Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,12}

Atlas Canonical Name {8,12}*768x

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(768,1088009)
Rank
3
Schläfli Type
{8,12}
Vertices, edges, …
32, 192, 48
Order of s0s1s2
6
Order of s0s1s2s1
8
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

32-fold

64-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)^4> of order 2

32 facets

16 vertex figures

P/N, where N=<(s0*s2*s1)^3> of order 2

24 facets

16 vertex figures

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

24 facets

16 vertex figures

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

16 facets

8 vertex figures

P/N, where N=<(s0*s1)^4, (s0*s2*s1)^3> of order 4

16 facets

8 vertex figures

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

16 facets

8 vertex figures

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

24 facets

8 vertex figures

P/N, where N=<(s0*s1)^4, s0*s1*s2*(s1*s0)^3*s1*s2*s1> of order 4

16 facets

8 vertex figures

Representations

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

References

None.

to this polytope.

Twisty Puzzle