Part of the Atlas of Small Regular Polytopes

Polytope of Type {24,6}

Atlas Canonical Name {24,6}*1152h

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1152,155812)
Rank
3
Schläfli Type
{24,6}
Vertices, edges, …
96, 288, 24
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

12 facets

48 vertex figures

P/N, where N=<(s0*s1)^8*s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2> of order 2

12 facets

48 vertex figures

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

12 facets

48 vertex figures

P/N, where N=<(s1*s2)^2> of order 3

8 facets

48 vertex figures

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

6 facets

24 vertex figures

P/N, where N=<s0*(s2*s1)^2*s0*(s1*s2)^2, (s0*s1)^10*s0*s2*s1*s0*s1*s2> of order 4

6 facets

24 vertex figures

P/N, where N=<s0*(s2*s1)^2*s0*(s1*s2)^2, (s0*s1)^10*(s0*s2*s1)^2*s2> of order 4

6 facets

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

References

None.

to this polytope.

Twisty Puzzle