Polytope of Type {72,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {72,4}*1152e
if this polytope has a name.
Group : SmallGroup(1152,154378)
Rank : 3
Schlafli Type : {72,4}
Number of vertices, edges, etc : 144, 288, 8
Order of s0s1s2 : 36
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {36,4}*576c
   3-fold quotients : {24,4}*384e
   4-fold quotients : {18,4}*288
   6-fold quotients : {12,4}*192c
   8-fold quotients : {9,4}*144, {18,4}*144b, {18,4}*144c
   12-fold quotients : {6,4}*96
   16-fold quotients : {9,4}*72, {18,2}*72
   24-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   32-fold quotients : {9,2}*36
   48-fold quotients : {3,4}*24, {6,2}*24
   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 := (  1,289)(  2,290)(  3,292)(  4,291)(  5,295)(  6,296)(  7,293)(  8,294)(  9,305)( 10,306)( 11,308)( 12,307)( 13,311)( 14,312)( 15,309)( 16,310)( 17,297)( 18,298)( 19,300)( 20,299)( 21,303)( 22,304)( 23,301)( 24,302)( 25,353)( 26,354)( 27,356)( 28,355)( 29,359)( 30,360)( 31,357)( 32,358)( 33,345)( 34,346)( 35,348)( 36,347)( 37,351)( 38,352)( 39,349)( 40,350)( 41,337)( 42,338)( 43,340)( 44,339)( 45,343)( 46,344)( 47,341)( 48,342)( 49,329)( 50,330)( 51,332)( 52,331)( 53,335)( 54,336)( 55,333)( 56,334)( 57,321)( 58,322)( 59,324)( 60,323)( 61,327)( 62,328)( 63,325)( 64,326)( 65,313)( 66,314)( 67,316)( 68,315)( 69,319)( 70,320)( 71,317)( 72,318)( 73,362)( 74,361)( 75,363)( 76,364)( 77,368)( 78,367)( 79,366)( 80,365)( 81,378)( 82,377)( 83,379)( 84,380)( 85,384)( 86,383)( 87,382)( 88,381)( 89,370)( 90,369)( 91,371)( 92,372)( 93,376)( 94,375)( 95,374)( 96,373)( 97,426)( 98,425)( 99,427)(100,428)(101,432)(102,431)(103,430)(104,429)(105,418)(106,417)(107,419)(108,420)(109,424)(110,423)(111,422)(112,421)(113,410)(114,409)(115,411)(116,412)(117,416)(118,415)(119,414)(120,413)(121,402)(122,401)(123,403)(124,404)(125,408)(126,407)(127,406)(128,405)(129,394)(130,393)(131,395)(132,396)(133,400)(134,399)(135,398)(136,397)(137,386)(138,385)(139,387)(140,388)(141,392)(142,391)(143,390)(144,389)(145,506)(146,505)(147,507)(148,508)(149,512)(150,511)(151,510)(152,509)(153,522)(154,521)(155,523)(156,524)(157,528)(158,527)(159,526)(160,525)(161,514)(162,513)(163,515)(164,516)(165,520)(166,519)(167,518)(168,517)(169,570)(170,569)(171,571)(172,572)(173,576)(174,575)(175,574)(176,573)(177,562)(178,561)(179,563)(180,564)(181,568)(182,567)(183,566)(184,565)(185,554)(186,553)(187,555)(188,556)(189,560)(190,559)(191,558)(192,557)(193,546)(194,545)(195,547)(196,548)(197,552)(198,551)(199,550)(200,549)(201,538)(202,537)(203,539)(204,540)(205,544)(206,543)(207,542)(208,541)(209,530)(210,529)(211,531)(212,532)(213,536)(214,535)(215,534)(216,533)(217,434)(218,433)(219,435)(220,436)(221,440)(222,439)(223,438)(224,437