Polytope of Type {48,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,12}*1152e
if this polytope has a name.
Group : SmallGroup(1152,32294)
Rank : 3
Schlafli Type : {48,12}
Number of vertices, edges, etc : 48, 288, 12
Order of s0s1s2 : 48
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {24,12}*576c
   3-fold quotients : {48,4}*384b, {16,12}*384b
   4-fold quotients : {24,6}*288a, {12,12}*288a
   6-fold quotients : {24,4}*192a, {8,12}*192a
   8-fold quotients : {6,12}*144a, {12,6}*144a
   9-fold quotients : {16,4}*128b
   12-fold quotients : {4,12}*96a, {12,4}*96a, {24,2}*96, {8,6}*96
   16-fold quotients : {6,6}*72a
   18-fold quotients : {8,4}*64a
   24-fold quotients : {2,12}*48, {12,2}*48, {4,6}*48a, {6,4}*48a
   36-fold quotients : {4,4}*32, {8,2}*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 := (  1,433)(  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);;
s1 := (  1,  4)(  2,  6)(  3,  5)(  8,  9)( 10, 13)( 11, 15)( 12, 14)( 17, 18)( 19, 31)( 20, 33)( 21, 32)( 22, 28)( 23, 30)( 24, 29)( 25, 34)( 26, 36)( 27, 35)( 37, 40)( 38, 42)( 39, 41)( 44, 45)( 46, 49)( 47, 51)( 48, 50)( 53, 54)( 55, 67)( 56, 69)( 57, 68)( 58, 64)( 59, 66)( 60, 65)( 61, 70)( 62, 72)( 63, 71)( 73, 94)( 74, 96)( 75, 95)( 76, 91)( 77, 93)( 78, 92)( 79, 97)( 80, 99)( 81, 98)( 82,103)( 83,105)( 84,104)( 85,100)( 86,102)( 87,101)( 88,106)( 89,108)( 90,107)(109,130)(110,132)(111,131)(112,127)(113,129)(114,128)(115,133)(116,135)(117,134)(118,139)(119,141)(120,140)(121,136)(122,138)(123,137)(124,142)(125,144)(126,143)(145,184)(146,186)(147,185)(148,181)(149,183)(150,182)(151,187)(152,189)(153,188)(154,193)(155,195)(156,194)(157,190)(158,192)(159,191)(160,196)(161,198)(162,197)(163,211)(164,213)(165,212)(166,208)(167,210)(168,209)(169,214)(170,216)(171,215)(172,202)(173,204)(174,203)(175,199)(176,201)(177,200)(178,205)(179,207)(180,206)(217,274)(218,276)(219,275)(220,271)(221,273)(222,272)(223,277)(224,279)(225,278)(226,283)(227,285)(228,284)(229,280)(230,282)(231,281)(232,286)(233,288)(234,287)(235,256)(236,258)(237,257)(238,253)(239,255)(240,254)(241,259)(242,261)(243,260)(244,265)(245,267)(246,266)(247,262)(248,264)(249,263)(250,268)(251,270)(252,269)(289,364)(290,366)(291,365)(292,361)(293,363)(294,362)(295,367)(296,369)(297,368)(298,373)(299,375)(300,374)(301,370)(302,372)(303,371)(304,376)(305,378)(306,377)(307,391)(308,393)(309,392)(310,388)(311,390)(312,389)(313,394)(314,396)(315,395)(316,382)(317,384)(318,383)(319,379)(320,381)(321,380)(322,385)(323,387)(324,386)(325,400)(326,402)(327,401)(328,397)(329,399)(330,398)(331,403)(332,405)(333,404)(334,409)(335,411)(336,410)(337,406)(338,408)(339,407)(340,412)(341,414)(342,413)(343,427)(344,429)(345,428)(346,424)(347,426)(348,425)(349,430)(350,432)(351,431)(352,418)(353,420)(354,419)(355,415)(356,417)(357,416)(358,421)(359,423)(360,422)(433,553)(434,555)(435,554)(436,550)(437,552)(438,551)(439