Polytope of Type {12,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6}*1728f
if this polytope has a name.
Group : SmallGroup(1728,30326)
Rank : 3
Schlafli Type : {12,6}
Number of vertices, edges, etc : 144, 432, 72
Order of s0s1s2 : 12
Order of s0s1s2s1 : 12
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 : {12,6}*864a
   3-fold quotients : {12,6}*576f
   4-fold quotients : {12,6}*432c, {12,3}*432
   6-fold quotients : {12,6}*288b
   8-fold quotients : {6,6}*216a
   9-fold quotients : {4,6}*192b
   12-fold quotients : {12,6}*144c, {12,3}*144
   16-fold quotients : {6,3}*108
   18-fold quotients : {4,6}*96
   24-fold quotients : {6,6}*72b
   36-fold quotients : {4,6}*48a, {4,3}*48, {4,6}*48b, {4,6}*48c
   48-fold quotients : {6,3}*36
   72-fold quotients : {4,3}*24, {2,6}*24
   108-fold quotients : {4,2}*16
   144-fold quotients : {2,3}*12
   216-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*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s2> of order 2.
      36 facets:
         36 of {12}*24
      72 vertex figures:
         72 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 2.
      36 facets:
         36 of {12}*24
      72 vertex figures:
         72 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1> of order 2.
      48 facets:
         24 of {6}*12
         24 of {12}*24
      72 vertex figures:
         72 of {6}*12
   P/N, where N=<s1*s2*s1*s2*s1*s2> of order 2.
      36 facets:
         36 of {12}*24
      108 vertex figures:
         72 of {3}*6
         36 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1> of order 3.
      40 facets:
         24 of {4}*8
         16 of {12}*24
      48 vertex figures:
         48 of {6}*12
   P/N, where N=<s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1> of order 4.
      24 facets:
         12 of {6}*12
         12 of {12}*24
      54 vertex figures:
         36 of {3}*6
         18 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1> of order 4.
      18 facets:
         18 of {12}*24
      36 vertex figures:
         36 of {6}*12
   P/N, where N=<s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1> of order 4.
      30 facets:
         6 of {12}*24
         24 of {6}*12
      36 vertex figures:
         36 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2> of order 6.
      20 facets:
         12 of {4}*8
         8 of {12}*24
      24 vertex figures:
         24 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1, s0*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2> of order 6.
      24 facets:
         12 of {4}*8
         4 of {12}*24
         8 of {6}*12
      24 vertex figures:
         24 of {6}*12
   P/N, where N=<s0*s1*s0*s1> of order 6.
      32 facets:
         24 of {2}*4
         8 of {12}*24
      24 vertex figures:
         24 of {6}*12
   P/N, where N=<s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1> of order 6.
      20 facets:
         12 of {4}*8
         8 of {12}*24
      36 vertex figures:
         24 of {3}*6
         12 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 6.
      20 facets:
         12 of {4}*8
         8 of {12}*24
      24 vertex figures:
         24 of {6}*12
   P/N, where N=<s0*s2*s1*s0*s1*s0*s1*s0*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 6.
      20 facets:
         8 of {12}*24
         12 of {4}*8
      24 vertex figures:
         24 of {6}*12
   P/N, where N=<s0*s2*s1*s0*s1*s2, s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1> of order 12.
      18 facets:
         2 of {12}*24
         12 of {2}*4
         4 of {6}*12
      12 vertex figures:
         12 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2, s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2> of order 12.
      14 facets:
         6 of {4}*8
         8 of {6}*12
      12 vertex figures:
         12 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1> of order 12.
      10 facets:
         6 of {4}*8
         4 of {12}*24
      12 vertex figures:
         12 of {6}*12
   P/N, where N=<s0*s1*s0*s1, s1*s2*s1*s2*s1*s2> of order 12.
      16 facets:
         12 of {2}*4
         4 of {12}*24
      18 vertex figures:
         12 of {3}*6
         6 of {6}*12
   P/N, where N=<s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1, s0*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1> of order 12.
