Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,45}

Atlas Canonical Name {4,45}*1440

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1440,4571)
Rank
3
Schläfli Type
{4,45}
Vertices, edges, …
16, 360, 180
Order of s0s1s2
45
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

3-fold

9-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*s0*s2*s1*s0*s1*s2*s1> of order 2

108 facets

8 vertex figures

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

90 facets

8 vertex figures

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

63 facets

4 vertex figures

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

54 facets

4 vertex figures

Representations

Permutation Representation (GAP) 
s0 := (  1,  9)(  2, 10)(  3, 11)(  4, 12)(  5, 13)(  6, 14)(  7, 15)(  8, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)(200,208)(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)(216,224)(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)(280,288)(289,297)(290,298)(291,299)(292,300)(293,301)(294,302)(295,303)(296,304)(305,313)(306,314)(307,315)(308,316)(309,317)(310,318)(311,319)(312,320)(321,329)(322,330)(323,331)(324,332)(325,333)(326,334)(327,335)(328,336)(337,345)(338,346)(339,347)(340,348)(341,349)(342,350)(343,351)(344,352)(353,361)(354,362)(355,363)(356,364)(357,365)(358,366)(359,367)(360,368)(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)(376,384)(385,393)(386,394)(387,395)(388,396)(389,397)(390,398)(391,399)(392,400)(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)(408,416)(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)(424,432)(433,441)(434,442)(435,443)(436,444)(437,445)(438,446)(439,447)(440,448)(449,457)(450,458)(451,459)(452,460)(453,461)(454,462)(455,463)(456,464)(465,473)(466,474)(467,475)(468,476)(469,477)(470,478)(471,479)(472,480)(481,489)(482,490)(483,491)(484,492)(485,493)(486,494)(487,495)(488,496)(497,505)(498,506)(499,507)(500,508)(501,509)(502,510)(503,511)(504,512)(513,521)(514,522)(515,523)(516,524)(517,525)(518,526)(519,527)(520,528)(529,537)(530,538)(531,539)(532,540)(533,541)(534,542)(535,543)(536,544)(545,553)(546,554)(547,555)(548,556)(549,557)(550,558)(551,559)(552,560)(561,569)(562,570)(563,571)(564,572)(565,573)(566,574)(567,575)(568,576)(577,585)(578,586)(579,587)(580,588)(581,589)(582,590)(583,591)(584,592)(593,601)(594,602)(595,603)(596,604)(597,605)(598,606)(599,607)(600,608)(609,617)(610,618)(611,619)(612,620)(613,621)(614,622)(615,623)(616,624)(625,633)(626,634)(627,635)(628,636)(629,637)(630,638)(631,639)(632,640)(641,649)(642,650)(643,651)(644,652)(645,653)(646,654)(647,655)(648,656)(657,665)(658,666)(659,667)(660,668)(661,669)(662,670)(663,671)(664,672)(673,681)(674,682)(675,683)(676,684)(677,685)(678,686)(679,687)(680,688)(689,697)(690,698)(691,699)(692,700)(693,701)(694,702)(695,703)(696,704)(705,713)(706,714)(707,715)(708,716)(709,717)(710,718)(711,719)(712,720);;
s1 := (  3,  4)(  5,  6)(  9, 16)( 10, 15)( 11, 13)( 12, 14)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 38)( 22, 37)( 23, 39)( 24, 40)( 25, 48)( 26, 47)( 27, 45)( 28, 46)( 29, 43)( 30, 44)( 31, 42)( 32, 41)( 49,193)( 50,194)( 51,196)( 52,195)( 53,198)( 54,197)( 55,199)( 56,200)( 57,208)( 58,207)( 59,205)( 60,206)( 61,203)( 62,204)( 63,202)( 64,201)( 65,225)( 66,226)( 67,228)( 68,227)( 69,230)( 70,229)( 71,231)( 72,232)( 73,240)( 74,239)( 75,237)( 76,238)( 77,235)( 78,236)( 79,234)( 80,233)( 81,209)( 82,210)( 83,212)( 84,211)( 85,214)( 86,213)( 87,215)( 88,216)( 89,224)( 90,223)( 91,221)( 92,222)( 93,219)( 94,220)( 95,218)( 96,217)( 97,145)( 98,146)( 99,148)(100,147)(101,150)(102,149)(103,151)(104,152)(105,160)(106,159)(107,157)(108,158)(109,155)(110,156)(111,154)(112,153)(113,177)(114,178)(115,180)(116,179)(117,182)(118,181)(119,183)(120,184)(121,192)(122,191)(123,189)(124,190)(125,187)(126,188)(127,186)(128,185)(129,161)(130,162)(131,164)(132,163)(133,166)(134,165)(135,167)(136,168)(137,176)(138,175)(139,173)(140,174)(141,171)(142,172)(143,170)(144,169)(241,513)(242,514)(243,516)(244,515)(245,518)(246,517)(247,519)(248,520)(249,528)(250,527)(251,525)(252,526)(253,523)(254,524)(255,522)(256,521)(257,497)(258,498)(259,500)(260,499)(261,502)(262,501)(263,503)(264,504)(265,512)(266,511)(267,509)(268,510)(269,507)(270,508)(271,506)(272,505)(273,481)(274,482)(275,484)(276,483)(277,486)(278,485)(279,487)(280,488)(281,496)(282,495)(283,493)(284,494)(285,491)(286,492)(287,490)(288,489)(289,705)(290,706)(291,708)(292,707)(293,710)(294,709)(295,711)(296,712)(297,720)(298,719)(299,717)(300,718)(301,715)(302,716)(303,714)(304,713)(305,689)(306,690)(307,692)(308,691)(309,694)(310,693)(311,695)(312,696)(313,704)(314,703)(315,701)(316,702)(317,699)(318,700)(319,698)(320,697)(321,673)(322,674)(323,676)(324,675)(325,678)(326,677)(327,679)(328,680)(329,688)(330,687)(331,685)(332,686)(333,683)(334,684)(335,682)(336,681)(337,657)(338,658)(339,660)(340,659)(341,662)(342,661)(343,663)(344,664)(345,672)(346,671)(347,669)(348,670)(349,667)(350,668)(351,666)(352,665)(353,641)(354,642)(355,644)(356,643)(357,646)(358,645)(359,647)(360,648)(361,656)(362,655)(363,653)(364,654)(365,651)(366,652)(367,650)(368,649)(369,625)(370,626)(371,628)(372,627)(373,630)(374,629)(375,631)(376,632)(377,640)(378,639)(379,637)(380,638)(381,635)(382,636)(383,634)(384,633)(385,609)(386,610)(387,612)(388,611)(389,614)(390,613)(391,615)(392,616)(393,624)(394,623)(395,621)(396,622)(397,619)(398,620)(399,618)(400,617)(401,593)(402,594)(403,596)(404,595)(405,598)(406,597)(407,599)(408,600)(409,608)(410,607)(411,605)(412,606)(413,603)(414,604)(415,602)(416,601)(417,577)(418,578)(419,580)(420,579)(421,582)(422,581)(423,583)(424,584)(425,592)(426,591)(427,589)(428,590)(429,587)(430,588)(431,586)(432,585)(433,561)(434,562)(435,564)(436,563)(437,566)(438,565)(439,567)(440,568)(441,576)(442,575)(443,573)(444,574)(445,571)(446,572)(447,570)(448,569)(449,545)(450,546)(451,548)(452,547)(453,550)(454,549)(455,551)(456,552)(457,560)(458,559)(459,557)(460,558)(461,555)(462,556)(463,554)(464,553)(465,529)(466,530)(467,532)(468,531)(469,534)(470,533)(471,535)(472,536)(473,544)(474,543)(475,541)(476,542)(477,539)(478,540)(479,538)(480,537);;
