Polytope of Type {72,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {72,8}*1152c
Also Known As : {72,8|2}. if this polytope has another name.
Group : SmallGroup(1152,12903)
Rank : 3
Schlafli Type : {72,8}
Number of vertices, edges, etc : 72, 288, 8
Order of s0s1s2 : 72
Order of s0s1s2s1 : 2
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 : {72,4}*576a, {36,8}*576a
   3-fold quotients : {24,8}*384b
   4-fold quotients : {36,4}*288a, {72,2}*288, {18,8}*288
   6-fold quotients : {24,4}*192a, {12,8}*192a
   8-fold quotients : {36,2}*144, {18,4}*144a
   9-fold quotients : {8,8}*128b
   12-fold quotients : {12,4}*96a, {24,2}*96, {6,8}*96
   16-fold quotients : {18,2}*72
   18-fold quotients : {4,8}*64a, {8,4}*64a
   24-fold quotients : {12,2}*48, {6,4}*48a
   32-fold quotients : {9,2}*36
   36-fold quotients : {4,4}*32, {2,8}*32, {8,2}*32
   48-fold quotients : {6,2}*24
   72-fold quotients : {2,4}*16, {4,2}*16
   96-fold quotients : {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)(  2,435)(  3,434)(  4,441)(  5,440)(  6,439)(  7,438)(  8,437)(  9,436)( 10,442)( 11,444)( 12,443)( 13,450)( 14,449)( 15,448)( 16,447)( 17,446)( 18,445)( 19,451)( 20,453)( 21,452)( 22,459)( 23,458)( 24,457)( 25,456)( 26,455)( 27,454)( 28,460)( 29,462)( 30,461)( 31,468)( 32,467)( 33,466)( 34,465)( 35,464)( 36,463)( 37,469)( 38,471)( 39,470)( 40,477)( 41,476)( 42,475)( 43,474)( 44,473)( 45,472)( 46,478)( 47,480)( 48,479)( 49,486)( 50,485)( 51,484)( 52,483)( 53,482)( 54,481)( 55,487)( 56,489)( 57,488)( 58,495)( 59,494)( 60,493)( 61,492)( 62,491)( 63,490)( 64,496)( 65,498)( 66,497)( 67,504)( 68,503)( 69,502)( 70,501)( 71,500)( 72,499)( 73,532)( 74,534)( 75,533)( 76,540)( 77,539)( 78,538)( 79,537)( 80,536)( 81,535)( 82,523)( 83,525)( 84,524)( 85,531)( 86,530)( 87,529)( 88,528)( 89,527)( 90,526)( 91,514)( 92,516)( 93,515)( 94,522)( 95,521)( 96,520)( 97,519)( 98,518)( 99,517)(100,505)(101,507)(102,506)(103,513)(104,512)(105,511)(106,510)(107,509)(108,508)(109,568)(110,570)(111,569)(112,576)(113,575)(114,574)(115,573)(116,572)(117,571)(118,559)(119,561)(120,560)(121,567)(122,566)(123,565)(124,564)(125,563)(126,562)(127,550)(128,552)(129,551)(130,558)(131,557)(132,556)(133,555)(134,554)(135,553)(136,541)(137,543)(138,542)(139,549)(140,548)(141,547)(142,546)(143,545)(144,544)(145,289)(146,291)(147,290)(148,297)(149,296)(150,295)(151,294)(152,293)(153,292)(154,298)(155,300)(156,299)(157,306)(158,305)(159,304)(160,303)(161,302)(162,301)(163,307)(164,309)(165,308)(166,315)(167,314)(168,313)(169,312)(170,311)(171,310)(172,316)(173,318)(174,317)(175,324)(176,323)(177,322)(178,321)(179,320)(180,319)(181,325)(182,327)(183,326)(184,333)(185,332)(186,331)(187,330)(188,329)(189,328)(190,334)(191,336)(192,335)(193,342)(194,341)(195,340)(196,339)(197,338)(198,337)(199,343)(200,345)(201,344)(202,351)(203,350)(204,349)(205,348)(206,347)(207,346)(208,352)(209,354)(210,353