,556)(440,558)(441,557)(442,544)(443,546)(444,545)(445,541)(446,543)(447,542)(448,547)(449,549)(450,548)(451,562)(452,564)(453,563)(454,559)(455,561)(456,560)(457,565)(458,567)(459,566)(460,571)(461,573)(462,572)(463,568)(464,570)(465,569)(466,574)(467,576)(468,575)(469,517)(470,519)(471,518)(472,514)(473,516)(474,515)(475,520)(476,522)(477,521)(478,508)(479,510)(480,509)(481,505)(482,507)(483,506)(484,511)(485,513)(486,512)(487,526)(488,528)(489,527)(490,523)(491,525)(492,524)(493,529)(494,531)(495,530)(496,535)(497,537)(498,536)(499,532)(500,534)(501,533)(502,538)(503,540)(504,539);;
s2 := (  1,149)(  2,151)(  3,147)(  4,152)(  5,145)(  6,150)(  7,146)(  8,148)(  9,153)( 10,158)( 11,160)( 12,156)( 13,161)( 14,154)( 15,159)( 16,155)( 17,157)( 18,162)( 19,167)( 20,169)( 21,165)( 22,170)( 23,163)( 24,168)( 25,164)( 26,166)( 27,171)( 28,176)( 29,178)( 30,174)( 31,179)( 32,172)( 33,177)( 34,173)( 35,175)( 36,180)( 37,185)( 38,187)( 39,183)( 40,188)( 41,181)( 42,186)( 43,182)( 44,184)( 45,189)( 46,194)( 47,196)( 48,192)( 49,197)( 50,190)( 51,195)( 52,191)( 53,193)( 54,198)( 55,203)( 56,205)( 57,201)( 58,206)( 59,199)( 60,204)( 61,200)( 62,202)( 63,207)( 64,212)( 65,214)( 66,210)( 67,215)( 68,208)( 69,213)( 70,209)( 71,211)( 72,216)( 73,230)( 74,232)( 75,228)( 76,233)( 77,226)( 78,231)( 79,227)( 80,229)( 81,234)( 82,221)( 83,223)( 84,219)( 85,224)( 86,217)( 87,222)( 88,218)( 89,220)( 90,225)( 91,248)( 92,250)( 93,246)( 94,251)( 95,244)( 96,249)( 97,245)( 98,247)( 99,252)(100,239)(101,241)(102,237)(103,242)(104,235)(105,240)(106,236)(107,238)(108,243)(109,266)(110,268)(111,264)(112,269)(113,262)(114,267)(115,263)(116,265)(117,270)(118,257)(119,259)(120,255)(121,260)(122,253)(123,258)(124,254)(125,256)(126,261)(127,284)(128,286)(129,282)(130,287)(131,280)(132,285)(133,281)(134,283)(135,288)(136,275)(137,277)(138,273)(139,278)(140,271)(141,276)(142,272)(143,274)(144,279)(289,437)(290,439)(291,435)(292,440)(293,433)(294,438)(295,434)(296,436)(297,441)(298,446)(299,448)(300,444)(301,449)(302,442)(303,447)(304,443)(305,445)(306,450)(307,455)(308,457)(309,453)(310,458)(311,451)(312,456)(313,452)(314,454)(315,459)(316,464)(317,466)(318,462)(319,467)(320,460)(321,465)(322,461)(323,463)(324,468)(325,473)(326,475)(327,471)(328,476)(329,469)(330,474)(331,470)(332,472)(333,477)(334,482)(335,484)(336,480)(337,485)(338,478)(339,483)(340,479)(341,481)(342,486)(343,491)(344,493)(345,489)(346,494)(347,487)(348,492)(349,488)(350,490)(351,495)(352,500)(353,502)(354,498)(355,503)(356,496)(357,501)(358,497)(359,499)(360,504)(361,518)(362,520)(363,516)(364,521)(365,514)(366,519)(367,515)(368,517)(369,522)(370,509)(371,511)(372,507)(373,512)(374,505)(375,510)(376,506)(377,508)(378,513)(379,536)(380,538)(381,534)(382,539)(383,532)(384,537)(385,533)(386,535)(387,540)(388,527)(389,529)(390,525)(391,530)(392,523)(393,528)(394,524)(395,526)(396,531)(397,554)(398,556)(399,552)(400,557)(401,550)(402,555)(403,551)(404,553)(405,558)(406,545)(407,547)(408,543)(409,548)(410,541)(411,546)(412,542)(413,544)(414,549)(415,572)(416,574)(417,570)(418,575)(419,568)(420,573)(421,569)(422,571)(423,576)(424,563)(425,565)(426,561)(427,566)(428,559)(429,564)(430,560)(431,562)(432,567);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := 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);
