Polytope of Type {4,4,34}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,34}*1088
Also Known As : {{4,4|2},{4,34|2}}. if this polytope has another name.
Group : SmallGroup(1088,1033)
Rank : 4
Schlafli Type : {4,4,34}
Number of vertices, edges, etc : 4, 8, 68, 34
Order of s0s1s2s3 : 68
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 : {2,4,34}*544, {4,2,34}*544
4-fold quotients : {4,2,17}*272, {2,2,34}*272
8-fold quotients : {2,2,17}*136
17-fold quotients : {4,4,2}*64
34-fold quotients : {2,4,2}*32, {4,2,2}*32
68-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,273)( 2,274)( 3,275)( 4,276)( 5,277)( 6,278)( 7,279)( 8,280)
( 9,281)( 10,282)( 11,283)( 12,284)( 13,285)( 14,286)( 15,287)( 16,288)
( 17,289)( 18,290)( 19,291)( 20,292)( 21,293)( 22,294)( 23,295)( 24,296)
( 25,297)( 26,298)( 27,299)( 28,300)( 29,301)( 30,302)( 31,303)( 32,304)
( 33,305)( 34,306)( 35,307)( 36,308)( 37,309)( 38,310)( 39,311)( 40,312)
( 41,313)( 42,314)( 43,315)( 44,316)( 45,317)( 46,318)( 47,319)( 48,320)
( 49,321)( 50,322)( 51,323)( 52,324)( 53,325)( 54,326)( 55,327)( 56,328)
( 57,329)( 58,330)( 59,331)( 60,332)( 61,333)( 62,334)( 63,335)( 64,336)
( 65,337)( 66,338)( 67,339)( 68,340)( 69,341)( 70,342)( 71,343)( 72,344)
( 73,345)( 74,346)( 75,347)( 76,348)( 77,349)( 78,350)( 79,351)( 80,352)
( 81,353)( 82,354)( 83,355)( 84,356)( 85,357)( 86,358)( 87,359)( 88,360)
( 89,361)( 90,362)( 91,363)( 92,364)( 93,365)( 94,366)( 95,367)( 96,368)
( 97,369)( 98,370)( 99,371)(100,372)(101,373)(102,374)(103,375)(104,376)
(105,377)(106,378)(107,379)(108,380)(109,381)(110,382)(111,383)(112,384)
(113,385)(114,386)(115,387)(116,388)(117,389)(118,390)(119,391)(120,392)
(121,393)(122,394)(123,395)(124,396)(125,397)(126,398)(127,399)(128,400)
(129,401)(130,402)(131,403)(132,404)(133,405)(134,406)(135,407)(136,408)
(137,409)(138,410)(139,411)(140,412)(141,413)(142,414)(143,415)(144,416)
(145,417)(146,418)(147,419)(148,420)(149,421)(150,422)(151,423)(152,424)
(153,425)(154,426)(155,427)(156,428)(157,429)(158,430)(159,431)(160,432)
(161,433)(162,434)(163,435)(164,436)(165,437)(166,438)(167,439)(168,440)
(169,441)(170,442)(171,443)(172,444)(173,445)(174,446)(175,447)(176,448)
(177,449)(178,450)(179,451)(180,452)(181,453)(182,454)(183,455)(184,456)
(185,457)(186,458)(187,459)(188,460)(189,461)(190,462)(191,463)(192,464)
(193,465)(194,466)(195,467)(196,468)(197,469)(198,470)(199,471)(200,472)
(201,473)(202,474)(203,475)(204,476)(205,477)(206,478)(207,479)(208,480)
(209,481)(210,482)(211,483)(212,484)(213,485)(214,486)(215,487)(216,488)
(217,489)(218,490)(219,491)(220,492)(221,493)(222,494)(223,495)(224,496)
(225,497)(226,498)(227,499)(228,500)(229,501)(230,502)(231,503)(232,504)
(233,505)(234,506)(235,507)(236,508)(237,509)(238,510)(239,511)(240,512)
