Polytope of Type {6,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4}*768c
if this polytope has a name.
Group : SmallGroup(768,1088556)
Rank : 3
Schlafli Type : {6,4}
Number of vertices, edges, etc : 96, 192, 64
Order of s0s1s2 : 12
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 : {6,4}*384a
   4-fold quotients : {6,4}*192a
   8-fold quotients : {6,4}*96
   16-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   32-fold quotients : {3,4}*24, {6,2}*24
   64-fold quotients : {3,2}*12
   96-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=<s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 2.
      32 facets:
         32 of {6}*12
      52 vertex figures:
         44 of {4}*8
         8 of {2}*4
   P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2> of order 2.
      32 facets:
         32 of {6}*12
      48 vertex figures:
         48 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1> of order 2.
      40 facets:
         16 of {3}*6
         24 of {6}*12
      48 vertex figures:
         48 of {4}*8
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      32 facets:
         32 of {6}*12
      48 vertex figures:
         48 of {4}*8
   P/N, where N=<s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 2.
      32 facets:
         32 of {6}*12
      48 vertex figures:
         48 of {4}*8
   P/N, where N=<s0*s1*s0*s1> of order 3.
      24 facets:
         4 of {2}*4
         20 of {6}*12
      32 vertex figures:
         32 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2, s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2> of order 4.
      16 facets:
         16 of {6}*12
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s1*s0*s2*s1*s0*s1*s0*s1*s2*s1, s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s0> of order 4.
      24 facets:
         8 of {6}*12
         16 of {3}*6
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1, s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2> of order 4.
      20 facets:
         8 of {3}*6
         12 of {6}*12
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s2*s1*s0*s1*s2*s1*s0*s2*s1*s2, s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2> of order 4.
      16 facets:
         16 of {6}*12
      30 vertex figures:
         18 of {4}*8
         12 of {2}*4
   P/N, where N=<s2*s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1> of order 4.
      16 facets:
         16 of {6}*12
      26 vertex figures:
         22 of {4}*8
         4 of {2}*4
   P/N, where N=<s2*s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 4.
      16 facets:
         16 of {6}*12
      26 vertex figures:
         22 of {4}*8
         4 of {2}*4
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0, s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 4.
      16 facets:
         16 of {6}*12
      28 vertex figures:
         20 of {4}*8
         8 of {2}*4
   P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2, s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1> of order 4.
      16 facets:
         16 of {6}*12
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1, s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 4.
      16 facets:
         16 of {6}*12
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 4.
      16 facets:
         16 of {6}*12
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2, s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1> of order 4.
      16 facets:
         16 of {6}*12
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2, s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1> of order 4.
      16 facets:
         16 of {6}*12
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s0*s1*s0*s1, s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 6.
      12 facets:
         2 of {2}*4
         10 of {6}*12
      16 vertex figures:
         16 of {4}*8
   P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 6.
      12 facets:
         2 of {2}*4
         10 of {6}*12
      16 vertex figures:
         16 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0, s2*s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1> of order 8.
      8 facets:
         8 of {6}*12
      14 vertex figures:
         10 of {4}*8
         4 of {2}*4
   P/N, where N=<s0*s2*s1*s0*s1*s2*s1*s0*s2*s1, s1*s0*s2*s1*s0*s1*s0*s1*s2*s1> of order 8.
      12 facets:
         4 of {6}*12
         8 of {3}*6
      12 vertex figures:
         12 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1> of order 8.
      8 facets:
         8 of {6}*12
      12 vertex figures:
         12 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0, s1*s0*s2*s1*s0*s1*s0*s1*s2*s1> of order 8.
      12 facets:
         4 of {6}*12
         8 of {3}*6
      14 vertex figures:
         10 of {4}*8
         4 of {2}*4
   P/N, where N=<s0*s2*s1*s0*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s0*s1*s2*s1, s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s0> of order 8.
      14 facets:
         2 of {6}*12
         12 of {3}*6
      12 vertex figures:
         12 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2, s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2> of order 8.
      10 facets:
         4 of {3}*6
         6 of {6}*12
      12 vertex figures:
         12 of {4}*8
   P/N, where N=<s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2> of order 12.
      8 facets:
         4 of {2}*4
         4 of {6}*12
      8 vertex figures:
         8 of {4}*8
   P/N, where N=<s0*s1*s0*s1, s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 12.
      8 facets:
         4 of {2}*4
         4 of {6}*12
      10 vertex figures:
         6 of {4}*8
         4 of {2}*4
   P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s0*s1*s0*s1*s2> of order 24.
      6 facets:
         2 of {2}*4
         4 of {3}*6
      4 vertex figures:
         4 of {4}*8

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

Twisty Puzzle