s1 := Sym(576)!(  1,  4)(  2,  6)(  3,  5)(  8,  9)( 10, 13)( 11, 15)( 12, 14)( 17, 18)( 19, 31)( 20, 33)( 21, 32)( 22, 28)( 23, 30)( 24, 29)( 25, 34)( 26, 36)( 27, 35)( 37, 40)( 38, 42)( 39, 41)( 44, 45)( 46, 49)( 47, 51)( 48, 50)( 53, 54)( 55, 67)( 56, 69)( 57, 68)( 58, 64)( 59, 66)( 60, 65)( 61, 70)( 62, 72)( 63, 71)( 73, 94)( 74, 96)( 75, 95)( 76, 91)( 77, 93)( 78, 92)( 79, 97)( 80, 99)( 81, 98)( 82,103)( 83,105)( 84,104)( 85,100)( 86,102)( 87,101)( 88,106)( 89,108)( 90,107)(109,130)(110,132)(111,131)(112,127)(113,129)(114,128)(115,133)(116,135)(117,134)(118,139)(119,141)(120,140)(121,136)(122,138)(123,137)(124,142)(125,144)(126,143)(145,184)(146,186)(147,185)(148,181)(149,183)(150,182)(151,187)(152,189)(153,188)(154,193)(155,195)(156,194)(157,190)(158,192)(159,191)(160,196)(161,198)(162,197)(163,211)(164,213)(165,212)(166,208)(167,210)(168,209)(169,214)(170,216)(171,215)(172,202)(173,204)(174,203)(175,199)(176,201)(177,200)(178,205)(179,207)(180,206)(217,274)(218,276)(219,275)(220,271)(221,273)(222,272)(223,277)(224,279)(225,278)(226,283)(227,285)(228,284)(229,280)(230,282)(231,281)(232,286)(233,288)(234,287)(235,256)(236,258)(237,257)(238,253)(239,255)(240,254)(241,259)(242,261)(243,260)(244,265)(245,267)(246,266)(247,262)(248,264)(249,263)(250,268)(251,270)(252,269)(289,364)(290,366)(291,365)(292,361)(293,363)(294,362)(295,367)(296,369)(297,368)(298,373)(299,375)(300,374)(301,370)(302,372)(303,371)(304,376)(305,378)(306,377)(307,391)(308,393)(309,392)(310,388)(311,390)(312,389)(313,394)(314,396)(315,395)(316,382)(317,384)(318,383)(319,379)(320,381)(321,380)(322,385)(323,387)(324,386)(325,400)(326,402)(327,401)(328,397)(329,399)(330,398)(331,403)(332,405)(333,404)(334,409)(335,411)(336,410)(337,406)(338,408)(339,407)(340,412)(341,414)(342,413)(343,427)(344,429)(345,428)(346,424)(347,426)(348,425)(349,430)(350,432)(351,431)(352,418)(353,420)(354,419)(355,415)(356,417)(357,416)(358,421)(359,423)(360,422)(433,553)(434,555)(435,554)(436,550)(437,552)(438,551)(439,556)(440,558)(441,557)(442,544)(443,546)(444,545)(445,541)(446,543)(447,542)(448,547)(449,549)(450,548)(451,562)(452,564)(453,563)(454,559)(455,561)(456,560)(457,565)(458,567)(459,566)(460,571)(461,573)(462,572)(463,568)(464,570)(465,569)(466,574)(467,576)(468,575)(469,517)(470,519)(471,518)(472,514)(473,516)(474,515)(475,520)(476,522)(477,521)(478,508)(479,510)(480,509)(481,505)(482,507)(483,506)(484,511)(485,513)(486,512)(487,526)(488,528)(489,527)(490,523)(491,525)(492,524)(493,529)(494,531)(495,530)(496,535)(497,537)(498,536)(499,532)(500,534)(501,533)(502,538)(503,540)(504,539);