(241,513)(242,514)(243,515)(244,516)(245,517)(246,518)(247,519)(248,520)
(249,521)(250,522)(251,523)(252,524)(253,525)(254,526)(255,527)(256,528)
(257,529)(258,530)(259,531)(260,532)(261,533)(262,534)(263,535)(264,536)
(265,537)(266,538)(267,539)(268,540)(269,541)(270,542)(271,543)(272,544);;
s1 := (137,154)(138,155)(139,156)(140,157)(141,158)(142,159)(143,160)(144,161)
(145,162)(146,163)(147,164)(148,165)(149,166)(150,167)(151,168)(152,169)
(153,170)(171,188)(172,189)(173,190)(174,191)(175,192)(176,193)(177,194)
(178,195)(179,196)(180,197)(181,198)(182,199)(183,200)(184,201)(185,202)
(186,203)(187,204)(205,222)(206,223)(207,224)(208,225)(209,226)(210,227)
(211,228)(212,229)(213,230)(214,231)(215,232)(216,233)(217,234)(218,235)
(219,236)(220,237)(221,238)(239,256)(240,257)(241,258)(242,259)(243,260)
(244,261)(245,262)(246,263)(247,264)(248,265)(249,266)(250,267)(251,268)
(252,269)(253,270)(254,271)(255,272)(273,307)(274,308)(275,309)(276,310)
(277,311)(278,312)(279,313)(280,314)(281,315)(282,316)(283,317)(284,318)
(285,319)(286,320)(287,321)(288,322)(289,323)(290,324)(291,325)(292,326)
(293,327)(294,328)(295,329)(296,330)(297,331)(298,332)(299,333)(300,334)
(301,335)(302,336)(303,337)(304,338)(305,339)(306,340)(341,375)(342,376)
(343,377)(344,378)(345,379)(346,380)(347,381)(348,382)(349,383)(350,384)
(351,385)(352,386)(353,387)(354,388)(355,389)(356,390)(357,391)(358,392)
(359,393)(360,394)(361,395)(362,396)(363,397)(364,398)(365,399)(366,400)
(367,401)(368,402)(369,403)(370,404)(371,405)(372,406)(373,407)(374,408)
(409,460)(410,461)(411,462)(412,463)(413,464)(414,465)(415,466)(416,467)
(417,468)(418,469)(419,470)(420,471)(421,472)(422,473)(423,474)(424,475)
(425,476)(426,443)(427,444)(428,445)(429,446)(430,447)(431,448)(432,449)
(433,450)(434,451)(435,452)(436,453)(437,454)(438,455)(439,456)(440,457)
(441,458)(442,459)(477,528)(478,529)(479,530)(480,531)(481,532)(482,533)
(483,534)(484,535)(485,536)(486,537)(487,538)(488,539)(489,540)(490,541)
(491,542)(492,543)(493,544)(494,511)(495,512)(496,513)(497,514)(498,515)
(499,516)(500,517)(501,518)(502,519)(503,520)(504,521)(505,522)(506,523)
(507,524)(508,525)(509,526)(510,527);;
s2 := ( 1,205)( 2,221)( 3,220)( 4,219)( 5,218)( 6,217)( 7,216)( 8,215)
( 9,214)( 10,213)( 11,212)( 12,211)( 13,210)( 14,209)( 15,208)( 16,207)
( 17,206)( 18,222)( 19,238)( 20,237)( 21,236)( 22,235)( 23,234)( 24,233)
( 25,232)( 26,231)( 27,230)( 28,229)( 29,228)( 30,227)( 31,226)( 32,225)
( 33,224)( 34,223)( 35,239)( 36,255)( 37,254)( 38,253)( 39,252)( 40,251)
( 41,250)( 42,249)( 43,248)( 44,247)( 45,246)( 46,245)( 47,244)( 48,243)
( 49,242)( 50,241)( 51,240)( 52,256)( 53,272)( 54,271)( 55,270)( 56,269)
( 57,268)( 58,267)( 59,266)( 60,265)( 61,264)( 62,263)( 63,262)( 64,261)
( 65,260)( 66,259)( 67,258)( 68,257)( 69,137)( 70,153)( 71,152)( 72,151)
