Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,8}

Atlas Canonical Name {12,8}*768r

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(768,1087633)
Rank
3
Schläfli Type
{12,8}
Vertices, edges, …
48, 192, 32
Order of s0s1s2
12
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

48-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*(s2*s1)^2)^2*s2> of order 2

16 facets

24 vertex figures

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

16 facets

24 vertex figures

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

16 facets

32 vertex figures

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

8 facets

16 vertex figures

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

8 facets

16 vertex figures

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

8 facets

24 vertex figures

P/N, where N=<s1*s0*(s1*s2)^3*s1*s0*s2*s1, (s0*s1)^2*(s0*s2*s1)^3*s0*s1*s2> of order 4

8 facets

16 vertex figures

P/N, where N=<s1*s0*(s1*s2)^3*s1*s0*s2*s1, (s0*s1)^2*(s0*s2*s1)^3*s0*s1> of order 4

8 facets

16 vertex figures

Representations

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

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