Polytope of Type {6,36}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,36}*1296l
if this polytope has a name.
Group : SmallGroup(1296,2007)
Rank : 3
Schlafli Type : {6,36}
Number of vertices, edges, etc : 18, 324, 108
Order of s0s1s2 : 36
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {6,18}*648i
   3-fold quotients : {6,36}*432a, {6,36}*432b, {6,12}*432g
   6-fold quotients : {6,18}*216a, {6,18}*216b, {6,6}*216d
   9-fold quotients : {2,36}*144, {6,12}*144a, {6,12}*144b, {6,12}*144c
   12-fold quotients : {6,9}*108
   18-fold quotients : {2,18}*72, {6,6}*72a, {6,6}*72b, {6,6}*72c
   27-fold quotients : {2,12}*48, {6,4}*48a
   36-fold quotients : {2,9}*36, {3,6}*36, {6,3}*36
   54-fold quotients : {2,6}*24, {6,2}*24
   81-fold quotients : {2,4}*16
   108-fold quotients : {2,3}*12, {3,2}*12
   162-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1> of order 3.
      36 facets:
         36 of {6}*12
      6 vertex figures:
         6 of {36}*72
   P/N, where N=<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> of order 3.
      36 facets:
         36 of {6}*12
      6 vertex figures:
         6 of {36}*72
   P/N, where N=<s0*s1*s0*s1> of order 3.
      72 facets:
         54 of {2}*4
         18 of {6}*12
      6 vertex figures:
         6 of {36}*72

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