( 73,150)( 74,149)( 75,148)( 76,147)( 77,146)( 78,145)( 79,144)( 80,143)
( 81,142)( 82,141)( 83,140)( 84,139)( 85,138)( 86,154)( 87,170)( 88,169)
( 89,168)( 90,167)( 91,166)( 92,165)( 93,164)( 94,163)( 95,162)( 96,161)
( 97,160)( 98,159)( 99,158)(100,157)(101,156)(102,155)(103,171)(104,187)
(105,186)(106,185)(107,184)(108,183)(109,182)(110,181)(111,180)(112,179)
(113,178)(114,177)(115,176)(116,175)(117,174)(118,173)(119,172)(120,188)
(121,204)(122,203)(123,202)(124,201)(125,200)(126,199)(127,198)(128,197)
(129,196)(130,195)(131,194)(132,193)(133,192)(134,191)(135,190)(136,189)
(273,477)(274,493)(275,492)(276,491)(277,490)(278,489)(279,488)(280,487)
(281,486)(282,485)(283,484)(284,483)(285,482)(286,481)(287,480)(288,479)
(289,478)(290,494)(291,510)(292,509)(293,508)(294,507)(295,506)(296,505)
(297,504)(298,503)(299,502)(300,501)(301,500)(302,499)(303,498)(304,497)
(305,496)(306,495)(307,511)(308,527)(309,526)(310,525)(311,524)(312,523)
(313,522)(314,521)(315,520)(316,519)(317,518)(318,517)(319,516)(320,515)
(321,514)(322,513)(323,512)(324,528)(325,544)(326,543)(327,542)(328,541)
(329,540)(330,539)(331,538)(332,537)(333,536)(334,535)(335,534)(336,533)
(337,532)(338,531)(339,530)(340,529)(341,409)(342,425)(343,424)(344,423)
(345,422)(346,421)(347,420)(348,419)(349,418)(350,417)(351,416)(352,415)
(353,414)(354,413)(355,412)(356,411)(357,410)(358,426)(359,442)(360,441)
(361,440)(362,439)(363,438)(364,437)(365,436)(366,435)(367,434)(368,433)
(369,432)(370,431)(371,430)(372,429)(373,428)(374,427)(375,443)(376,459)
(377,458)(378,457)(379,456)(380,455)(381,454)(382,453)(383,452)(384,451)
(385,450)(386,449)(387,448)(388,447)(389,446)(390,445)(391,444)(392,460)
(393,476)(394,475)(395,474)(396,473)(397,472)(398,471)(399,470)(400,469)
(401,468)(402,467)(403,466)(404,465)(405,464)(406,463)(407,462)(408,461);;
s3 := ( 1, 70)( 2, 69)( 3, 85)( 4, 84)( 5, 83)( 6, 82)( 7, 81)( 8, 80)
( 9, 79)( 10, 78)( 11, 77)( 12, 76)( 13, 75)( 14, 74)( 15, 73)( 16, 72)
( 17, 71)( 18, 87)( 19, 86)( 20,102)( 21,101)( 22,100)( 23, 99)( 24, 98)
( 25, 97)( 26, 96)( 27, 95)( 28, 94)( 29, 93)( 30, 92)( 31, 91)( 32, 90)
( 33, 89)( 34, 88)( 35,104)( 36,103)( 37,119)( 38,118)( 39,117)( 40,116)
( 41,115)( 42,114)( 43,113)( 44,112)( 45,111)( 46,110)( 47,109)( 48,108)
( 49,107)( 50,106)( 51,105)( 52,121)( 53,120)( 54,136)( 55,135)( 56,134)
( 57,133)( 58,132)( 59,131)( 60,130)( 61,129)( 62,128)( 63,127)( 64,126)
( 65,125)( 66,124)( 67,123)( 68,122)(137,206)(138,205)(139,221)(140,220)
(141,219)(142,218)(143,217)(144,216)(145,215)(146,214)(147,213)(148,212)
(149,211)(150,210)(151,209)(152,208)(153,207)(154,223)(155,222)(156,238)
(157,237)(158,236)(159,235)(160,234)(161,233)(162,232)(163,231)(164,230)
(165,229)(166,228)(167,227)(168,226)(169,225)(170,224)(171,240)(172,239)
