Polytope of Type {18,4}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle