Polytope of Type {12,48}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,48}*1152e
if this polytope has a name.
Group : SmallGroup(1152,32294)
Rank : 3
Schlafli Type : {12,48}
Number of vertices, edges, etc : 12, 288, 48
Order of s0s1s2 : 48
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,24}*576c
   3-fold quotients : {4,48}*384b, {12,16}*384b
   4-fold quotients : {6,24}*288a, {12,12}*288a
   6-fold quotients : {4,24}*192a, {12,8}*192a
   8-fold quotients : {6,12}*144a, {12,6}*144a
   9-fold quotients : {4,16}*128b
   12-fold quotients : {4,12}*96a, {12,4}*96a, {2,24}*96, {6,8}*96
   16-fold quotients : {6,6}*72a
   18-fold quotients : {4,8}*64a
   24-fold quotients : {2,12}*48, {12,2}*48, {4,6}*48a, {6,4}*48a
   36-fold quotients : {4,4}*32, {2,8}*32
   48-fold quotients : {2,6}*24, {6,2}*24
   72-fold quotients : {2,4}*16, {4,2}*16
   96-fold quotients : {2,3}*12, {3,2}*12
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   None.

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

Twisty Puzzle