)(225,450)(226,449)(227,451)(228,452)(229,456)(230,455)(231,454)(232,453)(233,442)(234,441)(235,443)(236,444)(237,448)(238,447)(239,446)(240,445)(241,498)(242,497)(243,499)(244,500)(245,504)(246,503)(247,502)(248,501)(249,490)(250,489)(251,491)(252,492)(253,496)(254,495)(255,494)(256,493)(257,482)(258,481)(259,483)(260,484)(261,488)(262,487)(263,486)(264,485)(265,474)(266,473)(267,475)(268,476)(269,480)(270,479)(271,478)(272,477)(273,466)(274,465)(275,467)(276,468)(277,472)(278,471)(279,470)(280,469)(281,458)(282,457)(283,459)(284,460)(285,464)(286,463)(287,462)(288,461);;
s1 := (  1,169)(  2,170)(  3,175)(  4,176)(  5,174)(  6,173)(  7,171)(  8,172)(  9,185)( 10,186)( 11,191)( 12,192)( 13,190)( 14,189)( 15,187)( 16,188)( 17,177)( 18,178)( 19,183)( 20,184)( 21,182)( 22,181)( 23,179)( 24,180)( 25,145)( 26,146)( 27,151)( 28,152)( 29,150)( 30,149)( 31,147)( 32,148)( 33,161)( 34,162)( 35,167)( 36,168)( 37,166)( 38,165)( 39,163)( 40,164)( 41,153)( 42,154)( 43,159)( 44,160)( 45,158)( 46,157)( 47,155)( 48,156)( 49,209)( 50,210)( 51,215)( 52,216)( 53,214)( 54,213)( 55,211)( 56,212)( 57,201)( 58,202)( 59,207)( 60,208)( 61,206)( 62,205)( 63,203)( 64,204)( 65,193)( 66,194)( 67,199)( 68,200)( 69,198)( 70,197)( 71,195)( 72,196)( 73,242)( 74,241)( 75,248)( 76,247)( 77,245)( 78,246)( 79,244)( 80,243)( 81,258)( 82,257)( 83,264)( 84,263)( 85,261)( 86,262)( 87,260)( 88,259)( 89,250)( 90,249)( 91,256)( 92,255)( 93,253)( 94,254)( 95,252)( 96,251)( 97,218)( 98,217)( 99,224)(100,223)(101,221)(102,222)(103,220)(104,219)(105,234)(106,233)(107,240)(108,239)(109,237)(110,238)(111,236)(112,235)(113,226)(114,225)(115,232)(116,231)(117,229)(118,230)(119,228)(120,227)(121,282)(122,281)(123,288)(124,287)(125,285)(126,286)(127,284)(128,283)(129,274)(130,273)(131,280)(132,279)(133,277)(134,278)(135,276)(136,275)(137,266)(138,265)(139,272)(140,271)(141,269)(142,270)(143,268)(144,267)(289,458)(290,457)(291,464)(292,463)(293,461)(294,462)(295,460)(296,459)(297,474)(298,473)(299,480)(300,479)(301,477)(302,478)(303,476)(304,475)(305,466)(306,465)(307,472)(308,471)(309,469)(310,470)(311,468)(312,467)(313,434)(314,433)(315,440)(316,439)(317,437)(318,438)(319,436)(320,435)(321,450)(322,449)(323,456)(324,455)(325,453)(326,454)(327,452)(328,451)(329,442)(330,441)(331,448)(332,447)(333,445)(334,446)(335,444)(336,443)(337,498)(338,497)(339,504)(340,503)(341,501)(342,502)(343,500)(344,499)(345,490)(346,489)(347,496)(348,495)(349,493)(350,494)(351,492)(352,491)(353,482)(354,481)(355,488)(356,487)(357,485)(358,486)(359,484)(360,483)(361,529)(362,530)(363,535)(364,536)(365,534)(366,533)(367,531)(368,532)(369,545)(370,546)(371,551)(372,552)(373,550)(374,549)(375,547)(376,548)(377,537)(378,538)(379,543)(380,544)(381,542)(382,541)(383,539)(384,540)(385,