)(211,360)(212,359)(213,358)(214,357)(215,356)(216,355)(217,388)(218,390)(219,389)(220,396)(221,395)(222,394)(223,393)(224,392)(225,391)(226,379)(227,381)(228,380)(229,387)(230,386)(231,385)(232,384)(233,383)(234,382)(235,370)(236,372)(237,371)(238,378)(239,377)(240,376)(241,375)(242,374)(243,373)(244,361)(245,363)(246,362)(247,369)(248,368)(249,367)(250,366)(251,365)(252,364)(253,424)(254,426)(255,425)(256,432)(257,431)(258,430)(259,429)(260,428)(261,427)(262,415)(263,417)(264,416)(265,423)(266,422)(267,421)(268,420)(269,419)(270,418)(271,406)(272,408)(273,407)(274,414)(275,413)(276,412)(277,411)(278,410)(279,409)(280,397)(281,399)(282,398)(283,405)(284,404)(285,403)(286,402)(287,401)(288,400);;
s1 := (  1,  4)(  2,  6)(  3,  5)(  7,  9)( 10, 13)( 11, 15)( 12, 14)( 16, 18)( 19, 22)( 20, 24)( 21, 23)( 25, 27)( 28, 31)( 29, 33)( 30, 32)( 34, 36)( 37, 49)( 38, 51)( 39, 50)( 40, 46)( 41, 48)( 42, 47)( 43, 54)( 44, 53)( 45, 52)( 55, 67)( 56, 69)( 57, 68)( 58, 64)( 59, 66)( 60, 65)( 61, 72)( 62, 71)( 63, 70)( 73, 94)( 74, 96)( 75, 95)( 76, 91)( 77, 93)( 78, 92)( 79, 99)( 80, 98)( 81, 97)( 82,103)( 83,105)( 84,104)( 85,100)( 86,102)( 87,101)( 88,108)( 89,107)( 90,106)(109,139)(110,141)(111,140)(112,136)(113,138)(114,137)(115,144)(116,143)(117,142)(118,130)(119,132)(120,131)(121,127)(122,129)(123,128)(124,135)(125,134)(126,133)(145,184)(146,186)(147,185)(148,181)(149,183)(150,182)(151,189)(152,188)(153,187)(154,193)(155,195)(156,194)(157,190)(158,192)(159,191)(160,198)(161,197)(162,196)(163,202)(164,204)(165,203)(166,199)(167,201)(168,200)(169,207)(170,206)(171,205)(172,211)(173,213)(174,212)(175,208)(176,210)(177,209)(178,216)(179,215)(180,214)(217,274)(218,276)(219,275)(220,271)(221,273)(222,272)(223,279)(224,278)(225,277)(226,283)(227,285)(228,284)(229,280)(230,282)(231,281)(232,288)(233,287)(234,286)(235,256)(236,258)(237,257)(238,253)(239,255)(240,254)(241,261)(242,260)(243,259)(244,265)(245,267)(246,266)(247,262)(248,264)(249,263)(250,270)(251,269)(252,268)(289,364)(290,366)(291,365)(292,361)(293,363)(294,362)(295,369)(296,368)(297,367)(298,373)(299,375)(300,374)(301,370)(302,372)(303,371)(304,378)(305,377)(306,376)(307,382)(308,384)(309,383)(310,379)(311,381)(312,380)(313,387)(314,386)(315,385)(316,391)(317,393)(318,392)(319,388)(320,390)(321,389)(322,396)(323,395)(324,394)(325,409)(326,411)(327,410)(328,406)(329,408)(330,407)(331,414)(332,413)(333,412)(334,400)(335,402)(336,401)(337,397)(338,399)(339,398)(340,405)(341,404)(342,403)(343,427)(344,429)(345,428)(346,424)(347,426)(348,425)(349,432)(350,431)(351,430)(352,418)(353,420)(354,419)(355,415)(356,417)(357,416)(358,423)(359,422)(360,421)(433,553)(434,555)(435,554)(436,550)(437,552)(438,551)(439,558)(440,557)(441,556)(442,544)(443,546)(444,545)(445,541)(446,543)(447,542)(448,549)(449,548)(450,547)(451,571)(452,573)(453,572)(454,568)(455,570)(456,569)(457,576)(458,575)(459,574)(460,562)(461,564)(462,563)(463,559)(464,561)(465,560)(466,567)(467,566)(468,565)(469,517)(470,519)(471,518)(472,514)(473,516)(474,515)(475,522)(476,521)(477,520)(478,508)(479,510)(480,509)(481,505)(482,507)(483,506)(484,513)(485,512)(486,511)(487,535)(488,537)(489,536)(490,532)(491,534)(492,533)(493,540)(494,539)(495,538)(496,526)(497,528)(498,527)(499,523)(500,525)(501,524)(502,531)(503,530)(504,529);;
