Polytope of Type {6,44}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,44}*1056
if this polytope has a name.
Group : SmallGroup(1056,1015)
Rank : 3
Schlafli Type : {6,44}
Number of vertices, edges, etc : 12, 264, 88
Order of s0s1s2 : 66
Order of s0s1s2s1 : 4
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 : {6,44}*528b
   4-fold quotients : {6,22}*264
   11-fold quotients : {6,4}*96
   12-fold quotients : {2,22}*88
   22-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   24-fold quotients : {2,11}*44
   44-fold quotients : {3,4}*24, {6,2}*24
   88-fold quotients : {3,2}*12
   132-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*s2*s1*s0*s1*s2*s1> of order 2.
      44 facets:
         44 of {6}*12
      8 vertex figures:
         4 of {44}*88
         4 of {22}*44
   P/N, where N=<s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      44 facets:
         44 of {6}*12
      6 vertex figures:
         6 of {44}*88

Permutation Representation (GAP) : 
s0 := (  3,  4)(  7,  8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)( 31, 32)( 35, 36)( 39, 40)( 43, 44)( 45, 89)( 46, 90)( 47, 92)( 48, 91)( 49, 93)( 50, 94)( 51, 96)( 52, 95)( 53, 97)( 54, 98)( 55,100)( 56, 99)( 57,101)( 58,102)( 59,104)( 60,103)( 61,105)( 62,106)( 63,108)( 64,107)( 65,109)( 66,110)( 67,112)( 68,111)( 69,113)( 70,114)( 71,116)( 72,115)( 73,117)( 74,118)( 75,120)( 76,119)( 77,121)( 78,122)( 79,124)( 80,123)( 81,125)( 82,126)( 83,128)( 84,127)( 85,129)( 86,130)( 87,132)( 88,131)(135,136)(139,140)(143,144)(147,148)(151,152)(155,156)(159,160)(163,164)(167,168)(171,172)(175,176)(177,221)(178,222)(179,224)(180,223)(181,225)(182,226)(183,228)(184,227)(185,229)(186,230)(187,232)(188,231)(189,233)(190,234)(191,236)(192,235)(193,237)(194,238)(195,240)(196,239)(197,241)(198,242)(199,244)(200,243)(201,245)(202,246)(203,248)(204,247)(205,249)(206,250)(207,252)(208,251)(209,253)(210,254)(211,256)(212,255)(213,257)(214,258)(215,260)(216,259)(217,261)(218,262)(219,264)(220,263);;
s1 := (  1, 45)(  2, 48)(  3, 47)(  4, 46)(  5, 85)(  6, 88)(  7, 87)(  8, 86)(  9, 81)( 10, 84)( 11, 83)( 12, 82)( 13, 77)( 14, 80)( 15, 79)( 16, 78)( 17, 73)( 18, 76)( 19, 75)( 20, 74)( 21, 69)( 22, 72)( 23, 71)( 24, 70)( 25, 65)( 26, 68)( 27, 67)( 28, 66)( 29, 61)( 30, 64)( 31, 63)( 32, 62)( 33, 57)( 34, 60)( 35, 59)( 36, 58)( 37, 53)( 38, 56)( 39, 55)( 40, 54)( 41, 49)( 42, 52)( 43, 51)( 44, 50)( 90, 92)( 93,129)( 94,132)( 95,131)( 96,130)( 97,125)( 98,128)( 