      12 facets:
         6 of {4}*8
         2 of {12}*24
         4 of {6}*12
      18 vertex figures:
         12 of {3}*6
         6 of {6}*12

Permutation Representation (GAP) : 
s0 := (  1,  3)(  2,  4)(  5, 11)(  6, 12)(  7,  9)(  8, 10)( 13, 27)( 14, 28)( 15, 25)( 16, 26)( 17, 35)( 18, 36)( 19, 33)( 20, 34)( 21, 31)( 22, 32)( 23, 29)( 24, 30)( 37, 39)( 38, 40)( 41, 47)( 42, 48)( 43, 45)( 44, 46)( 49, 63)( 50, 64)( 51, 61)( 52, 62)( 53, 71)( 54, 72)( 55, 69)( 56, 70)( 57, 67)( 58, 68)( 59, 65)( 60, 66)( 73, 75)( 74, 76)( 77, 83)( 78, 84)( 79, 81)( 80, 82)( 85, 99)( 86,100)( 87, 97)( 88, 98)( 89,107)( 90,108)( 91,105)( 92,106)( 93,103)( 94,104)( 95,101)( 96,102)(109,111)(110,112)(113,119)(114,120)(115,117)(116,118)(121,135)(122,136)(123,133)(124,134)(125,143)(126,144)(127,141)(128,142)(129,139)(130,140)(131,137)(132,138)(145,147)(146,148)(149,155)(150,156)(151,153)(152,154)(157,171)(158,172)(159,169)(160,170)(161,179)(162,180)(163,177)(164,178)(165,175)(166,176)(167,173)(168,174)(181,183)(182,184)(185,191)(186,192)(187,189)(188,190)(193,207)(194,208)(195,205)(196,206)(197,215)(198,216)(199,213)(200,214)(201,211)(202,212)(203,209)(204,210)(217,327)(218,328)(219,325)(220,326)(221,335)(222,336)(223,333)(224,334)(225,331)(226,332)(227,329)(228,330)(229,351)(230,352)(231,349)(232,350)(233,359)(234,360)(235,357)(236,358)(237,355)(238,356)(239,353)(240,354)(241,339)(242,340)(243,337)(244,338)(245,347)(246,348)(247,345)(248,346)(249,343)(250,344)(251,341)(252,342)(253,363)(254,364)(255,361)(256,362)(257,371)(258,372)(259,369)(260,370)(261,367)(262,368)(263,365)(264,366)(265,387)(266,388)(267,385)(268,386)(269,395)(270,396)(271,393)(272,394)(273,391)(274,392)(275,389)(276,390)(277,375)(278,376)(279,373)(280,374)(281,383)(282,384)(283,381)(284,382)(285,379)(286,380)(287,377)(288,378)(289,399)(290,400)(291,397)(292,398)(293,407)(294,408)(295,405)(296,406)(297,403)(298,404)(299,401)(300,402)(301,423)(302,424)(303,421)(304,422)(305,431)(306,432)(307,429)(308,430)(309,427)(310,428)(311,425)(312,426)(313,411)(314,412)(315,409)(316,410)(317,419)(318,420)(319,417)(320,418)(321,415)(322,416)(323,413)(324,414);;
s1 := (  1,229)(  2,230)(  3,232)(  4,231)(  5,233)(  6,234)(  7,236)(  8,235)(  9,237)( 10,238)( 11,240)( 12,239)( 13,217)( 14,218)( 15,220)( 16,219)( 17,221)( 18,222)( 19,224)( 20,223)( 21,225)( 22,226)( 23,228)( 24,227)( 25,241)( 26,242)( 27,244)( 28,243)( 29,245)( 30,246)( 31,248)( 32,247)( 33,249)( 34,250)( 35,252)( 36,251)( 37,301)( 38,302)( 39,304)( 40,303)( 41,305)( 42,306)( 43,308)( 44,307)( 45,309)( 46,310)( 47,312)( 48,311)( 49,289)( 50,290)( 51,292)( 52,291)( 53,293)( 54,294)( 55,296)( 56,295)( 57,297)( 58,298)( 59,300)( 60,299)( 61,313)( 62,314)( 63,316)( 64,315)( 65,317)( 66,318)( 67,320)( 68,319)( 69,321)( 70,322)( 71,324)( 72,323)( 73,265)( 74,266)( 75,268)( 76,267)( 77,269)( 78,270)( 79,272)( 80,271)( 81,273)( 82,274)( 83,276)( 84,275)( 85,253)( 86,254)( 87,256)( 88,255)( 89,257)( 90,258)( 91,260)( 92,259)( 93,261)( 94,262)( 95,264)( 96,263)( 97,277)( 98,278)( 