s2 := (  1,145)(  2,146)(  3,147)(  4,148)(  5,149)(  6,150)(  7,151)(  8,152)(  9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)( 16,160)( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)( 24,168)( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)( 32,176)( 33,177)( 34,178)( 35,179)( 36,180)( 37,190)( 38,191)( 39,192)( 40,193)( 41,194)( 42,195)( 43,196)( 44,197)( 45,198)( 46,181)( 47,182)( 48,183)( 49,184)( 50,185)( 51,186)( 52,187)( 53,188)( 54,189)( 55,208)( 56,209)( 57,210)( 58,211)( 59,212)( 60,213)( 61,214)( 62,215)( 63,216)( 64,199)( 65,200)( 66,201)( 67,202)( 68,203)( 69,204)( 70,205)( 71,206)( 72,207)( 73,226)( 74,227)( 75,228)( 76,229)( 77,230)( 78,231)( 79,232)( 80,233)( 81,234)( 82,217)( 83,218)( 84,219)( 85,220)( 86,221)( 87,222)( 88,223)( 89,224)( 90,225)( 91,244)( 92,245)( 93,246)( 94,247)( 95,248)( 96,249)( 97,250)( 98,251)( 99,252)(100,235)(101,236)(102,237)(103,238)(104,239)(105,240)(106,241)(107,242)(108,243)(109,253)(110,254)(111,255)(112,256)(113,257)(114,258)(115,259)(116,260)(117,261)(118,262)(119,263)(120,264)(121,265)(122,266)(123,267)(124,268)(125,269)(126,270)(127,271)(128,272)(129,273)(130,274)(131,275)(132,276)(133,277)(134,278)(135,279)(136,280)(137,281)(138,282)(139,283)(140,284)(141,285)(142,286)(143,287)(144,288)(289,433)(290,434)(291,435)(292,436)(293,437)(294,438)(295,439)(296,440)(297,441)(298,442)(299,443)(300,444)(301,445)(302,446)(303,447)(304,448)(305,449)(306,450)(307,451)(308,452)(309,453)(310,454)(311,455)(312,456)(313,457)(314,458)(315,459)(316,460)(317,461)(318,462)(319,463)(320,464)(321,465)(322,466)(323,467)(324,468)(325,478)(326,479)(327,480)(328,481)(329,482)(330,483)(331,484)(332,485)(333,486)(334,469)(335,470)(336,471)(337,472)(338,473)(339,474)(340,475)(341,476)(342,477)(343,496)(344,497)(345,498)(346,499)(347,500)(348,501)(349,502)(350,503)(351,504)(352,487)(353,488)(354,489)(355,490)(356,491)(357,492)(358,493)(359,494)(360,495)(361,514)(362,515)(363,516)(364,517)(365,518)(366,519)(367,520)(368,521)(369,522)(370,505)(371,506)(372,507)(373,508)(374,509)(375,510)(376,511)(377,512)(378,513)(379,532)(380,533)(381,534)(382,535)(383,536)(384,537)(385,538)(386,539)(387,540)(388,523)(389,524)(390,525)(391,526)(392,527)(393,528)(394,529)(395,530)(396,531)(397,541)(398,542)(399,543)(400,544)(401,545)(402,546)(403,547)(404,548)(405,549)(406,550)(407,551)(408,552)(409,553)(410,554)(411,555)(412,556)(413,557)(414,558)(415,559)(416,560)(417,561)(418,562)(419,563)(420,564)(421,565)(422,566)(423,567)(424,568)(425,569)(426,570)(427,571)(428,572)(429,573)(430,574)(431,575)(432,576);;