s2 := (  1,289)(  2,298)(  3,299)(  4,292)(  5,304)(  6,295)(  7,294)(  8,301)(  9,297)( 10,290)( 11,291)( 12,300)( 13,296)( 14,303)( 15,302)( 16,293)( 17,321)( 18,330)( 19,331)( 20,324)( 21,336)( 22,327)( 23,326)( 24,333)( 25,329)( 26,322)( 27,323)( 28,332)( 29,328)( 30,335)( 31,334)( 32,325)( 33,305)( 34,314)( 35,315)( 36,308)( 37,320)( 38,311)( 39,310)( 40,317)( 41,313)( 42,306)( 43,307)( 44,316)( 45,312)( 46,319)( 47,318)( 48,309)( 49,241)( 50,250)( 51,251)( 52,244)( 53,256)( 54,247)( 55,246)( 56,253)( 57,249)( 58,242)( 59,243)( 60,252)( 61,248)( 62,255)( 63,254)( 64,245)( 65,273)( 66,282)( 67,283)( 68,276)( 69,288)( 70,279)( 71,278)( 72,285)( 73,281)( 74,274)( 75,275)( 76,284)( 77,280)( 78,287)( 79,286)( 80,277)( 81,257)( 82,266)( 83,267)( 84,260)( 85,272)( 86,263)( 87,262)( 88,269)( 89,265)( 90,258)( 91,259)( 92,268)( 93,264)( 94,271)( 95,270)( 96,261)( 97,433)( 98,442)( 99,443)(100,436)(101,448)(102,439)(103,438)(104,445)(105,441)(106,434)(107,435)(108,444)(109,440)(110,447)(111,446)(112,437)(113,465)(114,474)(115,475)(116,468)(117,480)(118,471)(119,470)(120,477)(121,473)(122,466)(123,467)(124,476)(125,472)(126,479)(127,478)(128,469)(129,449)(130,458)(131,459)(132,452)(133,464)(134,455)(135,454)(136,461)(137,457)(138,450)(139,451)(140,460)(141,456)(142,463)(143,462)(144,453)(145,385)(146,394)(147,395)(148,388)(149,400)(150,391)(151,390)(152,397)(153,393)(154,386)(155,387)(156,396)(157,392)(158,399)(159,398)(160,389)(161,417)(162,426)(163,427)(164,420)(165,432)(166,423)(167,422)(168,429)(169,425)(170,418)(171,419)(172,428)(173,424)(174,431)(175,430)(176,421)(177,401)(178,410)(179,411)(180,404)(181,416)(182,407)(183,406)(184,413)(185,409)(186,402)(187,403)(188,412)(189,408)(190,415)(191,414)(192,405)(193,337)(194,346)(195,347)(196,340)(197,352)(198,343)(199,342)(200,349)(201,345)(202,338)(203,339)(204,348)(205,344)(206,351)(207,350)(208,341)(209,369)(210,378)(211,379)(212,372)(213,384)(214,375)(215,374)(216,381)(217,377)(218,370)(219,371)(220,380)(221,376)(222,383)(223,382)(224,373)(225,353)(226,362)(227,363)(228,356)(229,368)(230,359)(231,358)(232,365)(233,361)(234,354)(235,355)(236,364)(237,360)(238,367)(239,366)(240,357)(481,561)(482,570)(483,571)(484,564)(485,576)(486,567)(487,566)(488,573)(489,569)(490,562)(491,563)(492,572)(493,568)(494,575)(495,574)(496,565)(497,545)(498,554)(499,555)(500,548)(501,560)(502,551)(503,550)(504,557)(505,553)(506,546)(507,547)(508,556)(509,552)(510,559)(511,558)(512,549)(513,529)(514,538)(515,539)(516,532)(517,544)(518,535)(519,534)(520,541)(521,537)(522,530)(523,531)(524,540)(525,536)(526,543)(527,542)(528,533)(577,705)(578,714)(579,715)(580,708)(581,720)(582,711)(583,710)(584,717)(585,713)(586,706)(587,707)(588,716)(589,712)(590,719)(591,718)(592,709)(593,689)(594,698)(595,699)(596,692)(597,704)(598,695)(599,694)(600,701)(601,697)(602,690)(603,691)(604,700)(605,696)(606,703)(607,702)(608,693)(609,673)(610,682)(611,683)(612,676)(613,688)(614,679)(615,678)(616,685)(617,681)(618,674)(619,675)(620,684)(621,680)(622,687)(623,686)(624,677)(625,657)(626,666)(627,667)(628,660)(629,672)(630,663)(631,662)(632,669)(633,665)(634,658)(635,659)(636,668)(637,664)(638,671)(639,670)(640,661)(642,650)(643,651)(645,656)(646,647)(648,653)(654,655);;