99,127)(100,126)(101,121)(102,124)(103,123)(104,122)(105,117)(106,120)(107,119)(108,118)(109,113)(110,116)(111,115)(112,114)(133,177)(134,180)(135,179)(136,178)(137,217)(138,220)(139,219)(140,218)(141,213)(142,216)(143,215)(144,214)(145,209)(146,212)(147,211)(148,210)(149,205)(150,208)(151,207)(152,206)(153,201)(154,204)(155,203)(156,202)(157,197)(158,200)(159,199)(160,198)(161,193)(162,196)(163,195)(164,194)(165,189)(166,192)(167,191)(168,190)(169,185)(170,188)(171,187)(172,186)(173,181)(174,184)(175,183)(176,182)(222,224)(225,261)(226,264)(227,263)(228,262)(229,257)(230,260)(231,259)(232,258)(233,253)(234,256)(235,255)(236,254)(237,249)(238,252)(239,251)(240,250)(241,245)(242,248)(243,247)(244,246);;
s2 := (  1,138)(  2,137)(  3,140)(  4,139)(  5,134)(  6,133)(  7,136)(  8,135)(  9,174)( 10,173)( 11,176)( 12,175)( 13,170)( 14,169)( 15,172)( 16,171)( 17,166)( 18,165)( 19,168)( 20,167)( 21,162)( 22,161)( 23,164)( 24,163)( 25,158)( 26,157)( 27,160)( 28,159)( 29,154)( 30,153)( 31,156)( 32,155)( 33,150)( 34,149)( 35,152)( 36,151)( 37,146)( 38,145)( 39,148)( 40,147)( 41,142)( 42,141)( 43,144)( 44,143)( 45,182)( 46,181)( 47,184)( 48,183)( 49,178)( 50,177)( 51,180)( 52,179)( 53,218)( 54,217)( 55,220)( 56,219)( 57,214)( 58,213)( 59,216)( 60,215)( 61,210)( 62,209)( 63,212)( 64,211)( 65,206)( 66,205)( 67,208)( 68,207)( 69,202)( 70,201)( 71,204)( 72,203)( 73,198)( 74,197)( 75,200)( 76,199)( 77,194)( 78,193)( 79,196)( 80,195)( 81,190)( 82,189)( 83,192)( 84,191)( 85,186)( 86,185)( 87,188)( 88,187)( 89,226)( 90,225)( 91,228)( 92,227)( 93,222)( 94,221)( 95,224)( 96,223)( 97,262)( 98,261)( 99,264)(100,263)(101,258)(102,257)(103,260)(104,259)(105,254)(106,253)(107,256)(108,255)(109,250)(110,249)(111,252)(112,251)(113,246)(114,245)(115,248)(116,247)(117,242)(118,241)(119,244)(120,243)(121,238)(122,237)(123,240)(124,239)(125,234)(126,233)(127,236)(128,235)(129,230)(130,229)(131,232)(132,231);;
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*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*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*s0*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(264)!(  3,  4)(  7,  8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)( 31, 32)( 35, 36)( 39, 40)( 43, 44)( 45, 89)( 46, 90)( 47, 92)( 48, 91)( 49, 93)( 50, 94)( 51, 96)( 52, 95)( 53, 97)( 54, 98)( 55,100)( 56, 99)( 57,101)( 58,102)( 59,104)( 60,103)( 61,105)( 62,106)( 63,108)( 64,107)( 65,109)( 66,110)( 67,112)( 68,111)( 69,113)( 70,114)( 71,116)( 72,115)( 73,117)( 74,118)( 75,120)( 76,119)( 77,121)( 78,122)( 79,124)( 80,123)( 81,125)( 82,126)( 83,128)( 84,127)( 85,129)( 86,130)( 87,132)( 88,131)(135,136)(139,140)(143,144)(147,148)(151,152)(155,156)(159,160)(163,164)(167,168)(171,172)(175,176)(177,221)(178,222)(179,224)(180,223)(181,225)(182,226)(183,228)(184,227)(185,229)(186,230)(187,232)(188,231)(189,233)(190,234)(191,236)(192,235)(193,237)(194,238)(195,240)(196,239)(197,241)(198,242)(199,244)(200,243)(201,245)(202,246)(203,248)(204,247)(205,249)(206,250)(207,252)(208,251)(209,253)(210,254)(211,256)(212,255)(213,257)(214,258)(215,260)(216,259)(217,261)(218,262)(219,264)(220,263);