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, 
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*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*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*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*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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(576)!(  1,433)(  2,435)(  3,434)(  4,441)(  5,440)(  6,439)(  7,438)(  8,437)(  9,436)( 10,442)( 11,444)( 12,443)( 13,450)( 14,449)( 15,448)( 16,447)( 17,446)( 18,445)( 19,451)( 20,453)( 21,452)( 22,459)( 23,458)( 24,457)( 25,456)( 26,455)( 27,454)( 28,460)( 29,462)( 30,461)( 31,468)( 32,467)( 33,466)( 34,465)( 35,464)( 36,463)( 37,469)( 38,471)( 39,470)( 40,477)( 41,476)( 42,475)( 43,474)( 44,473)( 45,472)( 46,478)( 47,480)( 48,479)( 49,486)( 50,485)( 51,484)( 52,483)( 53,482)( 54,481)( 55,487)( 56,489)( 57,488)( 58,495)( 59,494)( 60,493)( 61,492)( 62,491)( 63,490)( 64,496)( 65,498)( 66,497)( 67,504)( 68,503)( 69,502)( 70,501)( 71,500)( 72,499)( 73,532)( 74,534)( 75,533)( 76,540)( 77,539)( 78,538)( 79,537)( 80,536)( 81,535)( 82,523)( 83,525)( 84,524)( 85,531)( 86,530)( 87,529)( 88,528)( 89,527)( 90,526)( 91,514)( 92,516)( 93,515)( 94,522)( 95,521)( 96,520)( 97,519)( 98,518)( 99,517)(100,505)(101,507)(102,506)(103,513)(104,512)(105,511)(106,510)(107,509)(108,508)(109,568)(110,570)(111,569)(112,576)(113,575)(114,574)(115,573)(116,572)(117,571)(118,559)(119,561)(120,560)(121,567)(122,566)(123,565)(124,564)(125,563)(126,562)(127,550)(128,552)(129,551)(130,558)(131,557)(132,556)(133,555)(134,554)(135,553)(136,541)(137,543)(138,542)(139,549)(140,548)(141,547)(142,546)(143,545)(144,544)(145,289)(146,291)(147,290)(148,297)(149,296)(150,295)(151,294)(152,293)(153,292)(154,298)(155,300)(156,299)(157,306)(158,305)(159,304)(160,303)(161,302)(162,301)(163,307)(164,309)(165,308)(166,315)(167,314)(168,313)(169,312)(170,311)(171,310)(172,316)(173,318)(174,317)(175,324)(176,323)(177,322)(178,321)(179,320)(180,319)(181,325)(182,327)(183,326)(184,333)(185,332)(186,331)(187,330)(188,329)(189,328)(190,334)(191,336)(192,335)(193,342)(194,341)(195,340)(196,339)(197,338)(198,337)(199,343)(200,345)(201,344)(202,351)(203,350)(204,349)(205,348)(206,347)(207,346)(208,352)(209,354)(210,353)(211,360)(212,359)(213,358)(214,357)(215,356)(216,355)(217,388)(218,390)(219,389)(220,396)(221,395)(222,394)(223,393)(224,392)(225,391)(226,379)(227,381)(228,380)(229,387)(230,386)(231,385)(232,384)(233,383)(234,382)(235,370)(236,372)(237,371)(238,378)(239,377)(240,376)(241,375)(242,374)(243,373)(244,361)(245,363)(246,362)(247,369)(248,368)(249,367)(250,366)(251,365)(252,364)(253,424)(254,426)(255,425)(256,432)(257,431)(258,430)(259,429)(260,428)(261,427)(262,415)(263,417)(264,416)(265,423)(266,422)(267,421)(268,420)(269,419)(270,418)(271,406)(272,408)(273,407)(274,414)(275,413)(276,412)(277,411)(278,410)(279,409)(280,397)(281,399)(282,398)(283,405)(284,404)(285,403)(286,402)(287,401)(288,400);