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, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(720)!(  1,  9)(  2, 10)(  3, 11)(  4, 12)(  5, 13)(  6, 14)(  7, 15)(  8, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)(200,208)(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)(216,224)(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)(280,288)(289,297)(290,298)(291,299)(292,300)(293,301)(294,302)(295,303)(296,304)(305,313)(306,314)(307,315)(308,316)(309,317)(310,318)(311,319)(312,320)(321,329)(322,330)(323,331)(324,332)(325,333)(326,334)(327,335)(328,336)(337,345)(338,346)(339,347)(340,348)(341,349)(342,350)(343,351)(344,352)(353,361)(354,362)(355,363)(356,364)(357,365)(358,366)(359,367)(360,368)(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)(376,384)(385,393)(386,394)(387,395)(388,396)(389,397)(390,398)(391,399)(392,400)(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)(408,416)(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)(424,432)(433,441)(434,442)(435,443)(436,444)(437,445)(438,446)(439,447)(440,448)(449,457)(450,458)(451,459)(452,460)(453,461)(454,462)(455,463)(456,464)(465,473)(466,474)(467,475)(468,476)(469,477)(470,478)(471,479)(472,480)(481,489)(482,490)(483,491)(484,492)(485,493)(486,494)(487,495)(488,496)(497,505)(498,506)(499,507)(500,508)(501,509)(502,510)(503,511)(504,512)(513,521)(514,522)(515,523)(516,524)(517,525)(518,526)(519,527)(520,528)(529,537)(530,538)(531,539)(532,540)(533,541)(534,542)(535,543)(536,544)(545,553)(546,554)(547,555)(548,556)(549,557)(550,558)(551,559)(552,560)(561,569)(562,570)(563,571)(564,572)(565,573)(566,574)(567,575)(568,576)(577,585)(578,586)(579,587)(580,588)(581,589)(582,590)(583,591)(584,592)(593,601)(594,602)(595,603)(596,604)(597,605)(598,606)(599,607)(600,608)(609,617)(610,618)(611,619)(612,620)(613,621)(614,622)(615,623)(616,624)(625,633)(626,634)(627,635)(628,636)(629,637)(630,638)(631,639)(632,640)(641,649)(642,650)(643,651)(644,652)(645,653)(646,654)(647,655)(648,656)(657,665)(658,666)(659,667)(660,668)(661,669)(662,670)(663,671)(664,672)(673,681)(674,682)(675,683)(676,684)(677,685)(678,686)(679,687)(680,688)(689,697)(690,698)(691,699)(692,700)(693,701)(694,702)(695,703)(696,704)(705,713)(706,714)(707,715)(708,716)(709,717)(710,718)(711,719)(712,720);
s1 := Sym(720)!(  3,  4)(  5,  6)(  9, 16)( 10, 15)( 11, 13)( 12, 14)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 38)( 22, 37)( 23, 39)( 24, 40)( 25, 48)( 26, 47)( 27, 45)( 28, 46)( 29, 43)( 30, 44)( 31, 42)( 32, 41)( 49,193)( 50,194)( 51,196)( 52,195)( 53,198)( 54,197)( 55,199)( 56,200)( 57,208)( 58,207)( 59,205)( 60,206)( 61,203)( 62,204)( 63,202)( 64,201)( 65,225)( 66,226)( 67,228)( 68,227)( 69,230)( 70,229)( 71,231)( 72,232)( 73,240)( 74,239)( 75,237)( 76,238)( 77,235)( 78,236)( 79,234)( 80,233)( 81,209)( 82,210)( 83,212)( 84,211)( 