s1 := Sym(264)!(  1, 45)(  2, 48)(  3, 47)(  4, 46)(  5, 85)(  6, 88)(  7, 87)(  8, 86)(  9, 81)( 10, 84)( 11, 83)( 12, 82)( 13, 77)( 14, 80)( 15, 79)( 16, 78)( 17, 73)( 18, 76)( 19, 75)( 20, 74)( 21, 69)( 22, 72)( 23, 71)( 24, 70)( 25, 65)( 26, 68)( 27, 67)( 28, 66)( 29, 61)( 30, 64)( 31, 63)( 32, 62)( 33, 57)( 34, 60)( 35, 59)( 36, 58)( 37, 53)( 38, 56)( 39, 55)( 40, 54)( 41, 49)( 42, 52)( 43, 51)( 44, 50)( 90, 92)( 93,129)( 94,132)( 95,131)( 96,130)( 97,125)( 98,128)( 99,127)(100,126)(101,121)(102,124)(103,123)(104,122)(105,117)(106,120)(107,119)(108,118)(109,113)(110,116)(111,115)(112,114)(133,177)(134,180)(135,179)(136,178)(137,217)(138,220)(139,219)(140,218)(141,213)(142,216)(143,215)(144,214)(145,209)(146,212)(147,211)(148,210)(149,205)(150,208)(151,207)(152,206)(153,201)(154,204)(155,203)(156,202)(157,197)(158,200)(159,199)(160,198)(161,193)(162,196)(163,195)(164,194)(165,189)(166,192)(167,191)(168,190)(169,185)(170,188)(171,187)(172,186)(173,181)(174,184)(175,183)(176,182)(222,224)(225,261)(226,264)(227,263)(228,262)(229,257)(230,260)(231,259)(232,258)(233,253)(234,256)(235,255)(236,254)(237,249)(238,252)(239,251)(240,250)(241,245)(242,248)(243,247)(244,246);
s2 := Sym(264)!(  1,138)(  2,137)(  3,140)(  4,139)(  5,134)(  6,133)(  7,136)(  8,135)(  9,174)( 10,173)( 11,176)( 12,175)( 13,170)( 14,169)( 15,172)( 16,171)( 17,166)( 18,165)( 19,168)( 20,167)( 21,162)( 22,161)( 23,164)( 24,163)( 25,158)( 26,157)( 27,160)( 28,159)( 29,154)( 30,153)( 31,156)( 32,155)( 33,150)( 34,149)( 35,152)( 36,151)( 37,146)( 38,145)( 39,148)( 40,147)( 41,142)( 42,141)( 43,144)( 44,143)( 45,182)( 46,181)( 47,184)( 48,183)( 49,178)( 50,177)( 51,180)( 52,179)( 53,218)( 54,217)( 55,220)( 56,219)( 57,214)( 58,213)( 59,216)( 60,215)( 61,210)( 62,209)( 63,212)( 64,211)( 65,206)( 66,205)( 67,208)( 68,207)( 69,202)( 70,201)( 71,204)( 72,203)( 73,198)( 74,197)( 75,200)( 76,199)( 77,194)( 78,193)( 79,196)( 80,195)( 81,190)( 82,189)( 83,192)( 84,191)( 85,186)( 86,185)( 87,188)( 88,187)( 89,226)( 90,225)( 91,228)( 92,227)( 93,222)( 94,221)( 95,224)( 96,223)( 97,262)( 98,261)( 99,264)(100,263)(101,258)(102,257)(103,260)(104,259)(105,254)(106,253)(107,256)(108,255)(109,250)(110,249)(111,252)(112,251)(113,246)(114,245)(115,248)(116,247)(117,242)(118,241)(119,244)(120,243)(121,238)(122,237)(123,240)(124,239)(125,234)(126,233)(127,236)(128,235)(129,230)(130,229)(131,232)(132,231);
poly := sub<Sym(264)|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*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*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*s0*s1*s2*s0*s1*s2*s1 >;
References : None.
to this polytope

Twisty Puzzle