99,280)(100,279)(101,281)(102,282)(103,284)(104,283)(105,285)(106,286)(107,288)(108,287)(109,337)(110,338)(111,340)(112,339)(113,341)(114,342)(115,344)(116,343)(117,345)(118,346)(119,348)(120,347)(121,325)(122,326)(123,328)(124,327)(125,329)(126,330)(127,332)(128,331)(129,333)(130,334)(131,336)(132,335)(133,349)(134,350)(135,352)(136,351)(137,353)(138,354)(139,356)(140,355)(141,357)(142,358)(143,360)(144,359)(145,409)(146,410)(147,412)(148,411)(149,413)(150,414)(151,416)(152,415)(153,417)(154,418)(155,420)(156,419)(157,397)(158,398)(159,400)(160,399)(161,401)(162,402)(163,404)(164,403)(165,405)(166,406)(167,408)(168,407)(169,421)(170,422)(171,424)(172,423)(173,425)(174,426)(175,428)(176,427)(177,429)(178,430)(179,432)(180,431)(181,373)(182,374)(183,376)(184,375)(185,377)(186,378)(187,380)(188,379)(189,381)(190,382)(191,384)(192,383)(193,361)(194,362)(195,364)(196,363)(197,365)(198,366)(199,368)(200,367)(201,369)(202,370)(203,372)(204,371)(205,385)(206,386)(207,388)(208,387)(209,389)(210,390)(211,392)(212,391)(213,393)(214,394)(215,396)(216,395);;
s2 := (  1, 37)(  2, 40)(  3, 39)(  4, 38)(  5, 41)(  6, 44)(  7, 43)(  8, 42)(  9, 45)( 10, 48)( 11, 47)( 12, 46)( 13, 69)( 14, 72)( 15, 71)( 16, 70)( 17, 61)( 18, 64)( 19, 63)( 20, 62)( 21, 65)( 22, 68)( 23, 67)( 24, 66)( 25, 53)( 26, 56)( 27, 55)( 28, 54)( 29, 57)( 30, 60)( 31, 59)( 32, 58)( 33, 49)( 34, 52)( 35, 51)( 36, 50)( 74, 76)( 78, 80)( 82, 84)( 85,105)( 86,108)( 87,107)( 88,106)( 89, 97)( 90,100)( 91, 99)( 92, 98)( 93,101)( 94,104)( 95,103)( 96,102)(109,145)(110,148)(111,147)(112,146)(113,149)(114,152)(115,151)(116,150)(117,153)(118,156)(119,155)(120,154)(121,177)(122,180)(123,179)(124,178)(125,169)(126,172)(127,171)(128,170)(129,173)(130,176)(131,175)(132,174)(133,161)(134,164)(135,163)(136,162)(137,165)(138,168)(139,167)(140,166)(141,157)(142,160)(143,159)(144,158)(182,184)(186,188)(190,192)(193,213)(194,216)(195,215)(196,214)(197,205)(198,208)(199,207)(200,206)(201,209)(202,212)(203,211)(204,210)(217,253)(218,256)(219,255)(220,254)(221,257)(222,260)(223,259)(224,258)(225,261)(226,264)(227,263)(228,262)(229,285)(230,288)(231,287)(232,286)(233,277)(234,280)(235,279)(236,278)(237,281)(238,284)(239,283)(240,282)(241,269)(242,272)(243,271)(244,270)(245,273)(246,276)(247,275)(248,274)(249,265)(250,268)(251,267)(252,266)(290,292)(294,296)(298,300)(301,321)(302,324)(303,323)(304,322)(305,313)(306,316)(307,315)(308,314)(309,317)(310,320)(311,319)(312,318)(325,361)(326,364)(327,363)(328,362)(329,365)(330,368)(331,367)(332,366)(333,369)(334,372)(335,371)(336,370)(337,393)(338,396)(339,395)(340,394)(341,385)(342,388)(343,387)(344,386)(345,389)(346,392)(347,391)(348,390)(349,377)(350,380)(351,379)(352,378)(353,381)(354,384)(355,383)(356,382)(357,373)(358,376)(359,375)(360,374)(398,400)(402,404)(406,408)(409,429)(410,432)(411,431)(412,430)(413,421)(414,424)(415,423)(416,422)(417,425)(418,428)(419,427)(420,426);;
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*s1*s2*s1*s2, 
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, 
