Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,24}

Atlas Canonical Name {12,24}*1152o

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1152,155800)
Rank
3
Schläfli Type
{12,24}
Vertices, edges, …
24, 288, 48
Order of s0s1s2
24
Order of s0s1s2s1
4
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

2-fold

3-fold

4-fold

6-fold

8-fold

12-fold

16-fold

24-fold

36-fold

48-fold

72-fold

96-fold

144-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s0*(s2*s1)^2*s0*(s1*s2)^2> of order 2

32 facets

12 vertex figures

P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2> of order 2

24 facets

12 vertex figures

P/N, where N=<s0*s1*s0*(s2*s1)^4*s0*(s2*s1)^7*s2> of order 2

24 facets

12 vertex figures

Representations

Permutation Representation (GAP) 
s0 := (  1,  3)(  2,  4)(  5, 11)(  6, 12)(  7,  9)(  8, 10)( 13, 15)( 14, 16)( 17, 23)( 18, 24)( 19, 21)( 20, 22)( 25, 27)( 26, 28)( 29, 35)( 30, 36)( 31, 33)( 32, 34)( 37, 39)( 38, 40)( 41, 47)( 42, 48)( 43, 45)( 44, 46)( 49, 51)( 50, 52)( 53, 59)( 54, 60)( 55, 57)( 56, 58)( 61, 63)( 62, 64)( 65, 71)( 66, 72)( 67, 69)( 68, 70)( 73, 75)( 74, 76)( 77, 83)( 78, 84)( 79, 81)( 80, 82)( 85, 87)( 86, 88)( 89, 95)( 90, 96)( 91, 93)( 92, 94)( 97, 99)( 98,100)(101,107)(102,108)(103,105)(104,106)(109,111)(110,112)(113,119)(114,120)(115,117)(116,118)(121,123)(122,124)(125,131)(126,132)(127,129)(128,130)(133,135)(134,136)(137,143)(138,144)(139,141)(140,142)(145,147)(146,148)(149,155)(150,156)(151,153)(152,154)(157,159)(158,160)(161,167)(162,168)(163,165)(164,166)(169,171)(170,172)(173,179)(174,180)(175,177)(176,178)(181,183)(182,184)(185,191)(186,192)(187,189)(188,190)(193,195)(194,196)(197,203)(198,204)(199,201)(200,202)(205,207)(206,208)(209,215)(210,216)(211,213)(212,214)(217,219)(218,220)(221,227)(222,228)(223,225)(224,226)(229,231)(230,232)(233,239)(234,240)(235,237)(236,238)(241,243)(242,244)(245,251)(246,252)(247,249)(248,250)(253,255)(254,256)(257,263)(258,264)(259,261)(260,262)(265,267)(266,268)(269,275)(270,276)(271,273)(272,274)(277,279)(278,280)(281,287)(282,288)(283,285)(284,286);;
s1 := (  1,  5)(  2,  6)(  3,  8)(  4,  7)( 11, 12)( 13, 29)( 14, 30)( 15, 32)( 16, 31)( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 37, 41)( 38, 42)( 39, 44)( 40, 43)( 47, 48)( 49, 65)( 50, 66)( 51, 68)( 52, 67)( 53, 61)( 54, 62)( 55, 64)( 56, 63)( 57, 69)( 58, 70)( 59, 72)( 60, 71)( 73,113)( 74,114)( 75,116)( 76,115)( 77,109)( 78,110)( 79,112)( 80,111)( 81,117)( 82,118)( 83,120)( 84,119)( 85,137)( 86,138)( 87,140)( 88,139)( 89,133)( 90,134)( 91,136)( 92,135)( 93,141)( 94,142)( 95,144)( 96,143)( 97,125)( 98,126)( 99,128)(100,127)(101,121)(102,122)(103,124)(104,123)(105,129)(106,130)(107,132)(108,131)(145,221)(146,222)(147,224)(148,223)(149,217)(150,218)(151,220)(152,219)(153,225)(154,226)(155,228)(156,227)(157,245)(158,246)(159,248)(160,247)(161,241)(162,242)(163,244)(164,243)(165,249)(166,250)(167,252)(168,251)(169,233)(170,234)(171,236)(172,235)(173,229)(174,230)(175,232)(176,231)(177,237)(178,238)(179,240)(180,239)(181,257)(182,258)(183,260)(184,259)(185,253)(186,254)(187,256)(188,255)(189,261)(190,262)(191,264)(192,263)(193,281)(194,282)(195,284)(196,283)(197,277)(198,278)(199,280)(200,279)(201,285)(202,286)(203,288)(204,287)(205,269)(206,270)(207,272)(208,271)(209,265)(210,266)(211,268)(212,267)(213,273)(214,274)(215,276)(216,275);;
