Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,12,6}

Atlas Canonical Name {4,12,6}*1152b

Overview

Group
SmallGroup(1152,99266)
Rank
4
Schläfli Type
{4,12,6}
Vertices, edges, …
8, 48, 72, 6
Order of s0s1s2s3
12
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

4-fold

6-fold

8-fold

9-fold

12-fold

18-fold

24-fold

36-fold

48-fold

72-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> of order 2

6 facets

4 vertex figures

P/N, where N=<(s1*s2)^6> of order 2

6 facets

6 vertex figures

Representations

Permutation Representation (GAP) 
s0 := ( 19, 28)( 20, 29)( 21, 30)( 22, 31)( 23, 32)( 24, 33)( 25, 34)( 26, 35)( 27, 36)( 55, 64)( 56, 65)( 57, 66)( 58, 67)( 59, 68)( 60, 69)( 61, 70)( 62, 71)( 63, 72)( 91,100)( 92,101)( 93,102)( 94,103)( 95,104)( 96,105)( 97,106)( 98,107)( 99,108)(127,136)(128,137)(129,138)(130,139)(131,140)(132,141)(133,142)(134,143)(135,144);;
s1 := (  1, 37)(  2, 44)(  3, 42)(  4, 43)(  5, 41)(  6, 39)(  7, 40)(  8, 38)(  9, 45)( 10, 46)( 11, 53)( 12, 51)( 13, 52)( 14, 50)( 15, 48)( 16, 49)( 17, 47)( 18, 54)( 19, 55)( 20, 62)( 21, 60)( 22, 61)( 23, 59)( 24, 57)( 25, 58)( 26, 56)( 27, 63)( 28, 64)( 29, 71)( 30, 69)( 31, 70)( 32, 68)( 33, 66)( 34, 67)( 35, 65)( 36, 72)( 73,127)( 74,134)( 75,132)( 76,133)( 77,131)( 78,129)( 79,130)( 80,128)( 81,135)( 82,136)( 83,143)( 84,141)( 85,142)( 86,140)( 87,138)( 88,139)( 89,137)( 90,144)( 91,109)( 92,116)( 93,114)( 94,115)( 95,113)( 96,111)( 97,112)( 98,110)( 99,117)(100,118)(101,125)(102,123)(103,124)(104,122)(105,120)(106,121)(107,119)(108,126);;
s2 := (  1, 76)(  2, 78)(  3, 77)(  4, 73)(  5, 75)(  6, 74)(  7, 79)(  8, 81)(  9, 80)( 10, 85)( 11, 87)( 12, 86)( 13, 82)( 14, 84)( 15, 83)( 16, 88)( 17, 90)( 18, 89)( 19, 94)( 20, 96)( 21, 95)( 22, 91)( 23, 93)( 24, 92)( 25, 97)( 26, 99)( 27, 98)( 28,103)( 29,105)( 30,104)( 31,100)( 32,102)( 33,101)( 34,106)( 35,108)( 36,107)( 37,112)( 38,114)( 39,113)( 40,109)( 41,111)( 42,110)( 43,115)( 44,117)( 45,116)( 46,121)( 47,123)( 48,122)( 49,118)( 50,120)( 51,119)( 52,124)( 53,126)( 54,125)( 55,130)( 56,132)( 57,131)( 58,127)( 59,129)( 60,128)( 61,133)( 62,135)( 63,134)( 64,139)( 65,141)( 66,140)( 67,136)( 68,138)( 69,137)( 70,142)( 71,144)( 72,143);;
s3 := (  1, 41)(  2, 43)(  3, 39)(  4, 44)(  5, 37)(  6, 42)(  7, 38)(  8, 40)(  9, 45)( 10, 50)( 11, 52)( 12, 48)( 13, 53)( 14, 46)( 15, 51)( 16, 47)( 17, 49)( 18, 54)( 19, 59)( 20, 61)( 21, 57)( 22, 62)( 23, 55)( 24, 60)( 25, 56)( 26, 58)( 27, 63)( 28, 68)( 29, 70)( 30, 66)( 31, 71)( 32, 64)( 33, 69)( 34, 65)( 35, 67)( 36, 72)( 73,113)( 74,115)( 75,111)( 76,116)( 77,109)( 78,114)( 79,110)( 80,112)( 81,117)( 82,122)( 83,124)( 84,120)( 85,125)( 86,118)( 87,123)( 88,119)( 89,121)( 90,126)( 91,131)( 92,133)( 93,129)( 94,134)( 95,127)( 96,132)( 97,128)( 98,130)( 99,135)(100,140)(101,142)(102,138)(103,143)(104,136)(105,141)(106,137)(107,139)(108,144);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*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)!