85,214)( 86,213)( 87,215)( 88,216)( 89,224)( 90,223)( 91,221)( 92,222)( 93,219)( 94,220)( 95,218)( 96,217)( 97,145)( 98,146)( 99,148)(100,147)(101,150)(102,149)(103,151)(104,152)(105,160)(106,159)(107,157)(108,158)(109,155)(110,156)(111,154)(112,153)(113,177)(114,178)(115,180)(116,179)(117,182)(118,181)(119,183)(120,184)(121,192)(122,191)(123,189)(124,190)(125,187)(126,188)(127,186)(128,185)(129,161)(130,162)(131,164)(132,163)(133,166)(134,165)(135,167)(136,168)(137,176)(138,175)(139,173)(140,174)(141,171)(142,172)(143,170)(144,169)(241,513)(242,514)(243,516)(244,515)(245,518)(246,517)(247,519)(248,520)(249,528)(250,527)(251,525)(252,526)(253,523)(254,524)(255,522)(256,521)(257,497)(258,498)(259,500)(260,499)(261,502)(262,501)(263,503)(264,504)(265,512)(266,511)(267,509)(268,510)(269,507)(270,508)(271,506)(272,505)(273,481)(274,482)(275,484)(276,483)(277,486)(278,485)(279,487)(280,488)(281,496)(282,495)(283,493)(284,494)(285,491)(286,492)(287,490)(288,489)(289,705)(290,706)(291,708)(292,707)(293,710)(294,709)(295,711)(296,712)(297,720)(298,719)(299,717)(300,718)(301,715)(302,716)(303,714)(304,713)(305,689)(306,690)(307,692)(308,691)(309,694)(310,693)(311,695)(312,696)(313,704)(314,703)(315,701)(316,702)(317,699)(318,700)(319,698)(320,697)(321,673)(322,674)(323,676)(324,675)(325,678)(326,677)(327,679)(328,680)(329,688)(330,687)(331,685)(332,686)(333,683)(334,684)(335,682)(336,681)(337,657)(338,658)(339,660)(340,659)(341,662)(342,661)(343,663)(344,664)(345,672)(346,671)(347,669)(348,670)(349,667)(350,668)(351,666)(352,665)(353,641)(354,642)(355,644)(356,643)(357,646)(358,645)(359,647)(360,648)(361,656)(362,655)(363,653)(364,654)(365,651)(366,652)(367,650)(368,649)(369,625)(370,626)(371,628)(372,627)(373,630)(374,629)(375,631)(376,632)(377,640)(378,639)(379,637)(380,638)(381,635)(382,636)(383,634)(384,633)(385,609)(386,610)(387,612)(388,611)(389,614)(390,613)(391,615)(392,616)(393,624)(394,623)(395,621)(396,622)(397,619)(398,620)(399,618)(400,617)(401,593)(402,594)(403,596)(404,595)(405,598)(406,597)(407,599)(408,600)(409,608)(410,607)(411,605)(412,606)(413,603)(414,604)(415,602)(416,601)(417,577)(418,578)(419,580)(420,579)(421,582)(422,581)(423,583)(424,584)(425,592)(426,591)(427,589)(428,590)(429,587)(430,588)(431,586)(432,585)(433,561)(434,562)(435,564)(436,563)(437,566)(438,565)(439,567)(440,568)(441,576)(442,575)(443,573)(444,574)(445,571)(446,572)(447,570)(448,569)(449,545)(450,546)(451,548)(452,547)(453,550)(454,549)(455,551)(456,552)(457,560)(458,559)(459,557)(460,558)(461,555)(462,556)(463,554)(464,553)(465,529)(466,530)(467,532)(468,531)(469,534)(470,533)(471,535)(472,536)(473,544)(474,543)(475,541)(476,542)(477,539)(478,540)(479,538)(480,537);
