Polytope of Type {12,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12}*1152t
if this polytope has a name.
Group : SmallGroup(1152,157851)
Rank : 3
Schlafli Type : {12,12}
Number of vertices, edges, etc : 48, 288, 48
Order of s0s1s2 : 6
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Dual
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 : {12,12}*576l
   4-fold quotients : {6,12}*288a, {12,6}*288a
   8-fold quotients : {6,12}*144d, {12,6}*144d
   12-fold quotients : {4,6}*96, {6,4}*96
   16-fold quotients : {6,6}*72a
   24-fold quotients : {3,4}*48, {4,3}*48, {4,6}*48b, {4,6}*48c, {6,4}*48b, {6,4}*48c
   48-fold quotients : {3,4}*24, {4,3}*24, {2,6}*24, {6,2}*24
   96-fold quotients : {2,3}*12, {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):
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1> of order 2.
      24 facets:
         24 of {12}*24
      32 vertex figures:
         16 of {12}*24
         16 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1> of order 2.
      32 facets:
         16 of {6}*12
         16 of {12}*24
      24 vertex figures:
         24 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1> of order 2.
      24 facets:
         24 of {12}*24
      24 vertex figures:
         24 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1> of order 2.
      24 facets:
         24 of {12}*24
      24 vertex figures:
         24 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1> of order 2.
      24 facets:
         24 of {12}*24
      24 vertex figures:
         24 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2> of order 2.
      24 facets:
         24 of {12}*24
      24 vertex figures:
         24 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1> of order 4.
      12 facets:
         12 of {12}*24
      16 vertex figures:
         8 of {12}*24
         8 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2> of order 4.
      16 facets:
         8 of {6}*12
         8 of {12}*24
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2> of order 4.
      16 facets:
         8 of {6}*12
         8 of {12}*24
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1> of order 4.
      16 facets:
         8 of {6}*12
         8 of {12}*24
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1> of order 4.
      16 facets:
         8 of {6}*12
         8 of {12}*24
      16 vertex figures:
         8 of {12}*24
         8 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 4.
      12 facets:
         12 of {12}*24
      16 vertex figures:
         8 of {12}*24
         8 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
      12 facets:
         12 of {12}*24
      16 vertex figures:
         8 of {12}*24
         8 of {6}*12

Permutation Representation (GAP) : 
s0 := (  1,  9)(  2, 10)(  3, 12)(  4, 11)(  5, 13)(  6, 14)(  7, 16)(  8, 15)( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 21, 29)( 22, 30)( 23, 32)( 24, 31)( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 49,105)( 50,106)( 51,108)( 52,107)( 53,109)( 54,110)( 55,112)( 56,111)( 57, 97)( 58, 98)( 59,100)( 60, 99)( 61,101)( 62,102)( 63,104)( 64,103)( 65,121)( 66,122)( 67,124)( 68,123)( 69,125)( 70,126)( 71,128)( 72,127)( 73,113)( 74,114)( 75,116)( 76,115)( 77,117)( 78,118)( 79,120)( 80,119)( 81,137)( 82,138)( 83,140)( 84,139)( 85,141)( 86,142)( 87,144)( 88,143)( 89,129)( 90,130)( 91,132)( 92,131)( 93,133)( 94,134)( 95,136)( 96,135)(145,153)(146,154)(147,156)(148,155)(149,157)(150,158)(151,160)(152,159)(161,169)(162,170)(163,172)(164,171)(165,173)(166,174)(167,176)(168,175)(177,185)(178,186)(179,188)(180,187)(181,189)(182,190)(183,192)(184,191)(193,249)(194,250)(195,252)(196,251)(197,253)(198,254)(199,256)(200,255)(201,241)(202,242)(203,244)(204,243)(205,245)(206,246)(207,248)(208,247)(209,265)(210,266)(211,268)(212,267)(213,269)(214,270)(215,272)(216,271)(217,257)(218,258)(219,260)(220,259)(221,261)(222,262)(223,264)(224,263)(225,281)(226,282)(227,284)(228,283)(229,285)(230,286)(231,288)(232,287)(233,273)(234,274)(235,276)(236,275)(237,277)(238,278)(239,280)(240,279);;