s2 := (  1,157)(  2,160)(  3,159)(  4,158)(  5,161)(  6,164)(  7,163)(  8,162)(  9,165)( 10,168)( 11,167)( 12,166)( 13,145)( 14,148)( 15,147)( 16,146)( 17,149)( 18,152)( 19,151)( 20,150)( 21,153)( 22,156)( 23,155)( 24,154)( 25,169)( 26,172)( 27,171)( 28,170)( 29,173)( 30,176)( 31,175)( 32,174)( 33,177)( 34,180)( 35,179)( 36,178)( 37,193)( 38,196)( 39,195)( 40,194)( 41,197)( 42,200)( 43,199)( 44,198)( 45,201)( 46,204)( 47,203)( 48,202)( 49,181)( 50,184)( 51,183)( 52,182)( 53,185)( 54,188)( 55,187)( 56,186)( 57,189)( 58,192)( 59,191)( 60,190)( 61,205)( 62,208)( 63,207)( 64,206)( 65,209)( 66,212)( 67,211)( 68,210)( 69,213)( 70,216)( 71,215)( 72,214)( 73,265)( 74,268)( 75,267)( 76,266)( 77,269)( 78,272)( 79,271)( 80,270)( 81,273)( 82,276)( 83,275)( 84,274)( 85,253)( 86,256)( 87,255)( 88,254)( 89,257)( 90,260)( 91,259)( 92,258)( 93,261)( 94,264)( 95,263)( 96,262)( 97,277)( 98,280)( 99,279)(100,278)(101,281)(102,284)(103,283)(104,282)(105,285)(106,288)(107,287)(108,286)(109,229)(110,232)(111,231)(112,230)(113,233)(114,236)(115,235)(116,234)(117,237)(118,240)(119,239)(120,238)(121,217)(122,220)(123,219)(124,218)(125,221)(126,224)(127,223)(128,222)(129,225)(130,228)(131,227)(132,226)(133,241)(134,244)(135,243)(136,242)(137,245)(138,248)(139,247)(140,246)(141,249)(142,252)(143,251)(144,250);;
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, 
s0*s1*s0*s1*s0*s1*s2*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, 
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(288)!(  1,  3)(  2,  4)(  5, 11)(  6, 12)(  7,  9)(  8, 10)( 13, 15)( 14, 16)( 17, 23)( 18, 24)( 19, 21)( 20, 22)( 25, 27)( 26, 28)( 29, 35)( 30, 36)( 31, 33)( 32, 34)( 37, 39)( 38, 40)( 41, 47)( 42, 48)( 43, 45)( 44, 46)( 49, 51)( 50, 52)( 53, 59)( 54, 60)( 55, 57)( 56, 58)( 61, 63)( 62, 64)( 65, 71)( 66, 72)( 67, 69)( 68, 70)( 73, 75)( 74, 76)( 77, 83)( 78, 84)( 79, 81)( 80, 82)( 85, 87)( 86, 88)( 89, 95)( 90, 96)( 91, 93)( 92, 94)( 97, 99)( 98,100)(101,107)(102,108)(103,105)(104,106)(109,111)(110,112)(113,119)(114,120)(115,117)(116,118)(121,123)(122,124)(125,131)(126,132)(127,129)(128,130)(133,135)(134,136)(137,143)(138,144)(139,141)(140,142)(145,147)(146,148)(149,155)(150,156)(151,153)(152,154)(157,159)(158,160)(161,167)(162,168)(163,165)(164,166)(169,171)(170,172)(173,179)(174,180)(175,177)(176,178)(181,183)(182,184)(185,191)(186,192)(187,189)(188,190)(193,195)(194,196)(197,203)(198,204)(199,201)(200,202)(205,207)(206,208)(209,215)(210,216)(211,213)(212,214)(217,219)(218,220)(221,227)(222,228)(223,225)(224,226)(229,231)(230,232)(233,239)(234,240)(235,237)(236,238)(241,243)(242,244)(245,251)(246,252)(247,249)(248,250)(253,255)(254,256)(257,263)(258,264)(259,261)(260,262)(265,267)(266,268)(269,275)(270,276)(271,273)(272,274)(277,279)(278,280)(281,287)(282,288)(283,285)(284,286);
