Polytope of Type {24,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,12}*1152r
if this polytope has a name.
Group : SmallGroup(1152,155801)
Rank : 3
Schlafli Type : {24,12}
Number of vertices, edges, etc : 48, 288, 24
Order of s0s1s2 : 24
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 : {12,12}*576e
   3-fold quotients : {24,4}*384d
   4-fold quotients : {6,12}*288b
   6-fold quotients : {12,4}*192b
   8-fold quotients : {12,6}*144b, {3,12}*144
   12-fold quotients : {12,4}*96b, {12,4}*96c, {6,4}*96
   16-fold quotients : {6,6}*72c
   24-fold quotients : {12,2}*48, {3,4}*48, {6,4}*48b, {6,4}*48c
   32-fold quotients : {3,6}*36
   48-fold quotients : {3,4}*24, {6,2}*24
   72-fold quotients : {4,2}*16
   96-fold quotients : {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=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2> of order 2.
      12 facets:
         12 of {24}*48
      32 vertex figures:
         16 of {12}*24
         16 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1> of order 2.
      12 facets:
         12 of {24}*48
      24 vertex figures:
         24 of {12}*24

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

Twisty Puzzle