s2 := Sym(720)!(  1,289)(  2,298)(  3,299)(  4,292)(  5,304)(  6,295)(  7,294)(  8,301)(  9,297)( 10,290)( 11,291)( 12,300)( 13,296)( 14,303)( 15,302)( 16,293)( 17,321)( 18,330)( 19,331)( 20,324)( 21,336)( 22,327)( 23,326)( 24,333)( 25,329)( 26,322)( 27,323)( 28,332)( 29,328)( 30,335)( 31,334)( 32,325)( 33,305)( 34,314)( 35,315)( 36,308)( 37,320)( 38,311)( 39,310)( 40,317)( 41,313)( 42,306)( 43,307)( 44,316)( 45,312)( 46,319)( 47,318)( 48,309)( 49,241)( 50,250)( 51,251)( 52,244)( 53,256)( 54,247)( 55,246)( 56,253)( 57,249)( 58,242)( 59,243)( 60,252)( 61,248)( 62,255)( 63,254)( 64,245)( 65,273)( 66,282)( 67,283)( 68,276)( 69,288)( 70,279)( 71,278)( 72,285)( 73,281)( 74,274)( 75,275)( 76,284)( 77,280)( 78,287)( 79,286)( 80,277)( 81,257)( 82,266)( 83,267)( 84,260)( 85,272)( 86,263)( 87,262)( 88,269)( 89,265)( 90,258)( 91,259)( 92,268)( 93,264)( 94,271)( 95,270)( 96,261)( 97,433)( 98,442)( 99,443)(100,436)(101,448)(102,439)(103,438)(104,445)(105,441)(106,434)(107,435)(108,444)(109,440)(110,447)(111,446)(112,437)(113,465)(114,474)(115,475)(116,468)(117,480)(118,471)(119,470)(120,477)(121,473)(122,466)(123,467)(124,476)(125,472)(126,479)(127,478)(128,469)(129,449)(130,458)(131,459)(132,452)(133,464)(134,455)(135,454)(136,461)(137,457)(138,450)(139,451)(140,460)(141,456)(142,463)(143,462)(144,453)(145,385)(146,394)(147,395)(148,388)(149,400)(150,391)(151,390)(152,397)(153,393)(154,386)(155,387)(156,396)(157,392)(158,399)(159,398)(160,389)(161,417)(162,426)(163,427)(164,420)(165,432)(166,423)(167,422)(168,429)(169,425)(170,418)(171,419)(172,428)(173,424)(174,431)(175,430)(176,421)(177,401)(178,410)(179,411)(180,404)(181,416)(182,407)(183,406)(184,413)(185,409)(186,402)(187,403)(188,412)(189,408)(190,415)(191,414)(192,405)(193,337)(194,346)(195,347)(196,340)(197,352)(198,343)(199,342)(200,349)(201,345)(202,338)(203,339)(204,348)(205,344)(206,351)(207,350)(208,341)(209,369)(210,378)(211,379)(212,372)(213,384)(214,375)(215,374)(216,381)(217,377)(218,370)(219,371)(220,380)(221,376)(222,383)(223,382)(224,373)(225,353)(226,362)(227,363)(228,356)(229,368)(230,359)(231,358)(232,365)(233,361)(234,354)(235,355)(236,364)(237,360)(238,367)(239,366)(240,357)(481,561)(482,570)(483,571)(484,564)(485,576)(486,567)(487,566)(488,573)(489,569)(490,562)(491,563)(492,572)(493,568)(494,575)(495,574)(496,565)(497,545)(498,554)(499,555)(500,548)(501,560)(502,551)(503,550)(504,557)(505,553)(506,546)(507,547)(508,556)(509,552)(510,559)(511,558)(512,549)(513,529)(514,538)(515,539)(516,532)(517,544)(518,535)(519,534)(520,541)(521,537)(522,530)(523,531)(524,540)(525,536)(526,543)(527,542)(528,533)(577,705)(578,714)(579,715)(580,708)(581,720)(582,711)(583,710)(584,717)(585,713)(586,706)(587,707)(588,716)(589,712)(590,719)(591,718)(592,709)(593,689)(594,698)(595,699)(596,692)(597,704)(598,695)(599,694)(600,701)(601,697)(602,690)(603,691)(604,700)(605,696)(606,703)(607,702)(608,693)(609,673)(610,682)(611,683)(612,676)(613,688)(614,679)(615,678)(616,685)(617,681)(618,674)(619,675)(620,684)(621,680)(622,687)(623,686)(624,677)(625,657)(626,666)(627,667)(628,660)(629,672)(630,663)(631,662)(632,669)(633,665)(634,658)(635,659)(636,668)(637,664)(638,671)(639,670)(640,661)(642,650)(643,651)(645,656)(646,647)(648,653)(654,655);
poly := sub<Sym(720)|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, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References

None.

to this polytope.

Twisty Puzzle