Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,12}

Atlas Canonical Name {12,12}*768b

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(768,1087743)
Rank
3
Schläfli Type
{12,12}
Vertices, edges, …
32, 192, 32
Order of s0s1s2
4
Order of s0s1s2s1
12
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable
  • Self-Dual

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

12-fold

16-fold

24-fold

32-fold

48-fold

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

16 facets

16 vertex figures

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

16 facets

24 vertex figures

P/N, where N=<(s0*s1)^6> of order 2

24 facets

16 vertex figures

Representations

Permutation Representation (GAP) 
s0 := (  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 15, 16)( 17, 21)( 18, 22)( 19, 24)( 20, 23)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)( 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, 85)( 74, 86)( 75, 88)( 76, 87)( 77, 93)( 78, 94)( 79, 96)( 80, 95)( 81, 89)( 82, 90)( 83, 92)( 84, 91)( 97,121)( 98,122)( 99,124)(100,123)(101,129)(102,130)(103,132)(104,131)(105,125)(106,126)(107,128)(108,127)(109,133)(110,134)(111,136)(112,135)(113,141)(114,142)(115,144)(116,143)(117,137)(118,138)(119,140)(120,139)(145,181)(146,182)(147,184)(148,183)(149,189)(150,190)(151,192)(152,191)(153,185)(154,186)(155,188)(156,187)(157,169)(158,170)(159,172)(160,171)(161,177)(162,178)(163,180)(164,179)(165,173)(166,174)(167,176)(168,175);;
s1 := (  1,129)(  2,131)(  3,130)(  4,132)(  5,125)(  6,127)(  7,126)(  8,128)(  9,121)( 10,123)( 11,122)( 12,124)( 13,141)( 14,143)( 15,142)( 16,144)( 17,137)( 18,139)( 19,138)( 20,140)( 21,133)( 22,135)( 23,134)( 24,136)( 25,105)( 26,107)( 27,106)( 28,108)( 29,101)( 30,103)( 31,102)( 32,104)( 33, 97)( 34, 99)( 35, 98)( 36,100)( 37,117)( 38,119)( 39,118)( 40,120)( 41,113)( 42,115)( 43,114)( 44,116)( 45,109)( 46,111)( 47,110)( 48,112)( 49,177)( 50,179)( 51,178)( 52,180)( 53,173)( 54,175)( 55,174)( 56,176)( 57,169)( 58,171)( 59,170)( 60,172)( 61,189)( 62,191)( 63,190)( 64,192)( 65,185)( 66,187)( 67,186)( 68,188)( 69,181)( 70,183)( 71,182)( 72,184)( 73,153)( 74,155)( 75,154)( 76,156)( 77,149)( 78,151)( 79,150)( 80,152)( 81,145)( 82,147)( 83,146)( 84,148)( 85,165)( 86,167)( 87,166)( 88,168)( 89,161)( 90,163)( 91,162)( 92,164)( 93,157)( 94,159)( 95,158)( 96,160);;
s2 := (  1,  2)(  5, 10)(  6,  9)(  7, 11)(  8, 12)( 13, 14)( 17, 22)( 18, 21)( 19, 23)( 20, 24)( 25, 38)( 26, 37)( 27, 39)( 28, 40)( 29, 46)( 30, 45)( 31, 47)( 32, 48)( 33, 42)( 34, 41)( 35, 43)( 36, 44)( 49, 62)( 50, 61)( 51, 63)( 52, 64)( 53, 70)( 54, 69)( 55, 71)( 56, 72)( 57, 66)( 58, 65)( 59, 67)( 60, 68)( 73, 74)( 77, 82)( 78, 81)( 79, 83)( 80, 84)( 85, 86)( 89, 94)( 90, 93)( 91, 95)( 92, 96)( 97,182)( 98,181)( 99,183)(100,184)(101,190)(102,189)(103,191)(104,192)(105,186)(106,185)(107,187)(108,188)(109,170)(110,169)(111,171)(112,172)(113,178)(114,177)(115,179)(116,180)(117,174)(118,173)(119,175)(120,176)(121,146)(122,145)(123,147)(124,148)(125,154)(126,153)(127,155)(128,156)(129,150)(130,149)(131,151)(132,152)(133,158)(134,157)(135,159)(136,160)(137,166)(138,165)(139,167)(140,168)(141,162)(142,161)(143,163)(144,164);;
