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# Polytope of Type {4,8,8}

Atlas Canonical Name : {4,8,8}*512f
if this polytope has a name.
Group : SmallGroup(512,154243)
Rank : 4
Schlafli Type : {4,8,8}
Number of vertices, edges, etc : 4, 16, 32, 8
Order of s0s1s2s3 : 8
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 : {2,8,8}*256c, {4,4,8}*256b, {4,8,4}*256d
4-fold quotients : {4,4,4}*128, {2,8,4}*128a, {4,8,2}*128a, {2,4,8}*128b
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 := (  1,161)(  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, 97)(  2, 98)(  3, 99)(  4,100)(  5,101)(  6,102)(  7,103)(  8,104)
(  9,106)( 10,105)( 11,108)( 12,107)( 13,110)( 14,109)( 15,112)( 16,111)
( 17,115)( 18,116)( 19,113)( 20,114)( 21,119)( 22,120)( 23,117)( 24,118)
( 25,124)( 26,123)( 27,122)( 28,121)( 29,128)( 30,127)( 31,126)( 32,125)
( 33, 65)( 34, 66)( 35, 67)( 36, 68)( 37, 69)( 38, 70)( 39, 71)( 40, 72)
( 41, 74)( 42, 73)( 43, 76)( 44, 75)( 45, 78)( 46, 77)( 47, 80)( 48, 79)
( 49, 83)( 50, 84)( 51, 81)( 52, 82)( 53, 87)( 54, 88)( 55, 85)( 56, 86)
( 57, 92)( 58, 91)( 59, 90)( 60, 89)( 61, 96)( 62, 95)( 63, 94)( 64, 93)
(129,225)(130,226)(131,227)(132,228)(133,229)(134,230)(135,231)(136,232)
(137,234)(138,233)(139,236)(140,235)(141,238)(142,237)(143,240)(144,239)
(145,243)(146,244)(147,241)(148,242)(149,247)(150,248)(151,245)(152,246)
(153,252)(154,251)(155,250)(156,249)(157,256)(158,255)(159,254)(160,253)
(161,193)(162,194)(163,195)(164,196)(165,197)(166,198)(167,199)(168,200)
(169,202)(170,201)(171,204)(172,203)(173,206)(174,205)(175,208)(176,207)
(177,211)(178,212)(179,209)(180,210)(181,215)(182,216)(183,213)(184,214)
(185,220)(186,219)(187,218)(188,217)(189,224)(190,223)(191,222)(192,221)
(257,353)(258,354)(259,355)(260,356)(261,357)(262,358)(263,359)(264,360)
(265,362)(266,361)(267,364)(268,363)(269,366)(270,365)(271,368)(272,367)
(273,371)(274,372)(275,369)(276,370)(277,375)(278,376)(279,373)(280,374)
(281,380)(282,379)(283,378)(284,377)(285,384)(286,383)(287,382)(288,381)
(289,321)(290,322)(291,323)(292,324)(293,325)(294,326)(295,327)(296,328)
(297,330)(298,329)(299,332)(300,331)(301,334)(302,333)(303,336)(304,335)
(305,339)(306,340)(307,337)(308,338)(309,343)(310,344)(311,341)(312,342)
(313,348)(314,347)(315,346)(316,345)(317,352)(318,351)(319,350)(320,349)
(385,481)(386,482)(387,483)(388,484)(389,485)(390,486)(391,487)(392,488)
(393,490)(394,489)(395,492)(396,491)(397,494)(398,493)(399,496)(400,495)
(401,499)(402,500)(403,497)(404,498)(405,503)(406,504)(407,501)(408,502)
(409,508)(410,507)(411,506)(412,505)(413,512)(414,511)(415,510)(416,509)
(417,449)(418,450)(419,451)(420,452)(421,453)(422,454)(423,455)(424,456)
(425,458)(426,457)(427,460)(428,459)(429,462)(430,461)(431,464)(432,463)
(433,467)(434,468)(435,465)(436,466)(437,471)(438,472)(439,469)(440,470)
(441,476)(442,475)(443,474)(444,473)(445,480)(446,479)(447,478)(448,477);;
s2 := (  1,257)(  2,258)(  3,259)(  4,260)(  5,261)(  6,262)(  7,263)(  8,264)
(  9,266)( 10,265)( 11,268)( 12,267)( 13,270)( 14,269)( 15,272)( 16,271)
( 17,275)( 18,276)( 19,273)( 20,274)( 21,279)( 22,280)( 23,277)( 24,278)
( 25,284)( 26,283)( 27,282)( 28,281)( 29,288)( 30,287)( 31,286)( 32,285)
( 33,305)( 34,306)( 35,307)( 36,308)( 37,309)( 38,310)( 39,311)( 40,312)
