Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,6}

Atlas Canonical Name {12,6}*1296q

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1296,3492)
Rank
3
Schläfli Type
{12,6}
Vertices, edges, …
108, 324, 54
Order of s0s1s2
18
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=<(s0*s1)^2*s0*s2*(s1*s0)^2*s2> of order 3

18 facets

36 vertex figures

P/N, where N=<((s1*s0)^3*s1*s2)^2> of order 3

18 facets

36 vertex figures

P/N, where N=<(s0*s1)^4> of order 3

30 facets

36 vertex figures

P/N, where N=<(s0*s1)^4, s0*s2*(s1*s0)^3*s1*s2> of order 9

14 facets

12 vertex figures

P/N, where N=<(s0*s1)^4, s0*s1*s2*(s1*s0)^2*s2*s1> of order 9

10 facets

12 vertex figures

P/N, where N=<s0*s1*s2*(s1*s0)^2*s2*s1, (s0*s1)^3*s2*(s1*s0)^3*s1*s2*s1> of order 9

6 facets

12 vertex figures

Representations

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

References

None.

to this polytope.

Twisty Puzzle