505)(386,506)(387,511)(388,512)(389,510)(390,509)(391,507)(392,508)(393,521)(394,522)(395,527)(396,528)(397,526)(398,525)(399,523)(400,524)(401,513)(402,514)(403,519)(404,520)(405,518)(406,517)(407,515)(408,516)(409,569)(410,570)(411,575)(412,576)(413,574)(414,573)(415,571)(416,572)(417,561)(418,562)(419,567)(420,568)(421,566)(422,565)(423,563)(424,564)(425,553)(426,554)(427,559)(428,560)(429,558)(430,557)(431,555)(432,556);;
s2 := (  1,291)(  2,292)(  3,290)(  4,289)(  5,295)(  6,296)(  7,294)(  8,293)(  9,299)( 10,300)( 11,298)( 12,297)( 13,303)( 14,304)( 15,302)( 16,301)( 17,307)( 18,308)( 19,306)( 20,305)( 21,311)( 22,312)( 23,310)( 24,309)( 25,315)( 26,316)( 27,314)( 28,313)( 29,319)( 30,320)( 31,318)( 32,317)( 33,323)( 34,324)( 35,322)( 36,321)( 37,327)( 38,328)( 39,326)( 40,325)( 41,331)( 42,332)( 43,330)( 44,329)( 45,335)( 46,336)( 47,334)( 48,333)( 49,339)( 50,340)( 51,338)( 52,337)( 53,343)( 54,344)( 55,342)( 56,341)( 57,347)( 58,348)( 59,346)( 60,345)( 61,351)( 62,352)( 63,350)( 64,349)( 65,355)( 66,356)( 67,354)( 68,353)( 69,359)( 70,360)( 71,358)( 72,357)( 73,364)( 74,363)( 75,361)( 76,362)( 77,368)( 78,367)( 79,365)( 80,366)( 81,372)( 82,371)( 83,369)( 84,370)( 85,376)( 86,375)( 87,373)( 88,374)( 89,380)( 90,379)( 91,377)( 92,378)( 93,384)( 94,383)( 95,381)( 96,382)( 97,388)( 98,387)( 99,385)(100,386)(101,392)(102,391)(103,389)(104,390)(105,396)(106,395)(107,393)(108,394)(109,400)(110,399)(111,397)(112,398)(113,404)(114,403)(115,401)(116,402)(117,408)(118,407)(119,405)(120,406)(121,412)(122,411)(123,409)(124,410)(125,416)(126,415)(127,413)(128,414)(129,420)(130,419)(131,417)(132,418)(133,424)(134,423)(135,421)(136,422)(137,428)(138,427)(139,425)(140,426)(141,432)(142,431)(143,429)(144,430)(145,507)(146,508)(147,506)(148,505)(149,511)(150,512)(151,510)(152,509)(153,515)(154,516)(155,514)(156,513)(157,519)(158,520)(159,518)(160,517)(161,523)(162,524)(163,522)(164,521)(165,527)(166,528)(167,526)(168,525)(169,531)(170,532)(171,530)(172,529)(173,535)(174,536)(175,534)(176,533)(177,539)(178,540)(179,538)(180,537)(181,543)(182,544)(183,542)(184,541)(185,547)(186,548)(187,546)(188,545)(189,551)(190,552)(191,550)(192,549)(193,555)(194,556)(195,554)(196,553)(197,559)(198,560)(199,558)(200,557)(201,563)(202,564)(203,562)(204,561)(205,567)(206,568)(207,566)(208,565)(209,571)(210,572)(211,570)(212,569)(213,575)(214,576)(215,574)(216,573)(217,435)(218,436)(219,434)(220,433)(221,439)(222,440)(223,438)(224,437)(225,443)(226,444)(227,442)(228,441)(229,447)(230,448)(231,446)(232,445)(233,451)(234,452)(235,450)(236,449)(237,455)(238,456)(239,454)(240,453)(241,459)(242,460)(243,458)(244,457)(245,463)(246,464)(247,462)(248,461)(249,467)(250,468)(251,466)(252,465)(253,471)(254,472)(255,470)(256,469)(257,475)(258,476)(259,474)(260,473)(261,479)(262,480)(263,478)(264,477)(265,483)(266,484)(267,482)(268,481)(269,487)(270,488)(271,486)(272,485)(273,491)(274,492)(275,490)(276,489)(277,495)(278,496)(279,494)(280,493)(281,499)(282,500)(283,498)(284,497)(285,503)(286,504)(287,502)(288,501);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(576)!