( 41,314)( 42,313)( 43,316)( 44,315)( 45,318)( 46,317)( 47,320)( 48,319)
( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)( 56,296)
( 57,298)( 58,297)( 59,300)( 60,299)( 61,302)( 62,301)( 63,304)( 64,303)
( 65,329)( 66,330)( 67,331)( 68,332)( 69,333)( 70,334)( 71,335)( 72,336)
( 73,321)( 74,322)( 75,323)( 76,324)( 77,325)( 78,326)( 79,327)( 80,328)
( 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)
( 97,377)( 98,378)( 99,379)(100,380)(101,381)(102,382)(103,383)(104,384)
(105,369)(106,370)(107,371)(108,372)(109,373)(110,374)(111,375)(112,376)
(113,361)(114,362)(115,363)(116,364)(117,365)(118,366)(119,367)(120,368)
(121,353)(122,354)(123,355)(124,356)(125,357)(126,358)(127,359)(128,360)
(129,401)(130,402)(131,403)(132,404)(133,405)(134,406)(135,407)(136,408)
(137,410)(138,409)(139,412)(140,411)(141,414)(142,413)(143,416)(144,415)
(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)(152,392)
(153,394)(154,393)(155,396)(156,395)(157,398)(158,397)(159,400)(160,399)
(161,417)(162,418)(163,419)(164,420)(165,421)(166,422)(167,423)(168,424)
(169,426)(170,425)(171,428)(172,427)(173,430)(174,429)(175,432)(176,431)
(177,435)(178,436)(179,433)(180,434)(181,439)(182,440)(183,437)(184,438)
(185,444)(186,443)(187,442)(188,441)(189,448)(190,447)(191,446)(192,445)
(193,473)(194,474)(195,475)(196,476)(197,477)(198,478)(199,479)(200,480)
(201,465)(202,466)(203,467)(204,468)(205,469)(206,470)(207,471)(208,472)
(209,457)(210,458)(211,459)(212,460)(213,461)(214,462)(215,463)(216,464)
(217,449)(218,450)(219,451)(220,452)(221,453)(222,454)(223,455)(224,456)
(225,489)(226,490)(227,491)(228,492)(229,493)(230,494)(231,495)(232,496)
(233,481)(234,482)(235,483)(236,484)(237,485)(238,486)(239,487)(240,488)
(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, 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, 51)( 18, 52)( 19, 49)( 20, 50)( 21, 55)( 22, 56)( 23, 53)( 24, 54)
( 25, 59)( 26, 60)( 27, 57)( 28, 58)( 29, 63)( 30, 64)( 31, 61)( 32, 62)
( 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)
( 81,115)( 82,116)( 83,113)( 84,114)( 85,119)( 86,120)( 87,117)( 88,118)
( 89,123)( 90,124)( 91,121)( 92,122)( 93,127)( 94,128)( 95,125)( 96,126)
(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)
(145,179)(146,180)(147,177)(148,178)(149,183)(150,184)(151,181)(152,182)
(153,187)(154,188)(155,185)(156,186)(157,191)(158,192)(159,189)(160,190)
(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)
(209,243)(210,244)(211,241)(212,242)(213,247)(214,248)(215,245)(216,246)
(217,251)(218,252)(219,249)(220,250)(221,255)(222,256)(223,253)(224,254)
(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)
(273,307)(274,308)(275,305)(276,306)(277,311)(278,312)(279,309)(280,310)
(281,315)(282,316)(283,313)(284,314)(285,319)(286,320)(287,317)(288,318)
(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)
(337,371)(338,372)(339,369)(340,370)(341,375)(342,376)(343,373)(344,374)
(345,379)(346,380)(347,377)(348,378)(349,383)(350,384)(351,381)(352,382)
(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)
(401,435)(402,436)(403,433)(404,434)(405,439)(406,440)(407,437)(408,438)
(409,443)(410,444)(411,441)(412,442)(413,447)(414,448)(415,445)(416,446)
(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)