s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*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*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(432)!(  1,  3)(  2,  4)(  5, 11)(  6, 12)(  7,  9)(  8, 10)( 13, 27)( 14, 28)( 15, 25)( 16, 26)( 17, 35)( 18, 36)( 19, 33)( 20, 34)( 21, 31)( 22, 32)( 23, 29)( 24, 30)( 37, 39)( 38, 40)( 41, 47)( 42, 48)( 43, 45)( 44, 46)( 49, 63)( 50, 64)( 51, 61)( 52, 62)( 53, 71)( 54, 72)( 55, 69)( 56, 70)( 57, 67)( 58, 68)( 59, 65)( 60, 66)( 73, 75)( 74, 76)( 77, 83)( 78, 84)( 79, 81)( 80, 82)( 85, 99)( 86,100)( 87, 97)( 88, 98)( 89,107)( 90,108)( 91,105)( 92,106)( 93,103)( 94,104)( 95,101)( 96,102)(109,111)(110,112)(113,119)(114,120)(115,117)(116,118)(121,135)(122,136)(123,133)(124,134)(125,143)(126,144)(127,141)(128,142)(129,139)(130,140)(131,137)(132,138)(145,147)(146,148)(149,155)(150,156)(151,153)(152,154)(157,171)(158,172)(159,169)(160,170)(161,179)(162,180)(163,177)(164,178)(165,175)(166,176)(167,173)(168,174)(181,183)(182,184)(185,191)(186,192)(187,189)(188,190)(193,207)(194,208)(195,205)(196,206)(197,215)(198,216)(199,213)(200,214)(201,211)(202,212)(203,209)(204,210)(217,327)(218,328)(219,325)(220,326)(221,335)(222,336)(223,333)(224,334)(225,331)(226,332)(227,329)(228,330)(229,351)(230,352)(231,349)(232,350)(233,359)(234,360)(235,357)(236,358)(237,355)(238,356)(239,353)(240,354)(241,339)(242,340)(243,337)(244,338)(245,347)(246,348)(247,345)(248,346)(249,343)(250,344)(251,341)(252,342)(253,363)(254,364)(255,361)(256,362)(257,371)(258,372)(259,369)(260,370)(261,367)(262,368)(263,365)(264,366)(265,387)(266,388)(267,385)(268,386)(269,395)(270,396)(271,393)(272,394)(273,391)(274,392)(275,389)(276,390)(277,375)(278,376)(279,373)(280,374)(281,383)(282,384)(283,381)(284,382)(285,379)(286,380)(287,377)(288,378)(289,399)(290,400)(291,397)(292,398)(293,407)(294,408)(295,405)(296,406)(297,403)(298,404)(299,401)(300,402)(301,423)(302,424)(303,421)(304,422)(305,431)(306,432)(307,429)(308,430)(309,427)(310,428)(311,425)(312,426)(313,411)(314,412)(315,409)(316,410)(317,419)(318,420)(319,417)(320,418)(321,415)(322,416)(323,413)(324,414);
s1 := Sym(432)!(  1,229)(  2,230)(  3,232)(  4,231)(  5,233)(  6,234)(  7,236)(  8,235)(  9,237)( 10,238)( 11,240)( 12,239)( 13,217)( 14,218)( 15,220)( 16,219)( 17,221)( 18,222)( 19,224)( 20,223)( 21,225)( 22,226)( 23,228)( 24,227)( 25,241)( 26,242)( 27,244)( 28,243)( 29,245)( 30,246)( 31,248)( 32,247)( 33,249)( 34,250)( 35,252)( 36,251)( 37,301)( 38,302)( 39,304)( 40,303)( 41,305)( 42,306)( 43,308)( 44,307)( 45,309)( 46,310)( 47,312)( 48,311)( 49,289)( 50,290)( 51,292)( 52,291)( 53,293)( 54,294)( 55,296)( 56,295)( 57,297)( 58,298)( 59,300)( 60,299)( 61,313)( 62,314)( 63,316)( 64,315)( 65,317)( 66,318)( 67,320)( 68,319)( 69,321)( 70,322)( 71,324)( 72,323)( 73,265)( 74,266)( 75,268)( 76,267)( 77,269)( 78,270)( 79,272)( 80,271)( 81,273)( 82,274)( 83,276)( 84,275)( 85,253)( 86,254)( 87,256)( 88,255)( 89,257)( 90,258)( 91,260)( 92,259)( 93,261)( 94,262)( 95,264)( 96,263)( 97,277)( 98,278)( 