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# Polytope of Type {4,8,4}

Atlas Canonical Name : {4,8,4}*512a
if this polytope has a name.
Group : SmallGroup(512,156035)
Rank : 4
Schlafli Type : {4,8,4}
Number of vertices, edges, etc : 8, 32, 32, 4
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 : {4,8,2}*256a, {4,4,4}*256b, {4,8,4}*256c, {4,8,4}*256d
4-fold quotients : {4,4,4}*128, {2,8,4}*128a, {4,8,2}*128a, {4,8,2}*128b, {4,4,2}*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, 43)( 10, 44)( 11, 41)( 12, 42)( 13, 47)( 14, 48)( 15, 45)( 16, 46)
( 17, 49)( 18, 50)( 19, 51)( 20, 52)( 21, 53)( 22, 54)( 23, 55)( 24, 56)
( 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)
( 73,107)( 74,108)( 75,105)( 76,106)( 77,111)( 78,112)( 79,109)( 80,110)
( 81,113)( 82,114)( 83,115)( 84,116)( 85,117)( 86,118)( 87,119)( 88,120)
( 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)
(137,171)(138,172)(139,169)(140,170)(141,175)(142,176)(143,173)(144,174)
(145,177)(146,178)(147,179)(148,180)(149,181)(150,182)(151,183)(152,184)
(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)
(201,235)(202,236)(203,233)(204,234)(205,239)(206,240)(207,237)(208,238)
(209,241)(210,242)(211,243)(212,244)(213,245)(214,246)(215,247)(216,248)
(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)
(265,299)(266,300)(267,297)(268,298)(269,303)(270,304)(271,301)(272,302)
(273,305)(274,306)(275,307)(276,308)(277,309)(278,310)(279,311)(280,312)
(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)
(329,363)(330,364)(331,361)(332,362)(333,367)(334,368)(335,365)(336,366)
(337,369)(338,370)(339,371)(340,372)(341,373)(342,374)(343,375)(344,376)
(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)
(393,427)(394,428)(395,425)(396,426)(397,431)(398,432)(399,429)(400,430)
(401,433)(402,434)(403,435)(404,436)(405,437)(406,438)(407,439)(408,440)
(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)
(457,491)(458,492)(459,489)(460,490)(461,495)(462,496)(463,493)(464,494)
(465,497)(466,498)(467,499)(468,500)(469,501)(470,502)(471,503)(472,504)
(473,507)(474,508)(475,505)(476,506)(477,511)(478,512)(479,509)(480,510);;
s1 := (  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)
( 17,273)( 18,274)( 19,275)( 20,276)( 21,277)( 22,278)( 23,279)( 24,280)
( 25,282)( 26,281)( 27,284)( 28,283)( 29,286)( 30,285)( 31,288)( 32,287)
( 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)
( 81,345)( 82,346)( 83,347)( 84,348)( 85,349)( 86,350)( 87,351)( 88,352)
( 89,337)( 90,338)( 91,339)( 92,340)( 93,341)( 94,342)( 95,343)( 96,344)
( 97,379)( 98,380)( 99,377)(100,378)(101,383)(102,384)(103,381)(104,382)
(105,371)(106,372)(107,369)(108,370)(109,375)(110,376)(111,373)(112,374)
(113,363)(114,364)(115,361)(116,362)(117,367)(118,368)(119,365)(120,366)
(121,355)(122,356)(123,353)(124,354)(125,359)(126,360)(127,357)(128,358)
(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)
(177,433)(178,434)(179,435)(180,436)(181,437)(182,438)(183,439)(184,440)
(185,442)(186,441)(187,444)(188,443)(189,446)(190,445)(191,448)(192,447)
(193,475)(194,476)(195,473)(196,474)(197,479)(198,480)(199,477)(200,478)
(201,467)(202,468)(203,465)(204,466)(205,471)(206,472)(207,469)(208,470)
(209,459)(210,460)(211,457)(212,458)(213,463)(214,464)(215,461)(216,462)
(217,451)(218,452)(219,449)(220,450)(221,455)(222,456)(223,453)(224,454)
(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)
(241,505)(242,506)(243,507)(244,508)(245,509)(246,510)(247,511)(248,512)
(249,497)(250,498)(251,499)(252,500)(253,501)(254,502)(255,503)(256,504);;
s2 := (  1, 65)(  2, 66)(  3, 67)(  4, 68)(  5, 69)(  6, 70)(  7, 71)(  8, 72)
(  9, 74)( 10, 73)( 11, 76)( 12, 75)( 13, 78)( 14, 77)( 15, 80)( 16, 79)
( 17, 83)( 18, 84)( 19, 81)( 20, 82)( 21, 87)( 22, 88)( 23, 85)( 24, 86)
( 25, 92)( 26, 91)( 27, 90)( 28, 89)( 29, 96)( 30, 95)( 31, 94)( 32, 93)