(173,255)(174,254)(175,253)(176,252)(177,251)(178,250)(179,249)(180,248)
(181,247)(182,246)(183,245)(184,244)(185,243)(186,242)(187,241)(188,257)
(189,256)(190,272)(191,271)(192,270)(193,269)(194,268)(195,267)(196,266)
(197,265)(198,264)(199,263)(200,262)(201,261)(202,260)(203,259)(204,258)
(273,342)(274,341)(275,357)(276,356)(277,355)(278,354)(279,353)(280,352)
(281,351)(282,350)(283,349)(284,348)(285,347)(286,346)(287,345)(288,344)
(289,343)(290,359)(291,358)(292,374)(293,373)(294,372)(295,371)(296,370)
(297,369)(298,368)(299,367)(300,366)(301,365)(302,364)(303,363)(304,362)
(305,361)(306,360)(307,376)(308,375)(309,391)(310,390)(311,389)(312,388)
(313,387)(314,386)(315,385)(316,384)(317,383)(318,382)(319,381)(320,380)
(321,379)(322,378)(323,377)(324,393)(325,392)(326,408)(327,407)(328,406)
(329,405)(330,404)(331,403)(332,402)(333,401)(334,400)(335,399)(336,398)
(337,397)(338,396)(339,395)(340,394)(409,478)(410,477)(411,493)(412,492)
(413,491)(414,490)(415,489)(416,488)(417,487)(418,486)(419,485)(420,484)
(421,483)(422,482)(423,481)(424,480)(425,479)(426,495)(427,494)(428,510)
(429,509)(430,508)(431,507)(432,506)(433,505)(434,504)(435,503)(436,502)
(437,501)(438,500)(439,499)(440,498)(441,497)(442,496)(443,512)(444,511)
(445,527)(446,526)(447,525)(448,524)(449,523)(450,522)(451,521)(452,520)
(453,519)(454,518)(455,517)(456,516)(457,515)(458,514)(459,513)(460,529)
(461,528)(462,544)(463,543)(464,542)(465,541)(466,540)(467,539)(468,538)
(469,537)(470,536)(471,535)(472,534)(473,533)(474,532)(475,531)(476,530);;
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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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(544)!( 1,273)( 2,274)( 3,275)( 4,276)( 5,277)( 6,278)( 7,279)
( 8,280)( 9,281)( 10,282)( 11,283)( 12,284)( 13,285)( 14,286)( 15,287)
( 16,288)( 17,289)( 18,290)( 19,291)( 20,292)( 21,293)( 22,294)( 23,295)
( 24,296)( 25,297)( 26,298)( 27,299)( 28,300)( 29,301)( 30,302)( 31,303)
( 32,304)( 33,305)( 34,306)( 35,307)( 36,308)( 37,309)( 38,310)( 39,311)
( 40,312)( 41,313)( 42,314)( 43,315)( 44,316)( 45,317)( 46,318)( 47,319)
( 48,320)( 49,321)( 50,322)( 51,323)( 52,324)( 53,325)( 54,326)( 55,327)
( 56,328)( 57,329)( 58,330)( 59,331)( 60,332)( 61,333)( 62,334)( 63,335)
( 64,336)( 65,337)( 66,338)( 67,339)( 68,340)( 69,341)( 70,342)( 71,343)
( 72,344)( 73,345)( 74,346)( 75,347)( 76,348)( 77,349)( 78,350)( 79,351)
( 80,352)( 81,353)( 82,354)( 83,355)( 84,356)( 85,357)( 86,358)( 87,359)
( 88,360)( 89,361)( 90,362)( 91,363)( 92,364)( 93,365)( 94,366)( 95,367)
( 96,368)( 97,369)( 98,370)( 99,371)(100,372)(101,373)(102,374)(103,375)
(104,376)(105,377)(106,378)(107,379)(108,380)(109,381)(110,382)(111,383)
(112,384)(113,385)(114,386)(115,387)(116,388)(117,389)(118,390)(119,391)
(120,392)(121,393)(122,394)(123,395)(124,396)(125,397)(126,398)(127,399)
