Polytope of Type {4,18}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,18}*1296d
if this polytope has a name.
Group : SmallGroup(1296,3492)
Rank : 3
Schlafli Type : {4,18}
Number of vertices, edges, etc : 36, 324, 162
Order of s0s1s2 : 9
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,9}*648
   27-fold quotients : {4,6}*48b
   54-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1> of order 3.
      54 facets:
         54 of {4}*8
      18 vertex figures:
         9 of {6}*12
         9 of {18}*36
   P/N, where N=<s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1> of order 3.
      54 facets:
         54 of {4}*8
      12 vertex figures:
         12 of {18}*36
   P/N, where N=<s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2> of order 3.
      54 facets:
         54 of {4}*8
      12 vertex figures:
         12 of {18}*36
   P/N, where N=<s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1> of order 9.
      18 facets:
         18 of {4}*8
      4 vertex figures:
         4 of {18}*36
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s2*s1, s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1> of order 9.
      18 facets:
         18 of {4}*8
      8 vertex figures:
         6 of {6}*12
         2 of {18}*36
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s2*s1, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1> of order 9.
      18 facets:
         18 of {4}*8
      6 vertex figures:
         3 of {18}*36
         3 of {6}*12

Permutation Representation (GAP) : 
s0 := (  1,379)(  2,381)(  3,380)(  4,385)(  5,387)(  6,386)(  7,382)(  8,384)(  9,383)( 10,388)( 11,390)( 12,389)( 13,394)( 14,396)( 15,395)( 16,391)( 17,393)( 18,392)( 19,397)( 20,399)( 21,398)( 22,403)( 23,405)( 24,404)( 25,400)( 26,402)( 27,401)( 28,406)( 29,408)( 30,407)( 31,412)( 32,414)( 33,413)( 34,409)( 35,411)( 36,410)( 37,415)( 38,417)( 39,416)( 40,421)( 41,423)( 42,422)( 43,418)( 44,420)( 45,419)( 46,424)( 47,426)( 48,425)( 49,430)( 50,432)( 51,431)( 52,427)( 53,429)( 54,428)( 55,325)( 56,327)( 57,326)( 58,331)( 59,333)( 60,332)( 61,328)( 62,330)( 63,329)( 64,334)( 65,336)( 66,335)( 67,340)( 68,342)( 69,341)( 70,337)( 71,339)( 72,338)( 73,343)( 74,345)( 75,344)( 76,349)( 77,351)( 78,350)( 79,346)( 80,348)( 81,347)( 82,352)( 83,354)( 84,353)( 85,358)( 86,360)( 87,359)( 88,355)( 89,357)( 90,356)( 91,361)( 92,363)( 93,362)( 94,367)( 95,369)( 96,368)( 97,364)( 98,366)( 