s1 := Sym(576)!(  1,  4)(  2,  6)(  3,  5)(  7,  9)( 10, 13)( 11, 15)( 12, 14)( 16, 18)( 19, 22)( 20, 24)( 21, 23)( 25, 27)( 28, 31)( 29, 33)( 30, 32)( 34, 36)( 37, 49)( 38, 51)( 39, 50)( 40, 46)( 41, 48)( 42, 47)( 43, 54)( 44, 53)( 45, 52)( 55, 67)( 56, 69)( 57, 68)( 58, 64)( 59, 66)( 60, 65)( 61, 72)( 62, 71)( 63, 70)( 73, 94)( 74, 96)( 75, 95)( 76, 91)( 77, 93)( 78, 92)( 79, 99)( 80, 98)( 81, 97)( 82,103)( 83,105)( 84,104)( 85,100)( 86,102)( 87,101)( 88,108)( 89,107)( 90,106)(109,139)(110,141)(111,140)(112,136)(113,138)(114,137)(115,144)(116,143)(117,142)(118,130)(119,132)(120,131)(121,127)(122,129)(123,128)(124,135)(125,134)(126,133)(145,184)(146,186)(147,185)(148,181)(149,183)(150,182)(151,189)(152,188)(153,187)(154,193)(155,195)(156,194)(157,190)(158,192)(159,191)(160,198)(161,197)(162,196)(163,202)(164,204)(165,203)(166,199)(167,201)(168,200)(169,207)(170,206)(171,205)(172,211)(173,213)(174,212)(175,208)(176,210)(177,209)(178,216)(179,215)(180,214)(217,274)(218,276)(219,275)(220,271)(221,273)(222,272)(223,279)(224,278)(225,277)(226,283)(227,285)(228,284)(229,280)(230,282)(231,281)(232,288)(233,287)(234,286)(235,256)(236,258)(237,257)(238,253)(239,255)(240,254)(241,261)(242,260)(243,259)(244,265)(245,267)(246,266)(247,262)(248,264)(249,263)(250,270)(251,269)(252,268)(289,364)(290,366)(291,365)(292,361)(293,363)(294,362)(295,369)(296,368)(297,367)(298,373)(299,375)(300,374)(301,370)(302,372)(303,371)(304,378)(305,377)(306,376)(307,382)(308,384)(309,383)(310,379)(311,381)(312,380)(313,387)(314,386)(315,385)(316,391)(317,393)(318,392)(319,388)(320,390)(321,389)(322,396)(323,395)(324,394)(325,409)(326,411)(327,410)(328,406)(329,408)(330,407)(331,414)(332,413)(333,412)(334,400)(335,402)(336,401)(337,397)(338,399)(339,398)(340,405)(341,404)(342,403)(343,427)(344,429)(345,428)(346,424)(347,426)(348,425)(349,432)(350,431)(351,430)(352,418)(353,420)(354,419)(355,415)(356,417)(357,416)(358,423)(359,422)(360,421)(433,553)(434,555)(435,554)(436,550)(437,552)(438,551)(439,558)(440,557)(441,556)(442,544)(443,546)(444,545)(445,541)(446,543)(447,542)(448,549)(449,548)(450,547)(451,571)(452,573)(453,572)(454,568)(455,570)(456,569)(457,576)(458,575)(459,574)(460,562)(461,564)(462,563)(463,559)(464,561)(465,560)(466,567)(467,566)(468,565)(469,517)(470,519)(471,518)(472,514)(473,516)(474,515)(475,522)(476,521)(477,520)(478,508)(479,510)(480,509)(481,505)(482,507)(483,506)(484,513)(485,512)(486,511)(487,535)(488,537)(489,536)(490,532)(491,534)(492,533)(493,540)(494,539)(495,538)(496,526)(497,528)(498,527)(499,523)(500,525)(501,524)(502,531)(503,530)(504,529);
