Part of the Atlas of Small Regular Polytopes

Polytope of Type {18,12}

Atlas Canonical Name {18,12}*1296n

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1296,3492)
Rank
3
Schläfli Type
{18,12}
Vertices, edges, …
54, 324, 36
Order of s0s1s2
6
Order of s0s1s2s1
12
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable

Quotients maximal quotients in bold

2-fold

27-fold

54-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s1*s0*(s1*s2)^3*s1*s0*s2*s1> of order 3

12 facets

30 vertex figures

Representations

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, 97)(  2, 98)(  3, 99)(  4, 94)(  5, 95)(  6, 96)(  7, 91)(  8, 92)(  9, 93)( 10, 88)( 11, 89)( 12, 90)( 13, 85)( 14, 86)( 15, 87)( 16, 82)( 17, 83)( 18, 84)( 19,106)( 20,107)( 21,108)( 22,103)( 23,104)( 24,105)( 25,100)( 26,101)( 27,102)( 28, 70)( 29, 71)( 30, 72)( 31, 67)( 32, 68)( 33, 69)( 34, 64)( 35, 65)( 36, 66)( 37, 61)( 38, 62)( 39, 63)( 40, 58)( 41, 59)( 42, 60)( 43, 55)( 44, 56)( 45, 57)( 46, 79)( 47, 80)( 48, 81)( 49, 76)( 50, 77)( 51, 78)( 52, 73)( 53, 74)( 54, 75)(109,205)(110,206)(111,207)(112,202)(113,203)(114,204)(115,199)(116,200)(117,201)(118,196)(119,197)(120,198)(121,193)(122,194)(123,195)(124,190)(125,191)(126,192)(127,214)(128,215)(129,216)(130,211)(131,212)(132,213)(133,208)(134,209)(135,210)(136,178)(137,179)(138,180)(139,175)(140,176)(141,177)(142,172)(143,173)(144,174)(145,169)(146,170)(147,171)(148,166)(149,167)(150,168)(151,163)(152,164)(153,165)(154,187)(155,188)(156,189)(157,184)(158,185)(159,186)(160,181)(161,182)(162,183)(217,313)(218,314)(219,315)(220,310)(221,311)(222,312)(223,307)(224,308)(225,309)(226,304)(227,305)(228,306)(229,301)(230,302)(231,303)(232,298)(233,299)(234,300)(235,322)(236,323)(237,324)(238,319)(239,320)(240,321)(241,316)(242,317)(243,318)(244,286)(245,287)(246,288)(247,283)(248,284)(249,285)(250,280)(251,281)(252,282)(253,277)(254,278)(255,279)(256,274)(257,275)(258,276)(259,271)(260,272)(261,273)(262,295)(263,296)(264,297)(265,292)(266,293)(267,294)(268,289)(269,290)(270,291)(325,421)(326,422)(327,423)(328,418)(329,419)(330,420)(331,415)(332,416)(333,417)(334,412)(335,413)(336,414)(337,409)(338,410)(339,411)(340,406)(341,407)(342,408)(343,430)(344,431)(345,432)(346,427)(347,428)(348,429)(349,424)(350,425)(351,426)(352,394)(353,395)(354,396)(355,391)(356,392)(357,393)(358,388)(359,389)(360,390)(361,385)(362,386)(363,387)(364,382)(365,383)(366,384)(367,379)(368,380)(369,381)(370,403)(371,404)(372,405)(373,400)(374,401)(375,402)(376,397)(377,398)(378,399)(433,529)(434,530)(435,531)(436,526)(437,527)(438,528)(439,523)(440,524)(441,525)(442,520)(443,521)(444,522)(445,517)(446,518)(447,519)(448,514)(449,515)(450,516)(451,538)(452,539)(453,540)(454,535)(455,536)(456,537)(457,532)(458,533)(459,534)(460,502)(461,503)(462,504)(463,499)(464,500)(465,501)(466,496)(467,497)(468,498)(469,493)(470,494)(471,495)(472,490)(473,491)(474,492)(475,487)(476,488)(477,489)(478,511)(479,512)(480,513)(481,508)(482,509)(483,510)(484,505)(485,506)(486,507)(541,637)(542,638)(543,639)(544,634)(545,635)(546,636)(547,631)(548,632)(549,633)(550,628)(551,629)(552,630)(553,625)(554,626)(555,627)(556,622)(557,623)(558,624)(559,646)(560,647)(561,648)(562,643)(563,644)(564,645)(565,640)(566,641)(567,642)(568,610)(569,611)(570,612)(571,607)(572,608)(573,609)(574,604)(575,605)(576,606)(577,601)(578,602)(579,603)(580,598)(581,599)(582,600)(583,595)(584,596)(585,597)(586,619)(587,620)(588,621)(589,616)(590,617)(591,618)(592,613)(593,614)(594,615);;