99,365)(100,370)(101,372)(102,371)(103,376)(104,378)(105,377)(106,373)(107,375)(108,374)(109,487)(110,489)(111,488)(112,493)(113,495)(114,494)(115,490)(116,492)(117,491)(118,496)(119,498)(120,497)(121,502)(122,504)(123,503)(124,499)(125,501)(126,500)(127,505)(128,507)(129,506)(130,511)(131,513)(132,512)(133,508)(134,510)(135,509)(136,514)(137,516)(138,515)(139,520)(140,522)(141,521)(142,517)(143,519)(144,518)(145,523)(146,525)(147,524)(148,529)(149,531)(150,530)(151,526)(152,528)(153,527)(154,532)(155,534)(156,533)(157,538)(158,540)(159,539)(160,535)(161,537)(162,536)(163,433)(164,435)(165,434)(166,439)(167,441)(168,440)(169,436)(170,438)(171,437)(172,442)(173,444)(174,443)(175,448)(176,450)(177,449)(178,445)(179,447)(180,446)(181,451)(182,453)(183,452)(184,457)(185,459)(186,458)(187,454)(188,456)(189,455)(190,460)(191,462)(192,461)(193,466)(194,468)(195,467)(196,463)(197,465)(198,464)(199,469)(200,471)(201,470)(202,475)(203,477)(204,476)(205,472)(206,474)(207,473)(208,478)(209,480)(210,479)(211,484)(212,486)(213,485)(214,481)(215,483)(216,482)(217,595)(218,597)(219,596)(220,601)(221,603)(222,602)(223,598)(224,600)(225,599)(226,604)(227,606)(228,605)(229,610)(230,612)(231,611)(232,607)(233,609)(234,608)(235,613)(236,615)(237,614)(238,619)(239,621)(240,620)(241,616)(242,618)(243,617)(244,622)(245,624)(246,623)(247,628)(248,630)(249,629)(250,625)(251,627)(252,626)(253,631)(254,633)(255,632)(256,637)(257,639)(258,638)(259,634)(260,636)(261,635)(262,640)(263,642)(264,641)(265,646)(266,648)(267,647)(268,643)(269,645)(270,644)(271,541)(272,543)(273,542)(274,547)(275,549)(276,548)(277,544)(278,546)(279,545)(280,550)(281,552)(282,551)(283,556)(284,558)(285,557)(286,553)(287,555)(288,554)(289,559)(290,561)(291,560)(292,565)(293,567)(294,566)(295,562)(296,564)(297,563)(298,568)(299,570)(300,569)(301,574)(302,576)(303,575)(304,571)(305,573)(306,572)(307,577)(308,579)(309,578)(310,583)(311,585)(312,584)(313,580)(314,582)(315,581)(316,586)(317,588)(318,587)(319,592)(320,594)(321,593)(322,589)(323,591)(324,590);;
s1 := (  2,  3)(  4, 19)(  5, 21)(  6, 20)(  7, 10)(  8, 12)(  9, 11)( 13, 25)( 14, 27)( 15, 26)( 17, 18)( 23, 24)( 28, 55)( 29, 57)( 30, 56)( 31, 73)( 32, 75)( 33, 74)( 34, 64)( 35, 66)( 36, 65)( 37, 61)( 38, 63)( 39, 62)( 40, 79)( 41, 81)( 42, 80)( 43, 70)( 44, 72)( 45, 71)( 46, 58)( 47, 60)( 48, 59)( 49, 76)( 50, 78)( 51, 77)( 52, 67)( 53, 69)( 54, 68)( 83, 84)( 85,100)( 86,102)( 87,101)( 88, 91)( 89, 93)( 90, 92)( 94,106)( 95,108)( 96,107)( 98, 99)(104,105)(109,217)(110,219)(111,218)(112,235)(113,237)(114,236)(115,226)(116,228)(117,227)(118,223)(119,225)(120,224)(121,241)(122,243)(123,242)(124,232)(125,234)(126,233)(127,220)(128,222)(129,221)(130,238)(131,240)(132,239)(133,229)(134,231)(135,230)(136,271)(137,273)(138,272)(139,289)(140,291)(141,290)(142,280)(143,282)(144,281)(145,277)(146,279)(147,278)(148,295)(149,297)(150,296)(151,286)(152,288)(153,287)(154,274)(155,276)(156,275)(157,292)(158,294)(159,293)(160,283)(161,285)(162,284)(163,244)(164,246)(165,245)(166,262)(167,264)(168,263)(169,253)(170,255)(171,254)(172,250)(173,252)(174,251)(175,268)(176,270)(177,269)(178,259)(179,261)(180,260)(181,247)(182,249)(183,248)(184,265)(185,267)(186,266)(187,256)(188,258)(189,257)(190,298)(191,300)(192,299)(193,316)(194,318)(195,317)(196,307)(197,309)(198,308)(199,304)(200,306)(201,305)(202,322)(203,324)(204,323)(205,313)(206,315)(207,314)(208,301)(209,303)(210,302)(211,319)(212,321)(213,320)(214,310)(215,312)(216,311)(326,327)(328,343)(329,345)(330,344)(331,334)(332,336)(333,335)(337,349)(338,351)(339,350)(341,342)(347,348)(352,379)(353,381)(354,380)(355,397)(356,399)(357,398)(358,388)(359,390)(360,389)(361,385)(362,387)(363,386)(364,403)(365,405)(366,404)(367,394)(368,396)(369,395)(370,382)(371,384)(372,383)(373,400)(374,402)(375,401)(376,391)(377,393)(378,392)(407,408)(409,424)(410,426)(411,425)(412,415)(413,417)(414,416)(418,430)(419,432)(420,431)(422,423)(428,429)(433,541)(434,543)(435,542)(436,559)(437,561)(438,560)(439,550)(440,552)(441,551)(442,547)(443,549)(444,548)(445,565)(446,567)(447,566)(448,556)(449,558)(450,557)(451,544)(452,546)(453,545)(454,562)(455,564)(456,563)(457,553)(458,555)(459,554)(460,595)(461,597)(462,596)(463,613)(464,615)(465,614)(466,604)(467,606)(468,605)(469,601)(470,603)(471,602)(472,619)(473,621)(474,620)(475,610)(476,612)(477,611)(478,598)(479,600)(480,599)(481,616)(482,618)(483,617)(484,607)(485,609)(486,608)(487,568)(488,570)(489,569)(490,586)(491,588)(492,587)(493,577)(494,579)(495,578)(496,574)(497,576)(498,575)(499,592)(500,594)(501,593)(502,583)(503,585)(504,584)(505,571)(506,573)(507,572)(508,589)(509,591)(510,590)(511,580)(512,582)(513,581)(514,622)(515,624)(516,623)(517,640)(518,642)(519,641)(520,631)(521,633)(522,632)(523,628)(524,630)(525,629)(526,646)(527,648)(528,647)(529,637)(530,639)(531,638)(532,625)(533,627)(534,626)(535,643)(536,645)(537,644)(538,634)(539,636)(540,635);;
s2 := (  1,550)(  2,556)(  3,553)(  4,552)(  5,558)(  6,555)(  7,551)(  8,557)(  9,554)( 10,541)( 11,547)( 12,544)( 13,543)( 14,549)( 15,546)( 16,542)( 17,548)( 18,545)( 19,559)( 20,565)( 21,562)( 22,561)( 23,567)( 24,564)( 25,560)( 26,566)( 27,563)( 28,631)( 29,637)( 30,634)( 31,633)( 32,639)( 33,636)( 34,632)( 35,638)( 36,635)( 37,622)( 38,628)( 39,625)( 40,624)( 41,630)( 42,627)( 43,623)( 44,629)( 45,626)( 46,640)( 47,646)( 48,643)( 49,642)( 50,648)( 51,645)( 52,641)( 53,647)( 54,644)( 55,604)( 56,610)( 57,607)( 58,606)( 59,612)( 60,609)( 61,605)( 62,611)( 63,608)( 64,595)( 65,601)( 66,598)( 67,597)( 68,603)( 69,600)( 70,596)( 71,602)( 72,599)( 73,613)( 74,619)( 75,616)( 76,615)( 77,621)( 78,618)( 79,614)( 80,620)( 81,617)( 82,577)( 83,583)( 84,580)( 85,579)( 86,585)( 87,582)( 88,578)( 89,584)( 90,581)( 91,568)( 92,574)( 93,571)( 94,570)( 95,576)( 96,573)( 97,569)( 