(  1,289)(  2,290)(  3,292)(  4,291)(  5,295)(  6,296)(  7,293)(  8,294)(  9,305)( 10,306)( 11,308)( 12,307)( 13,311)( 14,312)( 15,309)( 16,310)( 17,297)( 18,298)( 19,300)( 20,299)( 21,303)( 22,304)( 23,301)( 24,302)( 25,353)( 26,354)( 27,356)( 28,355)( 29,359)( 30,360)( 31,357)( 32,358)( 33,345)( 34,346)( 35,348)( 36,347)( 37,351)( 38,352)( 39,349)( 40,350)( 41,337)( 42,338)( 43,340)( 44,339)( 45,343)( 46,344)( 47,341)( 48,342)( 49,329)( 50,330)( 51,332)( 52,331)( 53,335)( 54,336)( 55,333)( 56,334)( 57,321)( 58,322)( 59,324)( 60,323)( 61,327)( 62,328)( 63,325)( 64,326)( 65,313)( 66,314)( 67,316)( 68,315)( 69,319)( 70,320)( 71,317)( 72,318)( 73,362)( 74,361)( 75,363)( 76,364)( 77,368)( 78,367)( 79,366)( 80,365)( 81,378)( 82,377)( 83,379)( 84,380)( 85,384)( 86,383)( 87,382)( 88,381)( 89,370)( 90,369)( 91,371)( 92,372)( 93,376)( 94,375)( 95,374)( 96,373)( 97,426)( 98,425)( 99,427)(100,428)(101,432)(102,431)(103,430)(104,429)(105,418)(106,417)(107,419)(108,420)(109,424)(110,423)(111,422)(112,421)(113,410)(114,409)(115,411)(116,412)(117,416)(118,415)(119,414)(120,413)(121,402)(122,401)(123,403)(124,404)(125,408)(126,407)(127,406)(128,405)(129,394)(130,393)(131,395)(132,396)(133,400)(134,399)(135,398)(136,397)(137,386)(138,385)(139,387)(140,388)(141,392)(142,391)(143,390)(144,389)(145,506)(146,505)(147,507)(148,508)(149,512)(150,511)(151,510)(152,509)(153,522)(154,521)(155,523)(156,524)(157,528)(158,527)(159,526)(160,525)(161,514)(162,513)(163,515)(164,516)(165,520)(166,519)(167,518)(168,517)(169,570)(170,569)(171,571)(172,572)(173,576)(174,575)(175,574)(176,573)(177,562)(178,561)(179,563)(180,564)(181,568)(182,567)(183,566)(184,565)(185,554)(186,553)(187,555)(188,556)(189,560)(190,559)(191,558)(192,557)(193,546)(194,545)(195,547)(196,548)(197,552)(198,551)(199,550)(200,549)(201,538)(202,537)(203,539)(204,540)(205,544)(206,543)(207,542)(208,541)(209,530)(210,529)(211,531)(212,532)(213,536)(214,535)(215,534)(216,533)(217,434)(218,433)(219,435)(220,436)(221,440)(222,439)(223,438)(224,437)(225,450)(226,449)(227,451)(228,452)(229,456)(230,455)(231,454)(232,453)(233,442)(234,441)(235,443)(236,444)(237,448)(238,447)(239,446)(240,445)(241,498)(242,497)(243,499)(244,500)(245,504)(246,503)(247,502)(248,501)(249,490)(250,489)(251,491)(252,492)(253,496)(254,495)(255,494)(256,493)(257,482)(258,481)(259,483)(260,484)(261,488)(262,487)(263,486)(264,485)(265,474)(266,473)(267,475)(268,476)(269,480)(270,479)(271,478)(272,477)(273,466)(274,465)(275,467)(276,468)(277,472)(278,471)(279,470)(280,469)(281,458)(282,457)(283,459)(284,460)(285,464)(286,463)(287,462)(288,461);