( 33, 97)( 34, 98)( 35, 99)( 36,100)( 37,101)( 38,102)( 39,103)( 40,104)
( 41,106)( 42,105)( 43,108)( 44,107)( 45,110)( 46,109)( 47,112)( 48,111)
( 49,115)( 50,116)( 51,113)( 52,114)( 53,119)( 54,120)( 55,117)( 56,118)
( 57,124)( 58,123)( 59,122)( 60,121)( 61,128)( 62,127)( 63,126)( 64,125)
(129,193)(130,194)(131,195)(132,196)(133,197)(134,198)(135,199)(136,200)
(137,202)(138,201)(139,204)(140,203)(141,206)(142,205)(143,208)(144,207)
(145,211)(146,212)(147,209)(148,210)(149,215)(150,216)(151,213)(152,214)
(153,220)(154,219)(155,218)(156,217)(157,224)(158,223)(159,222)(160,221)
(161,225)(162,226)(163,227)(164,228)(165,229)(166,230)(167,231)(168,232)
(169,234)(170,233)(171,236)(172,235)(173,238)(174,237)(175,240)(176,239)
(177,243)(178,244)(179,241)(180,242)(181,247)(182,248)(183,245)(184,246)
(185,252)(186,251)(187,250)(188,249)(189,256)(190,255)(191,254)(192,253)
(257,321)(258,322)(259,323)(260,324)(261,325)(262,326)(263,327)(264,328)
(265,330)(266,329)(267,332)(268,331)(269,334)(270,333)(271,336)(272,335)
(273,339)(274,340)(275,337)(276,338)(277,343)(278,344)(279,341)(280,342)
(281,348)(282,347)(283,346)(284,345)(285,352)(286,351)(287,350)(288,349)
(289,353)(290,354)(291,355)(292,356)(293,357)(294,358)(295,359)(296,360)
(297,362)(298,361)(299,364)(300,363)(301,366)(302,365)(303,368)(304,367)
(305,371)(306,372)(307,369)(308,370)(309,375)(310,376)(311,373)(312,374)
(313,380)(314,379)(315,378)(316,377)(317,384)(318,383)(319,382)(320,381)
(385,449)(386,450)(387,451)(388,452)(389,453)(390,454)(391,455)(392,456)
(393,458)(394,457)(395,460)(396,459)(397,462)(398,461)(399,464)(400,463)
(401,467)(402,468)(403,465)(404,466)(405,471)(406,472)(407,469)(408,470)
(409,476)(410,475)(411,474)(412,473)(413,480)(414,479)(415,478)(416,477)
(417,481)(418,482)(419,483)(420,484)(421,485)(422,486)(423,487)(424,488)
(425,490)(426,489)(427,492)(428,491)(429,494)(430,493)(431,496)(432,495)
(433,499)(434,500)(435,497)(436,498)(437,503)(438,504)(439,501)(440,502)
(441,508)(442,507)(443,506)(444,505)(445,512)(446,511)(447,510)(448,509);;
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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
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, 43)( 10, 44)( 11, 41)( 12, 42)( 13, 47)( 14, 48)( 15, 45)
( 16, 46)( 17, 49)( 18, 50)( 19, 51)( 20, 52)( 21, 53)( 22, 54)( 23, 55)
( 24, 56)( 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)( 73,107)( 74,108)( 75,105)( 76,106)( 77,111)( 78,112)( 79,109)
( 80,110)( 81,113)( 82,114)( 83,115)( 84,116)( 85,117)( 86,118)( 87,119)
( 88,120)( 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)(137,171)(138,172)(139,169)(140,170)(141,175)(142,176)(143,173)
(144,174)(145,177)(146,178)(147,179)(148,180)(149,181)(150,182)(151,183)
(152,184)(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)(201,235)(202,236)(203,233)(204,234)(205,239)(206,240)(207,237)
(208,238)(209,241)(210,242)(211,243)(212,244)(213,245)(214,246)(215,247)
(216,248)(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)(265,299)(266,300)(267,297)(268,298)(269,303)(270,304)(271,301)
(272,302)(273,305)(274,306)(275,307)(276,308)(277,309)(278,310)(279,311)
(280,312)(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)(329,363)(330,364)(331,361)(332,362)(333,367)(334,368)(335,365)
(336,366)(337,369)(338,370)(339,371)(340,372)(341,373)(342,374)(343,375)
(344,376)(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)(393,427)(394,428)(395,425)(396,426)(397,431)(398,432)(399,429)
(400,430)(401,433)(402,434)(403,435)(404,436)(405,437)(406,438)(407,439)
(408,440)(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)(457,491)(458,492)(459,489)(460,490)(461,495)(462,496)(463,493)
(464,494)(465,497)(466,498)(467,499)(468,500)(469,501)(470,502)(471,503)
(472,504)(473,507)(474,508)(475,505)(476,506)(477,511)(478,512)(479,509)
(480,510);