98,575)( 99,572)(100,586)(101,592)(102,589)(103,588)(104,594)(105,591)(106,587)(107,593)(108,590)(109,442)(110,448)(111,445)(112,444)(113,450)(114,447)(115,443)(116,449)(117,446)(118,433)(119,439)(120,436)(121,435)(122,441)(123,438)(124,434)(125,440)(126,437)(127,451)(128,457)(129,454)(130,453)(131,459)(132,456)(133,452)(134,458)(135,455)(136,523)(137,529)(138,526)(139,525)(140,531)(141,528)(142,524)(143,530)(144,527)(145,514)(146,520)(147,517)(148,516)(149,522)(150,519)(151,515)(152,521)(153,518)(154,532)(155,538)(156,535)(157,534)(158,540)(159,537)(160,533)(161,539)(162,536)(163,496)(164,502)(165,499)(166,498)(167,504)(168,501)(169,497)(170,503)(171,500)(172,487)(173,493)(174,490)(175,489)(176,495)(177,492)(178,488)(179,494)(180,491)(181,505)(182,511)(183,508)(184,507)(185,513)(186,510)(187,506)(188,512)(189,509)(190,469)(191,475)(192,472)(193,471)(194,477)(195,474)(196,470)(197,476)(198,473)(199,460)(200,466)(201,463)(202,462)(203,468)(204,465)(205,461)(206,467)(207,464)(208,478)(209,484)(210,481)(211,480)(212,486)(213,483)(214,479)(215,485)(216,482)(217,334)(218,340)(219,337)(220,336)(221,342)(222,339)(223,335)(224,341)(225,338)(226,325)(227,331)(228,328)(229,327)(230,333)(231,330)(232,326)(233,332)(234,329)(235,343)(236,349)(237,346)(238,345)(239,351)(240,348)(241,344)(242,350)(243,347)(244,415)(245,421)(246,418)(247,417)(248,423)(249,420)(250,416)(251,422)(252,419)(253,406)(254,412)(255,409)(256,408)(257,414)(258,411)(259,407)(260,413)(261,410)(262,424)(263,430)(264,427)(265,426)(266,432)(267,429)(268,425)(269,431)(270,428)(271,388)(272,394)(273,391)(274,390)(275,396)(276,393)(277,389)(278,395)(279,392)(280,379)(281,385)(282,382)(283,381)(284,387)(285,384)(286,380)(287,386)(288,383)(289,397)(290,403)(291,400)(292,399)(293,405)(294,402)(295,398)(296,404)(297,401)(298,361)(299,367)(300,364)(301,363)(302,369)(303,366)(304,362)(305,368)(306,365)(307,352)(308,358)(309,355)(310,354)(311,360)(312,357)(313,353)(314,359)(315,356)(316,370)(317,376)(318,373)(319,372)(320,378)(321,375)(322,371)(323,377)(324,374);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(648)!(  1,379)(  2,381)(  3,380)(  4,385)(  5,387)(  6,386)(  7,382)(  8,384)(  9,383)( 10,388)( 11,390)( 12,389)( 13,394)( 14,396)( 15,395)( 16,391)( 17,393)( 18,392)( 19,397)( 20,399)( 21,398)( 22,403)( 23,405)( 24,404)( 25,400)( 26,402)( 27,401)( 28,406)( 29,408)( 30,407)( 31,412)( 32,414)( 33,413)( 34,409)( 35,411)( 36,410)( 37,415)( 38,417)( 39,416)( 40,421)( 41,423)( 42,422)( 43,418)( 44,420)( 45,419)( 46,424)( 47,426)( 48,425)( 49,430)( 50,432)( 51,431)( 52,427)( 53,429)( 54,428)( 55,325)( 56,327)( 57,326)( 58,331)( 59,333)( 60,332)( 61,328)( 62,330)( 63,329)( 64,334)( 65,336)( 66,335)( 67,340)( 68,342)( 69,341)( 70,337)( 71,339)( 