Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,12}

Atlas Canonical Name {12,12}*576g

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(576,8312)
Rank
3
Schläfli Type
{12,12}
Vertices, edges, …
24, 144, 24
Order of s0s1s2
12
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

36-fold

48-fold

72-fold

Covers minimal covers in bold

2-fold

3-fold

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

12 vertex figures

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

12 facets

12 vertex figures

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

12 facets

12 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, 75)( 74, 76)( 77, 83)( 78, 84)( 79, 81)( 80, 82)( 85, 87)( 86, 88)( 89, 95)( 90, 96)( 91, 93)( 92, 94)( 97, 99)( 98,100)(101,107)(102,108)(103,105)(104,106)(109,111)(110,112)(113,119)(114,120)(115,117)(116,118)(121,123)(122,124)(125,131)(126,132)(127,129)(128,130)(133,135)(134,136)(137,143)(138,144)(139,141)(140,142);;
s1 := (  1,  5)(  2,  7)(  3,  6)(  4,  8)( 10, 11)( 13, 29)( 14, 31)( 15, 30)( 16, 32)( 17, 25)( 18, 27)( 19, 26)( 20, 28)( 21, 33)( 22, 35)( 23, 34)( 24, 36)( 37, 41)( 38, 43)( 39, 42)( 40, 44)( 46, 47)( 49, 65)( 50, 67)( 51, 66)( 52, 68)( 53, 61)( 54, 63)( 55, 62)( 56, 64)( 57, 69)( 58, 71)( 59, 70)( 60, 72)( 73,113)( 74,115)( 75,114)( 76,116)( 77,109)( 78,111)( 79,110)( 80,112)( 81,117)( 82,119)( 83,118)( 84,120)( 85,137)( 86,139)( 87,138)( 88,140)( 89,133)( 90,135)( 91,134)( 92,136)( 93,141)( 94,143)( 95,142)( 96,144)( 97,125)( 98,127)( 99,126)(100,128)(101,121)(102,123)(103,122)(104,124)(105,129)(106,131)(107,130)(108,132);;
s2 := (  1, 97)(  2,100)(  3, 99)(  4, 98)(  5,105)(  6,108)(  7,107)(  8,106)(  9,101)( 10,104)( 11,103)( 12,102)( 13, 85)( 14, 88)( 15, 87)( 16, 86)( 17, 93)( 18, 96)( 19, 95)( 20, 94)( 21, 89)( 22, 92)( 23, 91)( 24, 90)( 25, 73)( 26, 76)( 27, 75)( 28, 74)( 29, 81)( 30, 84)( 31, 83)( 32, 82)( 33, 77)( 34, 80)( 35, 79)( 36, 78)( 37,133)( 38,136)( 39,135)( 40,134)( 41,141)( 42,144)( 43,143)( 44,142)( 45,137)( 46,140)( 47,139)( 48,138)( 49,121)( 50,124)( 51,123)( 52,122)( 53,129)( 54,132)( 55,131)( 56,130)( 57,125)( 58,128)( 59,127)( 60,126)( 61,109)( 62,112)( 63,111)( 64,110)( 65,117)( 66,120)( 67,119)( 68,118)( 69,113)( 70,116)( 71,115)( 72,114);;
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1, 
s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(144)!(  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, 75)( 74, 76)( 77, 83)( 78, 84)( 79, 81)( 80, 82)( 85, 87)( 86, 88)( 89, 95)( 90, 96)( 91, 93)( 92, 94)( 97, 99)( 98,100)(101,107)(102,108)(103,105)(104,106)(109,111)(110,112)(113,119)(114,120)(115,117)(116,118)(121,123)(122,124)(125,131)(126,132)(127,129)(128,130)(133,135)(134,136)(137,143)(138,144)(139,141)(140,142);
s1 := Sym(144)!(  1,  5)(  2,  7)(  3,  6)(  4,  8)( 10, 11)( 13, 29)( 14, 31)( 15, 30)( 16, 32)( 17, 25)( 18, 27)( 19, 26)( 20, 28)( 21, 33)( 22, 35)( 23, 34)( 24, 36)( 37, 41)( 38, 43)( 39, 42)( 40, 44)( 46, 47)( 49, 65)( 50, 67)( 51, 66)( 52, 68)( 53, 61)( 54, 63)( 55, 62)( 56, 64)( 57, 69)( 58, 71)( 59, 70)( 60, 72)( 73,113)( 74,115)( 75,114)( 76,116)( 77,109)( 78,111)( 79,110)( 80,112)( 81,117)( 82,119)( 83,118)( 84,120)( 85,137)( 86,139)( 87,138)( 88,140)( 89,133)( 90,135)( 91,134)( 92,136)( 93,141)( 94,143)( 95,142)( 96,144)( 97,125)( 98,127)( 99,126)(100,128)(101,121)(102,123)(103,122)(104,124)(105,129)(106,131)(107,130)(108,132);
s2 := Sym(144)!(  1, 97)(  2,100)(  3, 99)(  4, 98)(  5,105)(  6,108)(  7,107)(  8,106)(  9,101)( 10,104)( 11,103)( 12,102)( 13, 85)( 14, 88)( 15, 87)( 16, 86)( 17, 93)( 18, 96)( 19, 95)( 20, 94)( 21, 89)( 22, 92)( 23, 91)( 24, 90)( 25, 73)( 26, 76)( 27, 75)( 28, 74)( 29, 81)( 30, 84)( 31, 83)( 32, 82)( 33, 77)( 34, 80)( 35, 79)( 36, 78)( 37,133)( 38,136)( 39,135)( 40,134)( 41,141)( 42,144)( 43,143)( 44,142)( 45,137)( 46,140)( 47,139)( 48,138)( 49,121)( 50,124)( 51,123)( 52,122)( 53,129)( 54,132)( 55,131)( 56,130)( 57,125)( 58,128)( 59,127)( 60,126)( 61,109)( 62,112)( 63,111)( 64,110)( 65,117)( 66,120)( 67,119)( 68,118)( 69,113)( 70,116)( 71,115)( 72,114);
poly := sub<Sym(144)|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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1, 
s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References

None.

to this polytope.

Twisty Puzzle