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*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0 ];;
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, 97)(  2, 98)(  3, 99)(  4, 94)(  5, 95)(  6, 96)(  7, 91)(  8, 92)(  9, 93)( 10, 88)( 11, 89)( 12, 90)( 13, 85)( 14, 86)( 15, 87)( 16, 82)( 17, 83)( 18, 84)( 19,106)( 20,107)( 21,108)( 22,103)( 23,104)( 24,105)( 25,100)( 26,101)( 27,102)( 28, 70)( 29, 71)( 30, 72)( 31, 67)( 32, 68)( 33, 69)( 34, 64)( 35, 65)( 36, 66)( 37, 61)( 38, 62)( 39, 63)( 40, 58)( 41, 59)( 42, 60)( 43, 55)( 44, 56)( 45, 57)( 46, 79)( 47, 80)( 48, 81)( 49, 76)( 50, 77)( 51, 78)( 52, 73)( 53, 74)( 54, 75)(109,205)(110,206)(111,207)(112,202)(113,203)(114,204)(115,199)(116,200)(117,201)(118,196)(119,197)(120,198)(121,193)(122,194)(123,195)(124,190)(125,191)(126,192)(127,214)(128,215)(129,216)(130,211)(131,212)(132,213)(133,208)(134,209)(135,210)(136,178)(137,179)(138,180)(139,175)(140,176)(141,177)(142,172)(143,173)(144,174)(145,169)(146,170)(147,171)(148,166)(149,167)(150,168)(151,163)(152,164)(153,165)(154,187)(155,188)(156,189)(157,184)(158,185)(159,186)(160,181)(161,182)(162,183)(217,313)(218,314)(219,315)(220,310)(221,311)(222,312)(223,307)(224,308)(225,309)(226,304)(227,305)(228,306)(229,301)(230,302)(231,303)(232,298)(233,299)(234,300)(235,322)(236,323)(237,324)(238,319)(239,320)(240,321)(241,316)(242,317)(243,318)(244,286)(245,287)(246,288)(247,283)(248,284)(249,285)(250,280)(251,281)(252,282)(253,277)(254,278)(255,279)(256,274)(257,275)(258,276)(259,271)(260,272)(261,273)(262,295)(263,296)(264,297)(265,292)(266,293)(267,294)(268,289)(269,290)(270,291)(325,421)(326,422)(327,423)(328,418)(329,419)(330,420)(331,415)(332,416)(333,417)(334,412)(335,413)(336,414)(337,409)(338,410)(339,411)(340,406)(341,407)(342,408)(343,430)(344,431)(345,432)(346,427)(347,428)(348,429)(349,424)(350,425)(351,426)(352,394)(353,395)(354,396)(355,391)(356,392)(357,393)(358,388)(359,389)(360,390)(361,385)(362,386)(363,387)(364,382)(365,383)(366,384)(367,379)(368,380)(369,381)(370,403)(371,404)(372,405)(373,400)(374,401)(375,402)(376,397)(377,398)(378,399)(433,529)(434,530)(435,531)(436,526)(437,527)(438,528)(439,523)(440,524)(441,525)(442,520)(443,521)(444,522)(445,517)(446,518)(447,519)(448,514)(449,515)(450,516)(451,538)(452,539)(453,540)(454,535)(455,536)(456,537)(457,532)(458,533)(459,534)(460,502)(461,503)(462,504)(463,499)(464,500)(465,501)(466,496)(467,497)(468,498)(469,493)(470,494)(471,495)(472,490)(473,491)(474,492)(475,487)(476,488)(477,489)(478,511)(479,512)(480,513)(481,508)(482,509)(483,510)(484,505)(485,506)(486,507)(541,637)(542,638)(543,639)(544,634)(545,635)(546,636)(547,631)(548,632)(549,633)(550,628)(551,629)(552,630)(553,625)(554,626)(555,627)(556,622)(557,623)(558,624)(559,646)(560,647)(561,648)(562,643)(563,644)(564,645)(565,640)(566,641)(567,642)(568,610)(569,611)(570,612)(571,607)(572,608)(573,609)(574,604)(575,605)(576,606)(577,601)(578,602)(579,603)(580,598)(581,599)(582,600)(583,595)(584,596)(585,597)(586,619)(587,620)(588,621)(589,616)(590,617)(591,618)(592,613)(593,614)(594,615);
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*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0 >;

References

None.

to this polytope.

Twisty Puzzle