s2 := Sym(576)!(  1,145)(  2,146)(  3,147)(  4,148)(  5,149)(  6,150)(  7,151)(  8,152)(  9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)( 16,160)( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)( 24,168)( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)( 32,176)( 33,177)( 34,178)( 35,179)( 36,180)( 37,190)( 38,191)( 39,192)( 40,193)( 41,194)( 42,195)( 43,196)( 44,197)( 45,198)( 46,181)( 47,182)( 48,183)( 49,184)( 50,185)( 51,186)( 52,187)( 53,188)( 54,189)( 55,208)( 56,209)( 57,210)( 58,211)( 59,212)( 60,213)( 61,214)( 62,215)( 63,216)( 64,199)( 65,200)( 66,201)( 67,202)( 68,203)( 69,204)( 70,205)( 71,206)( 72,207)( 73,226)( 74,227)( 75,228)( 76,229)( 77,230)( 78,231)( 79,232)( 80,233)( 81,234)( 82,217)( 83,218)( 84,219)( 85,220)( 86,221)( 87,222)( 88,223)( 89,224)( 90,225)( 91,244)( 92,245)( 93,246)( 94,247)( 95,248)( 96,249)( 97,250)( 98,251)( 99,252)(100,235)(101,236)(102,237)(103,238)(104,239)(105,240)(106,241)(107,242)(108,243)(109,253)(110,254)(111,255)(112,256)(113,257)(114,258)(115,259)(116,260)(117,261)(118,262)(119,263)(120,264)(121,265)(122,266)(123,267)(124,268)(125,269)(126,270)(127,271)(128,272)(129,273)(130,274)(131,275)(132,276)(133,277)(134,278)(135,279)(136,280)(137,281)(138,282)(139,283)(140,284)(141,285)(142,286)(143,287)(144,288)(289,433)(290,434)(291,435)(292,436)(293,437)(294,438)(295,439)(296,440)(297,441)(298,442)(299,443)(300,444)(301,445)(302,446)(303,447)(304,448)(305,449)(306,450)(307,451)(308,452)(309,453)(310,454)(311,455)(312,456)(313,457)(314,458)(315,459)(316,460)(317,461)(318,462)(319,463)(320,464)(321,465)(322,466)(323,467)(324,468)(325,478)(326,479)(327,480)(328,481)(329,482)(330,483)(331,484)(332,485)(333,486)(334,469)(335,470)(336,471)(337,472)(338,473)(339,474)(340,475)(341,476)(342,477)(343,496)(344,497)(345,498)(346,499)(347,500)(348,501)(349,502)(350,503)(351,504)(352,487)(353,488)(354,489)(355,490)(356,491)(357,492)(358,493)(359,494)(360,495)(361,514)(362,515)(363,516)(364,517)(365,518)(366,519)(367,520)(368,521)(369,522)(370,505)(371,506)(372,507)(373,508)(374,509)(375,510)(376,511)(377,512)(378,513)(379,532)(380,533)(381,534)(382,535)(383,536)(384,537)(385,538)(386,539)(387,540)(388,523)(389,524)(390,525)(391,526)(392,527)(393,528)(394,529)(395,530)(396,531)(397,541)(398,542)(399,543)(400,544)(401,545)(402,546)(403,547)(404,548)(405,549)(406,550)(407,551)(408,552)(409,553)(410,554)(411,555)(412,556)(413,557)(414,558)(415,559)(416,560)(417,561)(418,562)(419,563)(420,564)(421,565)(422,566)(423,567)(424,568)(425,569)(426,570)(427,571)(428,572)(429,573)(430,574)(431,575)(432,576);
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*s0*s1*s2*s1, 
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*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*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*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*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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope

Twisty Puzzle