Polytope of Type {12,18} with group SmallGroup(1296,3492)

Overview

Group: SmallGroup(1296,3492)
Rank: 3
Schläfli Type: {12,18}
Vertices, edges, …: 36, 324, 54
Order of s₀s₁s₂: 18
Order of s₀s₁s₂s₁: 4
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

{12,9}*648a

27-fold

{4,6}*48c

54-fold

{4,3}*24

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)^4> of order 3

30 facets

18 of {4}*8
12 of {12}*24

12 vertex figures

12 of {18}*36

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

References

None.

to this polytope.