( 19, 28)( 20, 29)( 21, 30)( 22, 31)( 23, 32)( 24, 33)( 25, 34)( 26, 35)( 27, 36)( 55, 64)( 56, 65)( 57, 66)( 58, 67)( 59, 68)( 60, 69)( 61, 70)( 62, 71)( 63, 72)( 91,100)( 92,101)( 93,102)( 94,103)( 95,104)( 96,105)( 97,106)( 98,107)( 99,108)(127,136)(128,137)(129,138)(130,139)(131,140)(132,141)(133,142)(134,143)(135,144);
s1 := Sym(144)!(  1, 37)(  2, 44)(  3, 42)(  4, 43)(  5, 41)(  6, 39)(  7, 40)(  8, 38)(  9, 45)( 10, 46)( 11, 53)( 12, 51)( 13, 52)( 14, 50)( 15, 48)( 16, 49)( 17, 47)( 18, 54)( 19, 55)( 20, 62)( 21, 60)( 22, 61)( 23, 59)( 24, 57)( 25, 58)( 26, 56)( 27, 63)( 28, 64)( 29, 71)( 30, 69)( 31, 70)( 32, 68)( 33, 66)( 34, 67)( 35, 65)( 36, 72)( 73,127)( 74,134)( 75,132)( 76,133)( 77,131)( 78,129)( 79,130)( 80,128)( 81,135)( 82,136)( 83,143)( 84,141)( 85,142)( 86,140)( 87,138)( 88,139)( 89,137)( 90,144)( 91,109)( 92,116)( 93,114)( 94,115)( 95,113)( 96,111)( 97,112)( 98,110)( 99,117)(100,118)(101,125)(102,123)(103,124)(104,122)(105,120)(106,121)(107,119)(108,126);
s2 := Sym(144)!(  1, 76)(  2, 78)(  3, 77)(  4, 73)(  5, 75)(  6, 74)(  7, 79)(  8, 81)(  9, 80)( 10, 85)( 11, 87)( 12, 86)( 13, 82)( 14, 84)( 15, 83)( 16, 88)( 17, 90)( 18, 89)( 19, 94)( 20, 96)( 21, 95)( 22, 91)( 23, 93)( 24, 92)( 25, 97)( 26, 99)( 27, 98)( 28,103)( 29,105)( 30,104)( 31,100)( 32,102)( 33,101)( 34,106)( 35,108)( 36,107)( 37,112)( 38,114)( 39,113)( 40,109)( 41,111)( 42,110)( 43,115)( 44,117)( 45,116)( 46,121)( 47,123)( 48,122)( 49,118)( 50,120)( 51,119)( 52,124)( 53,126)( 54,125)( 55,130)( 56,132)( 57,131)( 58,127)( 59,129)( 60,128)( 61,133)( 62,135)( 63,134)( 64,139)( 65,141)( 66,140)( 67,136)( 68,138)( 69,137)( 70,142)( 71,144)( 72,143);
s3 := Sym(144)!(  1, 41)(  2, 43)(  3, 39)(  4, 44)(  5, 37)(  6, 42)(  7, 38)(  8, 40)(  9, 45)( 10, 50)( 11, 52)( 12, 48)( 13, 53)( 14, 46)( 15, 51)( 16, 47)( 17, 49)( 18, 54)( 19, 59)( 20, 61)( 21, 57)( 22, 62)( 23, 55)( 24, 60)( 25, 56)( 26, 58)( 27, 63)( 28, 68)( 29, 70)( 30, 66)( 31, 71)( 32, 64)( 33, 69)( 34, 65)( 35, 67)( 36, 72)( 73,113)( 74,115)( 75,111)( 76,116)( 77,109)( 78,114)( 79,110)( 80,112)( 81,117)( 82,122)( 83,124)( 84,120)( 85,125)( 86,118)( 87,123)( 88,119)( 89,121)( 90,126)( 91,131)( 92,133)( 93,129)( 94,134)( 95,127)( 96,132)( 97,128)( 98,130)( 99,135)(100,140)(101,142)(102,138)(103,143)(104,136)(105,141)(106,137)(107,139)(108,144);
poly := sub<Sym(144)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*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.