(128,400)(129,401)(130,402)(131,403)(132,404)(133,405)(134,406)(135,407)
(136,408)(137,409)(138,410)(139,411)(140,412)(141,413)(142,414)(143,415)
(144,416)(145,417)(146,418)(147,419)(148,420)(149,421)(150,422)(151,423)
(152,424)(153,425)(154,426)(155,427)(156,428)(157,429)(158,430)(159,431)
(160,432)(161,433)(162,434)(163,435)(164,436)(165,437)(166,438)(167,439)
(168,440)(169,441)(170,442)(171,443)(172,444)(173,445)(174,446)(175,447)
(176,448)(177,449)(178,450)(179,451)(180,452)(181,453)(182,454)(183,455)
(184,456)(185,457)(186,458)(187,459)(188,460)(189,461)(190,462)(191,463)
(192,464)(193,465)(194,466)(195,467)(196,468)(197,469)(198,470)(199,471)
(200,472)(201,473)(202,474)(203,475)(204,476)(205,477)(206,478)(207,479)
(208,480)(209,481)(210,482)(211,483)(212,484)(213,485)(214,486)(215,487)
(216,488)(217,489)(218,490)(219,491)(220,492)(221,493)(222,494)(223,495)
(224,496)(225,497)(226,498)(227,499)(228,500)(229,501)(230,502)(231,503)
(232,504)(233,505)(234,506)(235,507)(236,508)(237,509)(238,510)(239,511)
(240,512)(241,513)(242,514)(243,515)(244,516)(245,517)(246,518)(247,519)
(248,520)(249,521)(250,522)(251,523)(252,524)(253,525)(254,526)(255,527)
(256,528)(257,529)(258,530)(259,531)(260,532)(261,533)(262,534)(263,535)
(264,536)(265,537)(266,538)(267,539)(268,540)(269,541)(270,542)(271,543)
(272,544);
s1 := Sym(544)!(137,154)(138,155)(139,156)(140,157)(141,158)(142,159)(143,160)
(144,161)(145,162)(146,163)(147,164)(148,165)(149,166)(150,167)(151,168)
(152,169)(153,170)(171,188)(172,189)(173,190)(174,191)(175,192)(176,193)
(177,194)(178,195)(179,196)(180,197)(181,198)(182,199)(183,200)(184,201)
(185,202)(186,203)(187,204)(205,222)(206,223)(207,224)(208,225)(209,226)
(210,227)(211,228)(212,229)(213,230)(214,231)(215,232)(216,233)(217,234)
(218,235)(219,236)(220,237)(221,238)(239,256)(240,257)(241,258)(242,259)
(243,260)(244,261)(245,262)(246,263)(247,264)(248,265)(249,266)(250,267)
(251,268)(252,269)(253,270)(254,271)(255,272)(273,307)(274,308)(275,309)
(276,310)(277,311)(278,312)(279,313)(280,314)(281,315)(282,316)(283,317)
(284,318)(285,319)(286,320)(287,321)(288,322)(289,323)(290,324)(291,325)
(292,326)(293,327)(294,328)(295,329)(296,330)(297,331)(298,332)(299,333)
(300,334)(301,335)(302,336)(303,337)(304,338)(305,339)(306,340)(341,375)
(342,376)(343,377)(344,378)(345,379)(346,380)(347,381)(348,382)(349,383)
(350,384)(351,385)(352,386)(353,387)(354,388)(355,389)(356,390)(357,391)
(358,392)(359,393)(360,394)(361,395)(362,396)(363,397)(364,398)(365,399)
(366,400)(367,401)(368,402)(369,403)(370,404)(371,405)(372,406)(373,407)
(374,408)(409,460)(410,461)(411,462)(412,463)(413,464)(414,465)(415,466)
(416,467)(417,468)(418,469)(419,470)(420,471)(421,472)(422,473)(423,474)
(424,475)(425,476)(426,443)(427,444)(428,445)(429,446)(430,447)(431,448)
