Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,24,12}

Atlas Canonical Name {2,24,12}*1152c

Overview

Group
SmallGroup(1152,97551)
Rank
4
Schläfli Type
{2,24,12}
Vertices, edges, …
2, 24, 144, 12
Order of s0s1s2s3
24
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

4-fold

6-fold

8-fold

9-fold

12-fold

16-fold

18-fold

24-fold

36-fold

48-fold

72-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)( 25, 26)( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 39, 48)( 40, 50)( 41, 49)( 42, 51)( 43, 53)( 44, 52)( 45, 54)( 46, 56)( 47, 55)( 57, 66)( 58, 68)( 59, 67)( 60, 69)( 61, 71)( 62, 70)( 63, 72)( 64, 74)( 65, 73)( 75,111)( 76,113)( 77,112)( 78,114)( 79,116)( 80,115)( 81,117)( 82,119)( 83,118)( 84,120)( 85,122)( 86,121)( 87,123)( 88,125)( 89,124)( 90,126)( 91,128)( 92,127)( 93,129)( 94,131)( 95,130)( 96,132)( 97,134)( 98,133)( 99,135)(100,137)(101,136)(102,138)(103,140)(104,139)(105,141)(106,143)(107,142)(108,144)(109,146)(110,145);;
s2 := (  3, 76)(  4, 75)(  5, 77)(  6, 82)(  7, 81)(  8, 83)(  9, 79)( 10, 78)( 11, 80)( 12, 85)( 13, 84)( 14, 86)( 15, 91)( 16, 90)( 17, 92)( 18, 88)( 19, 87)( 20, 89)( 21, 94)( 22, 93)( 23, 95)( 24,100)( 25, 99)( 26,101)( 27, 97)( 28, 96)( 29, 98)( 30,103)( 31,102)( 32,104)( 33,109)( 34,108)( 35,110)( 36,106)( 37,105)( 38,107)( 39,121)( 40,120)( 41,122)( 42,127)( 43,126)( 44,128)( 45,124)( 46,123)( 47,125)( 48,112)( 49,111)( 50,113)( 51,118)( 52,117)( 53,119)( 54,115)( 55,114)( 56,116)( 57,139)( 58,138)( 59,140)( 60,145)( 61,144)( 62,146)( 63,142)( 64,141)( 65,143)( 66,130)( 67,129)( 68,131)( 69,136)( 70,135)( 71,137)( 72,133)( 73,132)( 74,134);;
s3 := (  3,  6)(  4,  8)(  5,  7)( 10, 11)( 12, 15)( 13, 17)( 14, 16)( 19, 20)( 21, 24)( 22, 26)( 23, 25)( 28, 29)( 30, 33)( 31, 35)( 32, 34)( 37, 38)( 39, 42)( 40, 44)( 41, 43)( 46, 47)( 48, 51)( 49, 53)( 50, 52)( 55, 56)( 57, 60)( 58, 62)( 59, 61)( 64, 65)( 66, 69)( 67, 71)( 68, 70)( 73, 74)( 75, 96)( 76, 98)( 77, 97)( 78, 93)( 79, 95)( 80, 94)( 81, 99)( 82,101)( 83,100)( 84,105)( 85,107)( 86,106)( 87,102)( 88,104)( 89,103)( 90,108)( 91,110)( 92,109)(111,132)(112,134)(113,133)(114,129)(115,131)(116,130)(117,135)(118,137)(119,136)(120,141)(121,143)(122,142)(123,138)(124,140)(125,139)(126,144)(127,146)(128,145);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2, 
s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(146)!(1,2);
s1 := Sym(146)!(  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)( 25, 26)( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 39, 48)( 40, 50)( 41, 49)( 42, 51)( 43, 53)( 44, 52)( 45, 54)( 46, 56)( 47, 55)( 57, 66)( 58, 68)( 59, 67)( 60, 69)( 61, 71)( 62, 70)( 63, 72)( 64, 74)( 65, 73)( 75,111)( 76,113)( 77,112)( 78,114)( 79,116)( 80,115)( 81,117)( 82,119)( 83,118)( 84,120)( 85,122)( 86,121)( 87,123)( 88,125)( 89,124)( 90,126)( 91,128)( 92,127)( 93,129)( 94,131)( 95,130)( 96,132)( 97,134)( 98,133)( 99,135)(100,137)(101,136)(102,138)(103,140)(104,139)(105,141)(106,143)(107,142)(108,144)(109,146)(110,145);
s2 := Sym(146)!(  3, 76)(  4, 75)(  5, 77)(  6, 82)(  7, 81)(  8, 83)(  9, 79)( 10, 78)( 11, 80)( 12, 85)( 13, 84)( 14, 86)( 15, 91)( 16, 90)( 17, 92)( 18, 88)( 19, 87)( 20, 89)( 21, 94)( 22, 93)( 23, 95)( 24,100)( 25, 99)( 26,101)( 27, 97)( 28, 96)( 29, 98)( 30,103)( 31,102)( 32,104)( 33,109)( 34,108)( 35,110)( 36,106)( 37,105)( 38,107)( 39,121)( 40,120)( 41,122)( 42,127)( 43,126)( 44,128)( 45,124)( 46,123)( 47,125)( 48,112)( 49,111)( 50,113)( 51,118)( 52,117)( 53,119)( 54,115)( 55,114)( 56,116)( 57,139)( 58,138)( 59,140)( 60,145)( 61,144)( 62,146)( 63,142)( 64,141)( 65,143)( 66,130)( 67,129)( 68,131)( 69,136)( 70,135)( 71,137)( 72,133)( 73,132)( 74,134);
s3 := Sym(146)!(  3,  6)(  4,  8)(  5,  7)( 10, 11)( 12, 15)( 13, 17)( 14, 16)( 19, 20)( 21, 24)( 22, 26)( 23, 25)( 28, 29)( 30, 33)( 31, 35)( 32, 34)( 37, 38)( 39, 42)( 40, 44)( 41, 43)( 46, 47)( 48, 51)( 49, 53)( 50, 52)( 55, 56)( 57, 60)( 58, 62)( 59, 61)( 64, 65)( 66, 69)( 67, 71)( 68, 70)( 73, 74)( 75, 96)( 76, 98)( 77, 97)( 78, 93)( 79, 95)( 80, 94)( 81, 99)( 82,101)( 83,100)( 84,105)( 85,107)( 86,106)( 87,102)( 88,104)( 89,103)( 90,108)( 91,110)( 92,109)(111,132)(112,134)(113,133)(114,129)(115,131)(116,130)(117,135)(118,137)(119,136)(120,141)(121,143)(122,142)(123,138)(124,140)(125,139)(126,144)(127,146)(128,145);
poly := sub<Sym(146)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2, 
s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;