Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,6}

Atlas Canonical Name {12,6}*1152a

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1152,155788)
Rank
3
Schläfli Type
{12,6}
Vertices, edges, …
96, 288, 48
Order of s0s1s2
24
Order of s0s1s2s1
12
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

32-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*s1)^2*(s2*s1)^2*s0*s2*s1*s0> of order 2

24 facets

56 vertex figures

P/N, where N=<(s0*s1)^4> of order 3

20 facets

32 vertex figures

P/N, where N=<s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 3

16 facets

48 vertex figures

Representations

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