s1 := 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)( 17,273)( 18,274)( 19,275)( 20,276)( 21,277)( 22,278)( 23,279)
( 24,280)( 25,282)( 26,281)( 27,284)( 28,283)( 29,286)( 30,285)( 31,288)
( 32,287)( 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)( 81,345)( 82,346)( 83,347)( 84,348)( 85,349)( 86,350)( 87,351)
( 88,352)( 89,337)( 90,338)( 91,339)( 92,340)( 93,341)( 94,342)( 95,343)
( 96,344)( 97,379)( 98,380)( 99,377)(100,378)(101,383)(102,384)(103,381)
(104,382)(105,371)(106,372)(107,369)(108,370)(109,375)(110,376)(111,373)
(112,374)(113,363)(114,364)(115,361)(116,362)(117,367)(118,368)(119,365)
(120,366)(121,355)(122,356)(123,353)(124,354)(125,359)(126,360)(127,357)
(128,358)(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)(177,433)(178,434)(179,435)(180,436)(181,437)(182,438)(183,439)
(184,440)(185,442)(186,441)(187,444)(188,443)(189,446)(190,445)(191,448)
(192,447)(193,475)(194,476)(195,473)(196,474)(197,479)(198,480)(199,477)
(200,478)(201,467)(202,468)(203,465)(204,466)(205,471)(206,472)(207,469)
(208,470)(209,459)(210,460)(211,457)(212,458)(213,463)(214,464)(215,461)
(216,462)(217,451)(218,452)(219,449)(220,450)(221,455)(222,456)(223,453)
(224,454)(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)(241,505)(242,506)(243,507)(244,508)(245,509)(246,510)(247,511)
(248,512)(249,497)(250,498)(251,499)(252,500)(253,501)(254,502)(255,503)
(256,504);
s2 := Sym(512)!(  1, 65)(  2, 66)(  3, 67)(  4, 68)(  5, 69)(  6, 70)(  7, 71)
(  8, 72)(  9, 74)( 10, 73)( 11, 76)( 12, 75)( 13, 78)( 14, 77)( 15, 80)
( 16, 79)( 17, 83)( 18, 84)( 19, 81)( 20, 82)( 21, 87)( 22, 88)( 23, 85)
( 24, 86)( 25, 92)( 26, 91)( 27, 90)( 28, 89)( 29, 96)( 30, 95)( 31, 94)
( 32, 93)( 33, 97)( 34, 98)( 35, 99)( 36,100)( 37,101)( 38,102)( 39,103)
( 40,104)( 41,106)( 42,105)( 43,108)( 44,107)( 45,110)( 46,109)( 47,112)
( 48,111)( 49,115)( 50,116)( 51,113)( 52,114)( 53,119)( 54,120)( 55,117)
( 56,118)( 57,124)( 58,123)( 59,122)( 60,121)( 61,128)( 62,127)( 63,126)
( 64,125)(129,193)(130,194)(131,195)(132,196)(133,197)(134,198)(135,199)
(136,200)(137,202)(138,201)(139,204)(140,203)(141,206)(142,205)(143,208)
(144,207)(145,211)(146,212)(147,209)(148,210)(149,215)(150,216)(151,213)
(152,214)(153,220)(154,219)(155,218)(156,217)(157,224)(158,223)(159,222)
(160,221)(161,225)(162,226)(163,227)(164,228)(165,229)(166,230)(167,231)
(168,232)(169,234)(170,233)(171,236)(172,235)(173,238)(174,237)(175,240)
(176,239)(177,243)(178,244)(179,241)(180,242)(181,247)(182,248)(183,245)
(184,246)(185,252)(186,251)(187,250)(188,249)(189,256)(190,255)(191,254)
(192,253)(257,321)(258,322)(259,323)(260,324)(261,325)(262,326)(263,327)
(264,328)(265,330)(266,329)(267,332)(268,331)(269,334)(270,333)(271,336)
(272,335)(273,339)(274,340)(275,337)(276,338)(277,343)(278,344)(279,341)
(280,342)(281,348)(282,347)(283,346)(284,345)(285,352)(286,351)(287,350)
(288,349)(289,353)(290,354)(291,355)(292,356)(293,357)(294,358)(295,359)
(296,360)(297,362)(298,361)(299,364)(300,363)(301,366)(302,365)(303,368)
(304,367)(305,371)(306,372)(307,369)(308,370)(309,375)(310,376)(311,373)
(312,374)(313,380)(314,379)(315,378)(316,377)(317,384)(318,383)(319,382)
(320,381)(385,449)(386,450)(387,451)(388,452)(389,453)(390,454)(391,455)
(392,456)(393,458)(394,457)(395,460)(396,459)(397,462)(398,461)(399,464)
(400,463)(401,467)(402,468)(403,465)(404,466)(405,471)(406,472)(407,469)
(408,470)(409,476)(410,475)(411,474)(412,473)(413,480)(414,479)(415,478)
(416,477)(417,481)(418,482)(419,483)(420,484)(421,485)(422,486)(423,487)
(424,488)(425,490)(426,489)(427,492)(428,491)(429,494)(430,493)(431,496)
(432,495)(433,499)(434,500)(435,497)(436,498)(437,503)(438,504)(439,501)
(440,502)(441,508)(442,507)(443,506)(444,505)(445,512)(446,511)(447,510)
(448,509);
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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

```
References : None.
to this polytope