s1 := (  1, 49)(  2, 52)(  3, 51)(  4, 50)(  5, 53)(  6, 56)(  7, 55)(  8, 54)(  9, 61)( 10, 64)( 11, 63)( 12, 62)( 13, 57)( 14, 60)( 15, 59)( 16, 58)( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 85)( 22, 88)( 23, 87)( 24, 86)( 25, 93)( 26, 96)( 27, 95)( 28, 94)( 29, 89)( 30, 92)( 31, 91)( 32, 90)( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 37, 69)( 38, 72)( 39, 71)( 40, 70)( 41, 77)( 42, 80)( 43, 79)( 44, 78)( 45, 73)( 46, 76)( 47, 75)( 48, 74)( 98,100)(102,104)(105,109)(106,112)(107,111)(108,110)(113,129)(114,132)(115,131)(116,130)(117,133)(118,136)(119,135)(120,134)(121,141)(122,144)(123,143)(124,142)(125,137)(126,140)(127,139)(128,138)(145,193)(146,196)(147,195)(148,194)(149,197)(150,200)(151,199)(152,198)(153,205)(154,208)(155,207)(156,206)(157,201)(158,204)(159,203)(160,202)(161,225)(162,228)(163,227)(164,226)(165,229)(166,232)(167,231)(168,230)(169,237)(170,240)(171,239)(172,238)(173,233)(174,236)(175,235)(176,234)(177,209)(178,212)(179,211)(180,210)(181,213)(182,216)(183,215)(184,214)(185,221)(186,224)(187,223)(188,222)(189,217)(190,220)(191,219)(192,218)(242,244)(246,248)(249,253)(250,256)(251,255)(252,254)(257,273)(258,276)(259,275)(260,274)(261,277)(262,280)(263,279)(264,278)(265,285)(266,288)(267,287)(268,286)(269,281)(270,284)(271,283)(272,282);;
s2 := (  1,162)(  2,161)(  3,164)(  4,163)(  5,174)(  6,173)(  7,176)(  8,175)(  9,170)( 10,169)( 11,172)( 12,171)( 13,166)( 14,165)( 15,168)( 16,167)( 17,146)( 18,145)( 19,148)( 20,147)( 21,158)( 22,157)( 23,160)( 24,159)( 25,154)( 26,153)( 27,156)( 28,155)( 29,150)( 30,149)( 31,152)( 32,151)( 33,178)( 34,177)( 35,180)( 36,179)( 37,190)( 38,189)( 39,192)( 40,191)( 41,186)( 42,185)( 43,188)( 44,187)( 45,182)( 46,181)( 47,184)( 48,183)( 49,210)( 50,209)( 51,212)( 52,211)( 53,222)( 54,221)( 55,224)( 56,223)( 57,218)( 58,217)( 59,220)( 60,219)( 61,214)( 62,213)( 63,216)( 64,215)( 65,194)( 66,193)( 67,196)( 68,195)( 69,206)( 70,205)( 71,208)( 72,207)( 73,202)( 74,201)( 75,204)( 76,203)( 77,198)( 78,197)( 79,200)( 80,199)( 81,226)( 82,225)( 83,228)( 84,227)( 85,238)( 86,237)( 87,240)( 88,239)( 89,234)( 90,233)( 91,236)( 92,235)( 93,230)( 94,229)( 95,232)( 96,231)( 97,258)( 98,257)( 99,260)(100,259)(101,270)(102,269)(103,272)(104,271)(105,266)(106,265)(107,268)(108,267)(109,262)(110,261)(111,264)(112,263)(113,242)(114,241)(115,244)(116,243)(117,254)(118,253)(119,256)(120,255)(121,250)(122,249)(123,252)(124,251)(125,246)(126,245)(127,248)(128,247)(129,274)(130,273)(131,276)(132,275)(133,286)(134,285)(135,288)(136,287)(137,282)(138,281)(139,284)(140,283)(141,278)(142,277)(143,280)(144,279);;
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*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(288)!