s1 := Sym(576)!(  1,169)(  2,170)(  3,175)(  4,176)(  5,174)(  6,173)(  7,171)(  8,172)(  9,185)( 10,186)( 11,191)( 12,192)( 13,190)( 14,189)( 15,187)( 16,188)( 17,177)( 18,178)( 19,183)( 20,184)( 21,182)( 22,181)( 23,179)( 24,180)( 25,145)( 26,146)( 27,151)( 28,152)( 29,150)( 30,149)( 31,147)( 32,148)( 33,161)( 34,162)( 35,167)( 36,168)( 37,166)( 38,165)( 39,163)( 40,164)( 41,153)( 42,154)( 43,159)( 44,160)( 45,158)( 46,157)( 47,155)( 48,156)( 49,209)( 50,210)( 51,215)( 52,216)( 53,214)( 54,213)( 55,211)( 56,212)( 57,201)( 58,202)( 59,207)( 60,208)( 61,206)( 62,205)( 63,203)( 64,204)( 65,193)( 66,194)( 67,199)( 68,200)( 69,198)( 70,197)( 71,195)( 72,196)( 73,242)( 74,241)( 75,248)( 76,247)( 77,245)( 78,246)( 79,244)( 80,243)( 81,258)( 82,257)( 83,264)( 84,263)( 85,261)( 86,262)( 87,260)( 88,259)( 89,250)( 90,249)( 91,256)( 92,255)( 93,253)( 94,254)( 95,252)( 96,251)( 97,218)( 98,217)( 99,224)(100,223)(101,221)(102,222)(103,220)(104,219)(105,234)(106,233)(107,240)(108,239)(109,237)(110,238)(111,236)(112,235)(113,226)(114,225)(115,232)(116,231)(117,229)(118,230)(119,228)(120,227)(121,282)(122,281)(123,288)(124,287)(125,285)(126,286)(127,284)(128,283)(129,274)(130,273)(131,280)(132,279)(133,277)(134,278)(135,276)(136,275)(137,266)(138,265)(139,272)(140,271)(141,269)(142,270)(143,268)(144,267)(289,458)(290,457)(291,464)(292,463)(293,461)(294,462)(295,460)(296,459)(297,474)(298,473)(299,480)(300,479)(301,477)(302,478)(303,476)(304,475)(305,466)(306,465)(307,472)(308,471)(309,469)(310,470)(311,468)(312,467)(313,434)(314,433)(315,440)(316,439)(317,437)(318,438)(319,436)(320,435)(321,450)(322,449)(323,456)(324,455)(325,453)(326,454)(327,452)(328,451)(329,442)(330,441)(331,448)(332,447)(333,445)(334,446)(335,444)(336,443)(337,498)(338,497)(339,504)(340,503)(341,501)(342,502)(343,500)(344,499)(345,490)(346,489)(347,496)(348,495)(349,493)(350,494)(351,492)(352,491)(353,482)(354,481)(355,488)(356,487)(357,485)(358,486)(359,484)(360,483)(361,529)(362,530)(363,535)(364,536)(365,534)(366,533)(367,531)(368,532)(369,545)(370,546)(371,551)(372,552)(373,550)(374,549)(375,547)(376,548)(377,537)(378,538)(379,543)(380,544)(381,542)(382,541)(383,539)(384,540)(385,505)(386,506)(387,511)(388,512)(389,510)(390,509)(391,507)(392,508)(393,521)(394,522)(395,527)(396,528)(397,526)(398,525)(399,523)(400,524)(401,513)(402,514)(403,519)(404,520)(405,518)(406,517)(407,515)(408,516)(409,569)(410,570)(411,575)(412,576)(413,574)(414,573)(415,571)(416,572)(417,561)(418,562)(419,567)(420,568)(421,566)(422,565)(423,563)(424,564)(425,553)(426,554)(427,559)(428,560)(429,558)(430,557)(431,555)(432,556);