99,280)(100,279)(101,281)(102,282)(103,284)(104,283)(105,285)(106,286)(107,288)(108,287)(109,337)(110,338)(111,340)(112,339)(113,341)(114,342)(115,344)(116,343)(117,345)(118,346)(119,348)(120,347)(121,325)(122,326)(123,328)(124,327)(125,329)(126,330)(127,332)(128,331)(129,333)(130,334)(131,336)(132,335)(133,349)(134,350)(135,352)(136,351)(137,353)(138,354)(139,356)(140,355)(141,357)(142,358)(143,360)(144,359)(145,409)(146,410)(147,412)(148,411)(149,413)(150,414)(151,416)(152,415)(153,417)(154,418)(155,420)(156,419)(157,397)(158,398)(159,400)(160,399)(161,401)(162,402)(163,404)(164,403)(165,405)(166,406)(167,408)(168,407)(169,421)(170,422)(171,424)(172,423)(173,425)(174,426)(175,428)(176,427)(177,429)(178,430)(179,432)(180,431)(181,373)(182,374)(183,376)(184,375)(185,377)(186,378)(187,380)(188,379)(189,381)(190,382)(191,384)(192,383)(193,361)(194,362)(195,364)(196,363)(197,365)(198,366)(199,368)(200,367)(201,369)(202,370)(203,372)(204,371)(205,385)(206,386)(207,388)(208,387)(209,389)(210,390)(211,392)(212,391)(213,393)(214,394)(215,396)(216,395);
s2 := Sym(432)!(  1, 37)(  2, 40)(  3, 39)(  4, 38)(  5, 41)(  6, 44)(  7, 43)(  8, 42)(  9, 45)( 10, 48)( 11, 47)( 12, 46)( 13, 69)( 14, 72)( 15, 71)( 16, 70)( 17, 61)( 18, 64)( 19, 63)( 20, 62)( 21, 65)( 22, 68)( 23, 67)( 24, 66)( 25, 53)( 26, 56)( 27, 55)( 28, 54)( 29, 57)( 30, 60)( 31, 59)( 32, 58)( 33, 49)( 34, 52)( 35, 51)( 36, 50)( 74, 76)( 78, 80)( 82, 84)( 85,105)( 86,108)( 87,107)( 88,106)( 89, 97)( 90,100)( 91, 99)( 92, 98)( 93,101)( 94,104)( 95,103)( 96,102)(109,145)(110,148)(111,147)(112,146)(113,149)(114,152)(115,151)(116,150)(117,153)(118,156)(119,155)(120,154)(121,177)(122,180)(123,179)(124,178)(125,169)(126,172)(127,171)(128,170)(129,173)(130,176)(131,175)(132,174)(133,161)(134,164)(135,163)(136,162)(137,165)(138,168)(139,167)(140,166)(141,157)(142,160)(143,159)(144,158)(182,184)(186,188)(190,192)(193,213)(194,216)(195,215)(196,214)(197,205)(198,208)(199,207)(200,206)(201,209)(202,212)(203,211)(204,210)(217,253)(218,256)(219,255)(220,254)(221,257)(222,260)(223,259)(224,258)(225,261)(226,264)(227,263)(228,262)(229,285)(230,288)(231,287)(232,286)(233,277)(234,280)(235,279)(236,278)(237,281)(238,284)(239,283)(240,282)(241,269)(242,272)(243,271)(244,270)(245,273)(246,276)(247,275)(248,274)(249,265)(250,268)(251,267)(252,266)(290,292)(294,296)(298,300)(301,321)(302,324)(303,323)(304,322)(305,313)(306,316)(307,315)(308,314)(309,317)(310,320)(311,319)(312,318)(325,361)(326,364)(327,363)(328,362)(329,365)(330,368)(331,367)(332,366)(333,369)(334,372)(335,371)(336,370)(337,393)(338,396)(339,395)(340,394)(341,385)(342,388)(343,387)(344,386)(345,389)(346,392)(347,391)(348,390)(349,377)(350,380)(351,379)(352,378)(353,381)(354,384)(355,383)(356,382)(357,373)(358,376)(359,375)(360,374)(398,400)(402,404)(406,408)(409,429)(410,432)(411,431)(412,430)(413,421)(414,424)(415,423)(416,422)(417,425)(418,428)(419,427)(420,426);
poly := sub<Sym(432)|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*s1*s2*s1*s2, 
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, 
s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*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*s0*s1 >;
References : None.
to this polytope

Twisty Puzzle