(465,499)(466,500)(467,497)(468,498)(469,503)(470,504)(471,501)(472,502)
(473,507)(474,508)(475,505)(476,506)(477,511)(478,512)(479,509)(480,510);;
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, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*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, 97)(  2, 98)(  3, 99)(  4,100)(  5,101)(  6,102)(  7,103)
(  8,104)(  9,106)( 10,105)( 11,108)( 12,107)( 13,110)( 14,109)( 15,112)
( 16,111)( 17,115)( 18,116)( 19,113)( 20,114)( 21,119)( 22,120)( 23,117)
( 24,118)( 25,124)( 26,123)( 27,122)( 28,121)( 29,128)( 30,127)( 31,126)
( 32,125)( 33, 65)( 34, 66)( 35, 67)( 36, 68)( 37, 69)( 38, 70)( 39, 71)
( 40, 72)( 41, 74)( 42, 73)( 43, 76)( 44, 75)( 45, 78)( 46, 77)( 47, 80)
( 48, 79)( 49, 83)( 50, 84)( 51, 81)( 52, 82)( 53, 87)( 54, 88)( 55, 85)
( 56, 86)( 57, 92)( 58, 91)( 59, 90)( 60, 89)( 61, 96)( 62, 95)( 63, 94)
( 64, 93)(129,225)(130,226)(131,227)(132,228)(133,229)(134,230)(135,231)
(136,232)(137,234)(138,233)(139,236)(140,235)(141,238)(142,237)(143,240)
(144,239)(145,243)(146,244)(147,241)(148,242)(149,247)(150,248)(151,245)
(152,246)(153,252)(154,251)(155,250)(156,249)(157,256)(158,255)(159,254)
(160,253)(161,193)(162,194)(163,195)(164,196)(165,197)(166,198)(167,199)
(168,200)(169,202)(170,201)(171,204)(172,203)(173,206)(174,205)(175,208)
(176,207)(177,211)(178,212)(179,209)(180,210)(181,215)(182,216)(183,213)
(184,214)(185,220)(186,219)(187,218)(188,217)(189,224)(190,223)(191,222)
(192,221)(257,353)(258,354)(259,355)(260,356)(261,357)(262,358)(263,359)
(264,360)(265,362)(266,361)(267,364)(268,363)(269,366)(270,365)(271,368)
(272,367)(273,371)(274,372)(275,369)(276,370)(277,375)(278,376)(279,373)
(280,374)(281,380)(282,379)(283,378)(284,377)(285,384)(286,383)(287,382)
(288,381)(289,321)(290,322)(291,323)(292,324)(293,325)(294,326)(295,327)
(296,328)(297,330)(298,329)(299,332)(300,331)(301,334)(302,333)(303,336)
(304,335)(305,339)(306,340)(307,337)(308,338)(309,343)(310,344)(311,341)
(312,342)(313,348)(314,347)(315,346)(316,345)(317,352)(318,351)(319,350)
(320,349)(385,481)(386,482)(387,483)(388,484)(389,485)(390,486)(391,487)
(392,488)(393,490)(394,489)(395,492)(396,491)(397,494)(398,493)(399,496)
(400,495)(401,499)(402,500)(403,497)(404,498)(405,503)(406,504)(407,501)
(408,502)(409,508)(410,507)(411,506)(412,505)(413,512)(414,511)(415,510)
(416,509)(417,449)(418,450)(419,451)(420,452)(421,453)(422,454)(423,455)
(424,456)(425,458)(426,457)(427,460)(428,459)(429,462)(430,461)(431,464)
(432,463)(433,467)(434,468)(435,465)(436,466)(437,471)(438,472)(439,469)
(440,470)(441,476)(442,475)(443,474)(444,473)(445,480)(446,479)(447,478)
(448,477);
s2 := Sym(512)!(  1,257)(  2,258)(  3,259)(  4,260)(  5,261)(  6,262)(  7,263)
(  8,264)(  9,266)( 10,265)( 11,268)( 12,267)( 13,270)( 14,269)( 15,272)
( 16,271)( 17,275)( 18,276)( 19,273)( 20,274)( 21,279)( 22,280)( 23,277)
( 24,278)( 25,284)( 26,283)( 27,282)( 28,281)( 29,288)( 30,287)( 31,286)
( 32,285)( 33,305)( 34,306)( 35,307)( 36,308)( 37,309)( 38,310)( 39,311)
( 40,312)( 41,314)( 42,313)( 43,316)( 44,315)( 45,318)( 46,317)( 47,320)
( 48,319)( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)
( 56,296)( 57,298)( 58,297)( 59,300)( 60,299)( 61,302)( 62,301)( 63,304)
( 64,303)( 65,329)( 66,330)( 67,331)( 68,332)( 69,333)( 70,334)( 71,335)