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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*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(192)!(  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 15, 16)( 17, 21)( 18, 22)( 19, 24)( 20, 23)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)( 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, 85)( 74, 86)( 75, 88)( 76, 87)( 77, 93)( 78, 94)( 79, 96)( 80, 95)( 81, 89)( 82, 90)( 83, 92)( 84, 91)( 97,121)( 98,122)( 99,124)(100,123)(101,129)(102,130)(103,132)(104,131)(105,125)(106,126)(107,128)(108,127)(109,133)(110,134)(111,136)(112,135)(113,141)(114,142)(115,144)(116,143)(117,137)(118,138)(119,140)(120,139)(145,181)(146,182)(147,184)(148,183)(149,189)(150,190)(151,192)(152,191)(153,185)(154,186)(155,188)(156,187)(157,169)(158,170)(159,172)(160,171)(161,177)(162,178)(163,180)(164,179)(165,173)(166,174)(167,176)(168,175);
s1 := Sym(192)!(  1,129)(  2,131)(  3,130)(  4,132)(  5,125)(  6,127)(  7,126)(  8,128)(  9,121)( 10,123)( 11,122)( 12,124)( 13,141)( 14,143)( 15,142)( 16,144)( 17,137)( 18,139)( 19,138)( 20,140)( 21,133)( 22,135)( 23,134)( 24,136)( 25,105)( 26,107)( 27,106)( 28,108)( 29,101)( 30,103)( 31,102)( 32,104)( 33, 97)( 34, 99)( 35, 98)( 36,100)( 37,117)( 38,119)( 39,118)( 40,120)( 41,113)( 42,115)( 43,114)( 44,116)( 45,109)( 46,111)( 47,110)( 48,112)( 49,177)( 50,179)( 51,178)( 52,180)( 53,173)( 54,175)( 55,174)( 56,176)( 57,169)( 58,171)( 59,170)( 60,172)( 61,189)( 62,191)( 63,190)( 64,192)( 65,185)( 66,187)( 67,186)( 68,188)( 69,181)( 70,183)( 71,182)( 72,184)( 73,153)( 74,155)( 75,154)( 76,156)( 77,149)( 78,151)( 79,150)( 80,152)( 81,145)( 82,147)( 83,146)( 84,148)( 85,165)( 86,167)( 87,166)( 88,168)( 89,161)( 90,163)( 91,162)( 92,164)( 93,157)( 94,159)( 95,158)( 96,160);
s2 := Sym(192)!(  1,  2)(  5, 10)(  6,  9)(  7, 11)(  8, 12)( 13, 14)( 17, 22)( 18, 21)( 19, 23)( 20, 24)( 25, 38)( 26, 37)( 27, 39)( 28, 40)( 29, 46)( 30, 45)( 31, 47)( 32, 48)( 33, 42)( 34, 41)( 35, 43)( 36, 44)( 49, 62)( 50, 61)( 51, 63)( 52, 64)( 53, 70)( 54, 69)( 55, 71)( 56, 72)( 57, 66)( 58, 65)( 59, 67)( 60, 68)( 73, 74)( 77, 82)( 78, 81)( 79, 83)( 80, 84)( 85, 86)( 89, 94)( 90, 93)( 91, 95)( 92, 96)( 97,182)( 98,181)( 99,183)(100,184)(101,190)(102,189)(103,191)(104,192)(105,186)(106,185)(107,187)(108,188)(109,170)(110,169)(111,171)(112,172)(113,178)(114,177)(115,179)(116,180)(117,174)(118,173)(119,175)(120,176)(121,146)(122,145)(123,147)(124,148)(125,154)(126,153)(127,155)(128,156)(129,150)(130,149)(131,151)(132,152)(133,158)(134,157)(135,159)(136,160)(137,166)(138,165)(139,167)(140,168)(141,162)(142,161)(143,163)(144,164);
poly := sub<Sym(192)|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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*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