72,338)( 73,343)( 74,345)( 75,344)( 76,349)( 77,351)( 78,350)( 79,346)( 80,348)( 81,347)( 82,352)( 83,354)( 84,353)( 85,358)( 86,360)( 87,359)( 88,355)( 89,357)( 90,356)( 91,361)( 92,363)( 93,362)( 94,367)( 95,369)( 96,368)( 97,364)( 98,366)( 99,365)(100,370)(101,372)(102,371)(103,376)(104,378)(105,377)(106,373)(107,375)(108,374)(109,487)(110,489)(111,488)(112,493)(113,495)(114,494)(115,490)(116,492)(117,491)(118,496)(119,498)(120,497)(121,502)(122,504)(123,503)(124,499)(125,501)(126,500)(127,505)(128,507)(129,506)(130,511)(131,513)(132,512)(133,508)(134,510)(135,509)(136,514)(137,516)(138,515)(139,520)(140,522)(141,521)(142,517)(143,519)(144,518)(145,523)(146,525)(147,524)(148,529)(149,531)(150,530)(151,526)(152,528)(153,527)(154,532)(155,534)(156,533)(157,538)(158,540)(159,539)(160,535)(161,537)(162,536)(163,433)(164,435)(165,434)(166,439)(167,441)(168,440)(169,436)(170,438)(171,437)(172,442)(173,444)(174,443)(175,448)(176,450)(177,449)(178,445)(179,447)(180,446)(181,451)(182,453)(183,452)(184,457)(185,459)(186,458)(187,454)(188,456)(189,455)(190,460)(191,462)(192,461)(193,466)(194,468)(195,467)(196,463)(197,465)(198,464)(199,469)(200,471)(201,470)(202,475)(203,477)(204,476)(205,472)(206,474)(207,473)(208,478)(209,480)(210,479)(211,484)(212,486)(213,485)(214,481)(215,483)(216,482)(217,595)(218,597)(219,596)(220,601)(221,603)(222,602)(223,598)(224,600)(225,599)(226,604)(227,606)(228,605)(229,610)(230,612)(231,611)(232,607)(233,609)(234,608)(235,613)(236,615)(237,614)(238,619)(239,621)(240,620)(241,616)(242,618)(243,617)(244,622)(245,624)(246,623)(247,628)(248,630)(249,629)(250,625)(251,627)(252,626)(253,631)(254,633)(255,632)(256,637)(257,639)(258,638)(259,634)(260,636)(261,635)(262,640)(263,642)(264,641)(265,646)(266,648)(267,647)(268,643)(269,645)(270,644)(271,541)(272,543)(273,542)(274,547)(275,549)(276,548)(277,544)(278,546)(279,545)(280,550)(281,552)(282,551)(283,556)(284,558)(285,557)(286,553)(287,555)(288,554)(289,559)(290,561)(291,560)(292,565)(293,567)(294,566)(295,562)(296,564)(297,563)(298,568)(299,570)(300,569)(301,574)(302,576)(303,575)(304,571)(305,573)(306,572)(307,577)(308,579)(309,578)(310,583)(311,585)(312,584)(313,580)(314,582)(315,581)(316,586)(317,588)(318,587)(319,592)(320,594)(321,593)(322,589)(323,591)(324,590);
s1 := Sym(648)!(  2,  3)(  4, 19)(  5, 21)(  6, 20)(  7, 10)(  8, 12)(  9, 11)( 13, 25)( 14, 27)( 15, 26)( 17, 18)( 23, 24)( 28, 55)( 29, 57)( 30, 56)( 31, 73)( 32, 75)( 33, 74)( 34, 64)( 35, 66)( 36, 65)( 37, 61)( 38, 63)( 39, 62)( 40, 79)( 41, 81)( 42, 80)( 43, 70)( 44, 72)( 45, 71)( 46, 58)( 47, 60)( 48, 59)( 49, 76)( 50, 78)( 51, 77)( 52, 67)( 53, 69)( 54, 68)( 83, 84)( 85,100)( 86,102)( 87,101)( 88, 91)( 89, 93)( 90, 92)( 94,106)( 95,108)( 96,107)( 98, 