s2 := Sym(576)!(  1,149)(  2,151)(  3,147)(  4,152)(  5,145)(  6,150)(  7,146)(  8,148)(  9,153)( 10,158)( 11,160)( 12,156)( 13,161)( 14,154)( 15,159)( 16,155)( 17,157)( 18,162)( 19,167)( 20,169)( 21,165)( 22,170)( 23,163)( 24,168)( 25,164)( 26,166)( 27,171)( 28,176)( 29,178)( 30,174)( 31,179)( 32,172)( 33,177)( 34,173)( 35,175)( 36,180)( 37,185)( 38,187)( 39,183)( 40,188)( 41,181)( 42,186)( 43,182)( 44,184)( 45,189)( 46,194)( 47,196)( 48,192)( 49,197)( 50,190)( 51,195)( 52,191)( 53,193)( 54,198)( 55,203)( 56,205)( 57,201)( 58,206)( 59,199)( 60,204)( 61,200)( 62,202)( 63,207)( 64,212)( 65,214)( 66,210)( 67,215)( 68,208)( 69,213)( 70,209)( 71,211)( 72,216)( 73,230)( 74,232)( 75,228)( 76,233)( 77,226)( 78,231)( 79,227)( 80,229)( 81,234)( 82,221)( 83,223)( 84,219)( 85,224)( 86,217)( 87,222)( 88,218)( 89,220)( 90,225)( 91,248)( 92,250)( 93,246)( 94,251)( 95,244)( 96,249)( 97,245)( 98,247)( 99,252)(100,239)(101,241)(102,237)(103,242)(104,235)(105,240)(106,236)(107,238)(108,243)(109,266)(110,268)(111,264)(112,269)(113,262)(114,267)(115,263)(116,265)(117,270)(118,257)(119,259)(120,255)(121,260)(122,253)(123,258)(124,254)(125,256)(126,261)(127,284)(128,286)(129,282)(130,287)(131,280)(132,285)(133,281)(134,283)(135,288)(136,275)(137,277)(138,273)(139,278)(140,271)(141,276)(142,272)(143,274)(144,279)(289,437)(290,439)(291,435)(292,440)(293,433)(294,438)(295,434)(296,436)(297,441)(298,446)(299,448)(300,444)(301,449)(302,442)(303,447)(304,443)(305,445)(306,450)(307,455)(308,457)(309,453)(310,458)(311,451)(312,456)(313,452)(314,454)(315,459)(316,464)(317,466)(318,462)(319,467)(320,460)(321,465)(322,461)(323,463)(324,468)(325,473)(326,475)(327,471)(328,476)(329,469)(330,474)(331,470)(332,472)(333,477)(334,482)(335,484)(336,480)(337,485)(338,478)(339,483)(340,479)(341,481)(342,486)(343,491)(344,493)(345,489)(346,494)(347,487)(348,492)(349,488)(350,490)(351,495)(352,500)(353,502)(354,498)(355,503)(356,496)(357,501)(358,497)(359,499)(360,504)(361,518)(362,520)(363,516)(364,521)(365,514)(366,519)(367,515)(368,517)(369,522)(370,509)(371,511)(372,507)(373,512)(374,505)(375,510)(376,506)(377,508)(378,513)(379,536)(380,538)(381,534)(382,539)(383,532)(384,537)(385,533)(386,535)(387,540)(388,527)(389,529)(390,525)(391,530)(392,523)(393,528)(394,524)(395,526)(396,531)(397,554)(398,556)(399,552)(400,557)(401,550)(402,555)(403,551)(404,553)(405,558)(406,545)(407,547)(408,543)(409,548)(410,541)(411,546)(412,542)(413,544)(414,549)(415,572)(416,574)(417,570)(418,575)(419,568)(420,573)(421,569)(422,571)(423,576)(424,563)(425,565)(426,561)(427,566)(428,559)(429,564)(430,560)(431,562)(432,567);
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*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 >;
References : None.
to this polytope

Twisty Puzzle