,417)(386,418)(387,420)(388,419)(389,421)(390,422)(391,424)
(392,423)(393,426)(394,425)(395,427)(396,428)(397,430)(398,429)(399,431)
(400,432)(401,435)(402,436)(403,433)(404,434)(405,439)(406,440)(407,437)
(408,438)(409,444)(410,443)(411,442)(412,441)(413,448)(414,447)(415,446)
(416,445)(449,481)(450,482)(451,484)(452,483)(453,485)(454,486)(455,488)
(456,487)(457,490)(458,489)(459,491)(460,492)(461,494)(462,493)(463,495)
(464,496)(465,499)(466,500)(467,497)(468,498)(469,503)(470,504)(471,501)
(472,502)(473,508)(474,507)(475,506)(476,505)(477,512)(478,511)(479,510)
(480,509);
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*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2, 
s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2 >; 
 
References : None.
to this polytope