99)(104,105)(109,217)(110,219)(111,218)(112,235)(113,237)(114,236)(115,226)(116,228)(117,227)(118,223)(119,225)(120,224)(121,241)(122,243)(123,242)(124,232)(125,234)(126,233)(127,220)(128,222)(129,221)(130,238)(131,240)(132,239)(133,229)(134,231)(135,230)(136,271)(137,273)(138,272)(139,289)(140,291)(141,290)(142,280)(143,282)(144,281)(145,277)(146,279)(147,278)(148,295)(149,297)(150,296)(151,286)(152,288)(153,287)(154,274)(155,276)(156,275)(157,292)(158,294)(159,293)(160,283)(161,285)(162,284)(163,244)(164,246)(165,245)(166,262)(167,264)(168,263)(169,253)(170,255)(171,254)(172,250)(173,252)(174,251)(175,268)(176,270)(177,269)(178,259)(179,261)(180,260)(181,247)(182,249)(183,248)(184,265)(185,267)(186,266)(187,256)(188,258)(189,257)(190,298)(191,300)(192,299)(193,316)(194,318)(195,317)(196,307)(197,309)(198,308)(199,304)(200,306)(201,305)(202,322)(203,324)(204,323)(205,313)(206,315)(207,314)(208,301)(209,303)(210,302)(211,319)(212,321)(213,320)(214,310)(215,312)(216,311)(326,327)(328,343)(329,345)(330,344)(331,334)(332,336)(333,335)(337,349)(338,351)(339,350)(341,342)(347,348)(352,379)(353,381)(354,380)(355,397)(356,399)(357,398)(358,388)(359,390)(360,389)(361,385)(362,387)(363,386)(364,403)(365,405)(366,404)(367,394)(368,396)(369,395)(370,382)(371,384)(372,383)(373,400)(374,402)(375,401)(376,391)(377,393)(378,392)(407,408)(409,424)(410,426)(411,425)(412,415)(413,417)(414,416)(418,430)(419,432)(420,431)(422,423)(428,429)(433,541)(434,543)(435,542)(436,559)(437,561)(438,560)(439,550)(440,552)(441,551)(442,547)(443,549)(444,548)(445,565)(446,567)(447,566)(448,556)(449,558)(450,557)(451,544)(452,546)(453,545)(454,562)(455,564)(456,563)(457,553)(458,555)(459,554)(460,595)(461,597)(462,596)(463,613)(464,615)(465,614)(466,604)(467,606)(468,605)(469,601)(470,603)(471,602)(472,619)(473,621)(474,620)(475,610)(476,612)(477,611)(478,598)(479,600)(480,599)(481,616)(482,618)(483,617)(484,607)(485,609)(486,608)(487,568)(488,570)(489,569)(490,586)(491,588)(492,587)(493,577)(494,579)(495,578)(496,574)(497,576)(498,575)(499,592)(500,594)(501,593)(502,583)(503,585)(504,584)(505,571)(506,573)(507,572)(508,589)(509,591)(510,590)(511,580)(512,582)(513,581)(514,622)(515,624)(516,623)(517,640)(518,642)(519,641)(520,631)(521,633)(522,632)(523,628)(524,630)(525,629)(526,646)(527,648)(528,647)(529,637)(530,639)(531,638)(532,625)(533,627)(534,626)(535,643)(536,645)(537,644)(538,634)(539,636)(540,635);