s2 := Sym(576)!(  1,291)(  2,292)(  3,290)(  4,289)(  5,295)(  6,296)(  7,294)(  8,293)(  9,299)( 10,300)( 11,298)( 12,297)( 13,303)( 14,304)( 15,302)( 16,301)( 17,307)( 18,308)( 19,306)( 20,305)( 21,311)( 22,312)( 23,310)( 24,309)( 25,315)( 26,316)( 27,314)( 28,313)( 29,319)( 30,320)( 31,318)( 32,317)( 33,323)( 34,324)( 35,322)( 36,321)( 37,327)( 38,328)( 39,326)( 40,325)( 41,331)( 42,332)( 43,330)( 44,329)( 45,335)( 46,336)( 47,334)( 48,333)( 49,339)( 50,340)( 51,338)( 52,337)( 53,343)( 54,344)( 55,342)( 56,341)( 57,347)( 58,348)( 59,346)( 60,345)( 61,351)( 62,352)( 63,350)( 64,349)( 65,355)( 66,356)( 67,354)( 68,353)( 69,359)( 70,360)( 71,358)( 72,357)( 73,364)( 74,363)( 75,361)( 76,362)( 77,368)( 78,367)( 79,365)( 80,366)( 81,372)( 82,371)( 83,369)( 84,370)( 85,376)( 86,375)( 87,373)( 88,374)( 89,380)( 90,379)( 91,377)( 92,378)( 93,384)( 94,383)( 95,381)( 96,382)( 97,388)( 98,387)( 99,385)(100,386)(101,392)(102,391)(103,389)(104,390)(105,396)(106,395)(107,393)(108,394)(109,400)(110,399)(111,397)(112,398)(113,404)(114,403)(115,401)(116,402)(117,408)(118,407)(119,405)(120,406)(121,412)(122,411)(123,409)(124,410)(125,416)(126,415)(127,413)(128,414)(129,420)(130,419)(131,417)(132,418)(133,424)(134,423)(135,421)(136,422)(137,428)(138,427)(139,425)(140,426)(141,432)(142,431)(143,429)(144,430)(145,507)(146,508)(147,506)(148,505)(149,511)(150,512)(151,510)(152,509)(153,515)(154,516)(155,514)(156,513)(157,519)(158,520)(159,518)(160,517)(161,523)(162,524)(163,522)(164,521)(165,527)(166,528)(167,526)(168,525)(169,531)(170,532)(171,530)(172,529)(173,535)(174,536)(175,534)(176,533)(177,539)(178,540)(179,538)(180,537)(181,543)(182,544)(183,542)(184,541)(185,547)(186,548)(187,546)(188,545)(189,551)(190,552)(191,550)(192,549)(193,555)(194,556)(195,554)(196,553)(197,559)(198,560)(199,558)(200,557)(201,563)(202,564)(203,562)(204,561)(205,567)(206,568)(207,566)(208,565)(209,571)(210,572)(211,570)(212,569)(213,575)(214,576)(215,574)(216,573)(217,435)(218,436)(219,434)(220,433)(221,439)(222,440)(223,438)(224,437)(225,443)(226,444)(227,442)(228,441)(229,447)(230,448)(231,446)(232,445)(233,451)(234,452)(235,450)(236,449)(237,455)(238,456)(239,454)(240,453)(241,459)(242,460)(243,458)(244,457)(245,463)(246,464)(247,462)(248,461)(249,467)(250,468)(251,466)(252,465)(253,471)(254,472)(255,470)(256,469)(257,475)(258,476)(259,474)(260,473)(261,479)(262,480)(263,478)(264,477)(265,483)(266,484)(267,482)(268,481)(269,487)(270,488)(271,486)(272,485)(273,491)(274,492)(275,490)(276,489)(277,495)(278,496)(279,494)(280,493)(281,499)(282,500)(283,498)(284,497)(285,503)(286,504)(287,502)(288,501);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1 >;
References : None.
to this polytope

Twisty Puzzle