(432,449)(433,450)(434,451)(435,452)(436,453)(437,454)(438,455)(439,456)
(440,457)(441,458)(442,459)(477,528)(478,529)(479,530)(480,531)(481,532)
(482,533)(483,534)(484,535)(485,536)(486,537)(487,538)(488,539)(489,540)
(490,541)(491,542)(492,543)(493,544)(494,511)(495,512)(496,513)(497,514)
(498,515)(499,516)(500,517)(501,518)(502,519)(503,520)(504,521)(505,522)
(506,523)(507,524)(508,525)(509,526)(510,527);
s2 := Sym(544)!( 1,205)( 2,221)( 3,220)( 4,219)( 5,218)( 6,217)( 7,216)
( 8,215)( 9,214)( 10,213)( 11,212)( 12,211)( 13,210)( 14,209)( 15,208)
( 16,207)( 17,206)( 18,222)( 19,238)( 20,237)( 21,236)( 22,235)( 23,234)
( 24,233)( 25,232)( 26,231)( 27,230)( 28,229)( 29,228)( 30,227)( 31,226)
( 32,225)( 33,224)( 34,223)( 35,239)( 36,255)( 37,254)( 38,253)( 39,252)
( 40,251)( 41,250)( 42,249)( 43,248)( 44,247)( 45,246)( 46,245)( 47,244)
( 48,243)( 49,242)( 50,241)( 51,240)( 52,256)( 53,272)( 54,271)( 55,270)
( 56,269)( 57,268)( 58,267)( 59,266)( 60,265)( 61,264)( 62,263)( 63,262)
( 64,261)( 65,260)( 66,259)( 67,258)( 68,257)( 69,137)( 70,153)( 71,152)
( 72,151)( 73,150)( 74,149)( 75,148)( 76,147)( 77,146)( 78,145)( 79,144)
( 80,143)( 81,142)( 82,141)( 83,140)( 84,139)( 85,138)( 86,154)( 87,170)
( 88,169)( 89,168)( 90,167)( 91,166)( 92,165)( 93,164)( 94,163)( 95,162)
( 96,161)( 97,160)( 98,159)( 99,158)(100,157)(101,156)(102,155)(103,171)
(104,187)(105,186)(106,185)(107,184)(108,183)(109,182)(110,181)(111,180)
(112,179)(113,178)(114,177)(115,176)(116,175)(117,174)(118,173)(119,172)
(120,188)(121,204)(122,203)(123,202)(124,201)(125,200)(126,199)(127,198)
(128,197)(129,196)(130,195)(131,194)(132,193)(133,192)(134,191)(135,190)
(136,189)(273,477)(274,493)(275,492)(276,491)(277,490)(278,489)(279,488)
(280,487)(281,486)(282,485)(283,484)(284,483)(285,482)(286,481)(287,480)
(288,479)(289,478)(290,494)(291,510)(292,509)(293,508)(294,507)(295,506)
(296,505)(297,504)(298,503)(299,502)(300,501)(301,500)(302,499)(303,498)
(304,497)(305,496)(306,495)(307,511)(308,527)(309,526)(310,525)(311,524)
(312,523)(313,522)(314,521)(315,520)(316,519)(317,518)(318,517)(319,516)
(320,515)(321,514)(322,513)(323,512)(324,528)(325,544)(326,543)(327,542)
(328,541)(329,540)(330,539)(331,538)(332,537)(333,536)(334,535)(335,534)
(336,533)(337,532)(338,531)(339,530)(340,529)(341,409)(342,425)(343,424)
(344,423)(345,422)(346,421)(347,420)(348,419)(349,418)(350,417)(351,416)
(352,415)(353,414)(354,413)(355,412)(356,411)(357,410)(358,426)(359,442)
(360,441)(361,440)(362,439)(363,438)(364,437)(365,436)(366,435)(367,434)
(368,433)(369,432)(370,431)(371,430)(372,429)(373,428)(374,427)(375,443)
(376,459)(377,458)(378,457)(379,456)(380,455)(381,454)(382,453)(383,452)
(384,451)(385,450)(386,449)(387,448)(388,447)(389,446)(390,445)(391,444)