s2 := Sym(648)!(  1,550)(  2,556)(  3,553)(  4,552)(  5,558)(  6,555)(  7,551)(  8,557)(  9,554)( 10,541)( 11,547)( 12,544)( 13,543)( 14,549)( 15,546)( 16,542)( 17,548)( 18,545)( 19,559)( 20,565)( 21,562)( 22,561)( 23,567)( 24,564)( 25,560)( 26,566)( 27,563)( 28,631)( 29,637)( 30,634)( 31,633)( 32,639)( 33,636)( 34,632)( 35,638)( 36,635)( 37,622)( 38,628)( 39,625)( 40,624)( 41,630)( 42,627)( 43,623)( 44,629)( 45,626)( 46,640)( 47,646)( 48,643)( 49,642)( 50,648)( 51,645)( 52,641)( 53,647)( 54,644)( 55,604)( 56,610)( 57,607)( 58,606)( 59,612)( 60,609)( 61,605)( 62,611)( 63,608)( 64,595)( 65,601)( 66,598)( 67,597)( 68,603)( 69,600)( 70,596)( 71,602)( 72,599)( 73,613)( 74,619)( 75,616)( 76,615)( 77,621)( 78,618)( 79,614)( 80,620)( 81,617)( 82,577)( 83,583)( 84,580)( 85,579)( 86,585)( 87,582)( 88,578)( 89,584)( 90,581)( 91,568)( 92,574)( 93,571)( 94,570)( 95,576)( 96,573)( 97,569)( 98,575)( 99,572)(100,586)(101,592)(102,589)(103,588)(104,594)(105,591)(106,587)(107,593)(108,590)(109,442)(110,448)(111,445)(112,444)(113,450)(114,447)(115,443)(116,449)(117,446)(118,433)(119,439)(120,436)(121,435)(122,441)(123,438)(124,434)(125,440)(126,437)(127,451)(128,457)(129,454)(130,453)(131,459)(132,456)(133,452)(134,458)(135,455)(136,523)(137,529)(138,526)(139,525)(140,531)(141,528)(142,524)(143,530)(144,527)(145,514)(146,520)(147,517)(148,516)(149,522)(150,519)(151,515)(152,521)(153,518)(154,532)(155,538)(156,535)(157,534)(158,540)(159,537)(160,533)(161,539)(162,536)(163,496)(164,502)(165,499)(166,498)(167,504)(168,501)(169,497)(170,503)(171,500)(172,487)(173,493)(174,490)(175,489)(176,495)(177,492)(178,488)(179,494)(180,491)(181,505)(182,511)(183,508)(184,507)(185,513)(186,510)(187,506)(188,512)(189,509)(190,469)(191,475)(192,472)(193,471)(194,477)(195,474)(196,470)(197,476)(198,473)(199,460)(200,466)(201,463)(202,462)(203,468)(204,465)(205,461)(206,467)(207,464)(208,478)(209,484)(210,481)(211,480)(212,486)(213,483)(214,479)(215,485)(216,482)(217,334)(218,340)(219,337)(220,336)(221,342)(222,339)(223,335)(224,341)(225,338)(226,325)(227,331)(228,328)(229,327)(230,333)(231,330)(232,326)(233,332)(234,329)(235,343)(236,349)(237,346)(238,345)(239,351)(240,348)(241,344)(242,350)(243,347)(244,415)(245,421)(246,418)(247,417)(248,423)(249,420)(250,416)(251,422)(252,419)(253,406)(254,412)(255,409)(256,408)(257,414)(258,411)(259,407)(260,413)(261,410)(262,424)(263,430)(264,427)(265,426)(266,432)(267,429)(268,425)(269,431)(270,428)(271,388)(272,394)(273,391)(274,390)(275,396)(276,393)(277,389)(278,395)(279,392)(280,379)(281,385)(282,382)(283,381)(284,387)(285,384)(286,380)(287,386)(288,383)(289,397)(290,403)(291,400)(292,399)(293,405)(294,402)(295,398)(296,404)(297,401)(298,361)(299,367)(300,364)(301,363)(302,369)(303,366)(304,362)(305,368)(306,365)(307,352)(308,358)(309,355)(310,354)(311,360)(312,357)(313,353)(314,359)(315,356)(316,370)(317,376)(318,373)(319,372)(320,378)(321,375)(322,371)(323,377)(324,374);
poly := sub<Sym(648)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0 >;
References : None.
to this polytope

Twisty Puzzle