(  1,  9)(  2, 10)(  3, 12)(  4, 11)(  5, 13)(  6, 14)(  7, 16)(  8, 15)( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 21, 29)( 22, 30)( 23, 32)( 24, 31)( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 49,105)( 50,106)( 51,108)( 52,107)( 53,109)( 54,110)( 55,112)( 56,111)( 57, 97)( 58, 98)( 59,100)( 60, 99)( 61,101)( 62,102)( 63,104)( 64,103)( 65,121)( 66,122)( 67,124)( 68,123)( 69,125)( 70,126)( 71,128)( 72,127)( 73,113)( 74,114)( 75,116)( 76,115)( 77,117)( 78,118)( 79,120)( 80,119)( 81,137)( 82,138)( 83,140)( 84,139)( 85,141)( 86,142)( 87,144)( 88,143)( 89,129)( 90,130)( 91,132)( 92,131)( 93,133)( 94,134)( 95,136)( 96,135)(145,153)(146,154)(147,156)(148,155)(149,157)(150,158)(151,160)(152,159)(161,169)(162,170)(163,172)(164,171)(165,173)(166,174)(167,176)(168,175)(177,185)(178,186)(179,188)(180,187)(181,189)(182,190)(183,192)(184,191)(193,249)(194,250)(195,252)(196,251)(197,253)(198,254)(199,256)(200,255)(201,241)(202,242)(203,244)(204,243)(205,245)(206,246)(207,248)(208,247)(209,265)(210,266)(211,268)(212,267)(213,269)(214,270)(215,272)(216,271)(217,257)(218,258)(219,260)(220,259)(221,261)(222,262)(223,264)(224,263)(225,281)(226,282)(227,284)(228,283)(229,285)(230,286)(231,288)(232,287)(233,273)(234,274)(235,276)(236,275)(237,277)(238,278)(239,280)(240,279);
s1 := Sym(288)!(  1, 49)(  2, 52)(  3, 51)(  4, 50)(  5, 53)(  6, 56)(  7, 55)(  8, 54)(  9, 61)( 10, 64)( 11, 63)( 12, 62)( 13, 57)( 14, 60)( 15, 59)( 16, 58)( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 85)( 22, 88)( 23, 87)( 24, 86)( 25, 93)( 26, 96)( 27, 95)( 28, 94)( 29, 89)( 30, 92)( 31, 91)( 32, 90)( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 37, 69)( 38, 72)( 39, 71)( 40, 70)( 41, 77)( 42, 80)( 43, 79)( 44, 78)( 45, 73)( 46, 76)( 47, 75)( 48, 74)( 98,100)(102,104)(105,109)(106,112)(107,111)(108,110)(113,129)(114,132)(115,131)(116,130)(117,133)(118,136)(119,135)(120,134)(121,141)(122,144)(123,143)(124,142)(125,137)(126,140)(127,139)(128,138)(145,193)(146,196)(147,195)(148,194)(149,197)(150,200)(151,199)(152,198)(153,205)(154,208)(155,207)(156,206)(157,201)(158,204)(159,203)(160,202)(161,225)(162,228)(163,227)(164,226)(165,229)(166,232)(167,231)(168,230)(169,237)(170,240)(171,239)(172,238)(173,233)(174,236)(175,235)(176,234)(177,209)(178,212)(179,211)(180,210)(181,213)(182,216)(183,215)(184,214)(185,221)(186,224)(187,223)(188,222)(189,217)(190,220)(191,219)(192,218)(242,244)(246,248)(249,253)(250,256)(251,255)(252,254)(257,273)(258,276)(259,275)(260,274)(261,277)(262,280)(263,279)(264,278)(265,285)(266,288)(267,287)(268,286)(269,281)(270,284)(271,283)(272,282);
s2 := Sym(288)!(  1,162)(  2,161)(  3,164)(  4,163)(  5,174)(  6,173)(  7,176)(  8,175)(  9,170)( 10,169)( 11,172)( 12,171)( 13,166)( 14,165)( 15,168)( 16,167)( 17,146)( 18,145)( 19,148)( 20,147)( 21,158)( 22,157)( 23,160)( 24,159)( 25,154)( 26,153)( 27,156)( 28,155)( 29,150)( 30,149)( 31,152)( 32,151)( 33,178)( 34,177)( 35,180)( 36,179)( 37,190)( 38,189)( 39,192)( 40,191)( 41,186)( 42,185)( 43,188)( 44,187)( 45,182)( 46,181)( 47,184)( 48,183)( 49,210)( 50,209)( 51,212)( 52,211)( 53,222)( 54,221)( 55,224)( 56,223)( 57,218)( 58,217)( 59,220)( 60,219)( 61,214)( 62,213)( 63,216)( 64,215)( 65,194)( 66,193)( 67,196)( 68,195)( 69,206)( 70,205)( 71,208)( 72,207)( 73,202)( 74,201)( 75,204)( 76,203)( 77,198)( 78,197)( 79,200)( 80,199)( 81,226)( 82,225)( 83,228)( 84,227)( 85,238)( 86,237)( 87,240)( 88,239)( 89,234)( 90,233)( 91,236)( 92,235)( 93,230)( 94,229)( 95,232)( 96,231)( 97,258)( 98,257)( 99,260)(100,259)(101,270)(102,269)(103,272)(104,271)(105,266)(106,265)(107,268)(108,267)(109,262)(110,261)(111,264)(112,263)(113,242)(114,241)(115,244)(116,243)(117,254)(118,253)(119,256)(120,255)(121,250)(122,249)(123,252)(124,251)(125,246)(126,245)(127,248)(128,247)(129,274)(130,273)(131,276)(132,275)(133,286)(134,285)(135,288)(136,287)(137,282)(138,281)(139,284)(140,283)(141,278)(142,277)(143,280)(144,279);
poly := sub<Sym(288)|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*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*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 >;
References : None.
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