(392,460)(393,476)(394,475)(395,474)(396,473)(397,472)(398,471)(399,470)
(400,469)(401,468)(402,467)(403,466)(404,465)(405,464)(406,463)(407,462)
(408,461);
s3 := Sym(544)!( 1, 70)( 2, 69)( 3, 85)( 4, 84)( 5, 83)( 6, 82)( 7, 81)
( 8, 80)( 9, 79)( 10, 78)( 11, 77)( 12, 76)( 13, 75)( 14, 74)( 15, 73)
( 16, 72)( 17, 71)( 18, 87)( 19, 86)( 20,102)( 21,101)( 22,100)( 23, 99)
( 24, 98)( 25, 97)( 26, 96)( 27, 95)( 28, 94)( 29, 93)( 30, 92)( 31, 91)
( 32, 90)( 33, 89)( 34, 88)( 35,104)( 36,103)( 37,119)( 38,118)( 39,117)
( 40,116)( 41,115)( 42,114)( 43,113)( 44,112)( 45,111)( 46,110)( 47,109)
( 48,108)( 49,107)( 50,106)( 51,105)( 52,121)( 53,120)( 54,136)( 55,135)
( 56,134)( 57,133)( 58,132)( 59,131)( 60,130)( 61,129)( 62,128)( 63,127)
( 64,126)( 65,125)( 66,124)( 67,123)( 68,122)(137,206)(138,205)(139,221)
(140,220)(141,219)(142,218)(143,217)(144,216)(145,215)(146,214)(147,213)
(148,212)(149,211)(150,210)(151,209)(152,208)(153,207)(154,223)(155,222)
(156,238)(157,237)(158,236)(159,235)(160,234)(161,233)(162,232)(163,231)
(164,230)(165,229)(166,228)(167,227)(168,226)(169,225)(170,224)(171,240)
(172,239)(173,255)(174,254)(175,253)(176,252)(177,251)(178,250)(179,249)
(180,248)(181,247)(182,246)(183,245)(184,244)(185,243)(186,242)(187,241)
(188,257)(189,256)(190,272)(191,271)(192,270)(193,269)(194,268)(195,267)
(196,266)(197,265)(198,264)(199,263)(200,262)(201,261)(202,260)(203,259)
(204,258)(273,342)(274,341)(275,357)(276,356)(277,355)(278,354)(279,353)
(280,352)(281,351)(282,350)(283,349)(284,348)(285,347)(286,346)(287,345)
(288,344)(289,343)(290,359)(291,358)(292,374)(293,373)(294,372)(295,371)
(296,370)(297,369)(298,368)(299,367)(300,366)(301,365)(302,364)(303,363)
(304,362)(305,361)(306,360)(307,376)(308,375)(309,391)(310,390)(311,389)
(312,388)(313,387)(314,386)(315,385)(316,384)(317,383)(318,382)(319,381)
(320,380)(321,379)(322,378)(323,377)(324,393)(325,392)(326,408)(327,407)
(328,406)(329,405)(330,404)(331,403)(332,402)(333,401)(334,400)(335,399)
(336,398)(337,397)(338,396)(339,395)(340,394)(409,478)(410,477)(411,493)
(412,492)(413,491)(414,490)(415,489)(416,488)(417,487)(418,486)(419,485)
(420,484)(421,483)(422,482)(423,481)(424,480)(425,479)(426,495)(427,494)
(428,510)(429,509)(430,508)(431,507)(432,506)(433,505)(434,504)(435,503)
(436,502)(437,501)(438,500)(439,499)(440,498)(441,497)(442,496)(443,512)
(444,511)(445,527)(446,526)(447,525)(448,524)(449,523)(450,522)(451,521)
(452,520)(453,519)(454,518)(455,517)(456,516)(457,515)(458,514)(459,513)
(460,529)(461,528)(462,544)(463,543)(464,542)(465,541)(466,540)(467,539)
(468,538)(469,537)(470,536)(471,535)(472,534)(473,533)(474,532)(475,531)
(476,530);
poly := sub<Sym(544)|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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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