s1 := Sym(288)!(  1,  5)(  2,  6)(  3,  8)(  4,  7)( 11, 12)( 13, 29)( 14, 30)( 15, 32)( 16, 31)( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 37, 41)( 38, 42)( 39, 44)( 40, 43)( 47, 48)( 49, 65)( 50, 66)( 51, 68)( 52, 67)( 53, 61)( 54, 62)( 55, 64)( 56, 63)( 57, 69)( 58, 70)( 59, 72)( 60, 71)( 73,113)( 74,114)( 75,116)( 76,115)( 77,109)( 78,110)( 79,112)( 80,111)( 81,117)( 82,118)( 83,120)( 84,119)( 85,137)( 86,138)( 87,140)( 88,139)( 89,133)( 90,134)( 91,136)( 92,135)( 93,141)( 94,142)( 95,144)( 96,143)( 97,125)( 98,126)( 99,128)(100,127)(101,121)(102,122)(103,124)(104,123)(105,129)(106,130)(107,132)(108,131)(145,221)(146,222)(147,224)(148,223)(149,217)(150,218)(151,220)(152,219)(153,225)(154,226)(155,228)(156,227)(157,245)(158,246)(159,248)(160,247)(161,241)(162,242)(163,244)(164,243)(165,249)(166,250)(167,252)(168,251)(169,233)(170,234)(171,236)(172,235)(173,229)(174,230)(175,232)(176,231)(177,237)(178,238)(179,240)(180,239)(181,257)(182,258)(183,260)(184,259)(185,253)(186,254)(187,256)(188,255)(189,261)(190,262)(191,264)(192,263)(193,281)(194,282)(195,284)(196,283)(197,277)(198,278)(199,280)(200,279)(201,285)(202,286)(203,288)(204,287)(205,269)(206,270)(207,272)(208,271)(209,265)(210,266)(211,268)(212,267)(213,273)(214,274)(215,276)(216,275);
s2 := Sym(288)!(  1,157)(  2,160)(  3,159)(  4,158)(  5,161)(  6,164)(  7,163)(  8,162)(  9,165)( 10,168)( 11,167)( 12,166)( 13,145)( 14,148)( 15,147)( 16,146)( 17,149)( 18,152)( 19,151)( 20,150)( 21,153)( 22,156)( 23,155)( 24,154)( 25,169)( 26,172)( 27,171)( 28,170)( 29,173)( 30,176)( 31,175)( 32,174)( 33,177)( 34,180)( 35,179)( 36,178)( 37,193)( 38,196)( 39,195)( 40,194)( 41,197)( 42,200)( 43,199)( 44,198)( 45,201)( 46,204)( 47,203)( 48,202)( 49,181)( 50,184)( 51,183)( 52,182)( 53,185)( 54,188)( 55,187)( 56,186)( 57,189)( 58,192)( 59,191)( 60,190)( 61,205)( 62,208)( 63,207)( 64,206)( 65,209)( 66,212)( 67,211)( 68,210)( 69,213)( 70,216)( 71,215)( 72,214)( 73,265)( 74,268)( 75,267)( 76,266)( 77,269)( 78,272)( 79,271)( 80,270)( 81,273)( 82,276)( 83,275)( 84,274)( 85,253)( 86,256)( 87,255)( 88,254)( 89,257)( 90,260)( 91,259)( 92,258)( 93,261)( 94,264)( 95,263)( 96,262)( 97,277)( 98,280)( 99,279)(100,278)(101,281)(102,284)(103,283)(104,282)(105,285)(106,288)(107,287)(108,286)(109,229)(110,232)(111,231)(112,230)(113,233)(114,236)(115,235)(116,234)(117,237)(118,240)(119,239)(120,238)(121,217)(122,220)(123,219)(124,218)(125,221)(126,224)(127,223)(128,222)(129,225)(130,228)(131,227)(132,226)(133,241)(134,244)(135,243)(136,242)(137,245)(138,248)(139,247)(140,246)(141,249)(142,252)(143,251)(144,250);
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, 
s0*s1*s0*s1*s0*s1*s2*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, 
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References

None.

to this polytope.

Twisty Puzzle