Polytope of Type {8,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*576a
if this polytope has a name.
Group : SmallGroup(576,5307)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 24, 144, 36
Order of s0s1s2 : 8
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {8,12,2} of size 1152
Vertex Figure Of :
   {2,8,12} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,6}*288, {4,12}*288
   4-fold quotients : {4,6}*144
   8-fold quotients : {4,6}*72
   9-fold quotients : {8,4}*64a
   18-fold quotients : {4,4}*32, {8,2}*32
   36-fold quotients : {2,4}*16, {4,2}*16
   72-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,12}*1152a, {8,24}*1152b, {8,24}*1152c, {16,12}*1152a, {16,12}*1152b
   3-fold covers : {8,12}*1728a, {24,12}*1728g, {24,12}*1728h, {8,12}*1728g, {24,12}*1728s, {24,12}*1728u
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s2*s1*s2*s1*s0*s2> of order 3.
      12 facets:
         12 of {8}*16
      16 vertex figures:
         4 of {12}*24
         12 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2> of order 3.
      12 facets:
         12 of {8}*16
      8 vertex figures:
         8 of {12}*24

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

Twisty Puzzle