( 72,336)( 73,321)( 74,322)( 75,323)( 76,324)( 77,325)( 78,326)( 79,327)
( 80,328)( 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)( 97,377)( 98,378)( 99,379)(100,380)(101,381)(102,382)(103,383)
(104,384)(105,369)(106,370)(107,371)(108,372)(109,373)(110,374)(111,375)
(112,376)(113,361)(114,362)(115,363)(116,364)(117,365)(118,366)(119,367)
(120,368)(121,353)(122,354)(123,355)(124,356)(125,357)(126,358)(127,359)
(128,360)(129,401)(130,402)(131,403)(132,404)(133,405)(134,406)(135,407)
(136,408)(137,410)(138,409)(139,412)(140,411)(141,414)(142,413)(143,416)
(144,415)(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)
(152,392)(153,394)(154,393)(155,396)(156,395)(157,398)(158,397)(159,400)
(160,399)(161,417)(162,418)(163,419)(164,420)(165,421)(166,422)(167,423)
(168,424)(169,426)(170,425)(171,428)(172,427)(173,430)(174,429)(175,432)
(176,431)(177,435)(178,436)(179,433)(180,434)(181,439)(182,440)(183,437)
(184,438)(185,444)(186,443)(187,442)(188,441)(189,448)(190,447)(191,446)
(192,445)(193,473)(194,474)(195,475)(196,476)(197,477)(198,478)(199,479)
(200,480)(201,465)(202,466)(203,467)(204,468)(205,469)(206,470)(207,471)
(208,472)(209,457)(210,458)(211,459)(212,460)(213,461)(214,462)(215,463)
(216,464)(217,449)(218,450)(219,451)(220,452)(221,453)(222,454)(223,455)
(224,456)(225,489)(226,490)(227,491)(228,492)(229,493)(230,494)(231,495)
(232,496)(233,481)(234,482)(235,483)(236,484)(237,485)(238,486)(239,487)
(240,488)(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, 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, 51)( 18, 52)( 19, 49)( 20, 50)( 21, 55)( 22, 56)( 23, 53)
( 24, 54)( 25, 59)( 26, 60)( 27, 57)( 28, 58)( 29, 63)( 30, 64)( 31, 61)
( 32, 62)( 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)( 81,115)( 82,116)( 83,113)( 84,114)( 85,119)( 86,120)( 87,117)
( 88,118)( 89,123)( 90,124)( 91,121)( 92,122)( 93,127)( 94,128)( 95,125)
( 96,126)(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)(145,179)(146,180)(147,177)(148,178)(149,183)(150,184)(151,181)
(152,182)(153,187)(154,188)(155,185)(156,186)(157,191)(158,192)(159,189)
(160,190)(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)(209,243)(210,244)(211,241)(212,242)(213,247)(214,248)(215,245)
(216,246)(217,251)(218,252)(219,249)(220,250)(221,255)(222,256)(223,253)
(224,254)(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)(273,307)(274,308)(275,305)(276,306)(277,311)(278,312)(279,309)
(280,310)(281,315)(282,316)(283,313)(284,314)(285,319)(286,320)(287,317)
(288,318)(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)(337,371)(338,372)(339,369)(340,370)(341,375)(342,376)(343,373)
(344,374)(345,379)(346,380)(347,377)(348,378)(349,383)(350,384)(351,381)
(352,382)(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)(401,435)(402,436)(403,433)(404,434)(405,439)(406,440)(407,437)
(408,438)(409,443)(410,444)(411,441)(412,442)(413,447)(414,448)(415,445)
(416,446)(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)(465,499)(466,500)(467,497)(468,498)(469,503)(470,504)(471,501)
(472,502)(473,507)(474,508)(475,505)(476,506)(477,511)(478,512)(479,509)
(480,510);
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,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2 >;

```
References : None.
to this polytope