Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,12,24}

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

Overview

Group
SmallGroup(1152,97551)
Rank
4
Schläfli Type
{2,12,24}
Vertices, edges, …
2, 12, 144, 24
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)(  6,  9)(  7, 11)(  8, 10)( 13, 14)( 15, 18)( 16, 20)( 17, 19)( 22, 23)( 24, 27)( 25, 29)( 26, 28)( 31, 32)( 33, 36)( 34, 38)( 35, 37)( 40, 41)( 42, 45)( 43, 47)( 44, 46)( 49, 50)( 51, 54)( 52, 56)( 53, 55)( 58, 59)( 60, 63)( 61, 65)( 62, 64)( 67, 68)( 69, 72)( 70, 74)( 71, 73)( 75, 93)( 76, 95)( 77, 94)( 78, 99)( 79,101)( 80,100)( 81, 96)( 82, 98)( 83, 97)( 84,102)( 85,104)( 86,103)( 87,108)( 88,110)( 89,109)( 90,105)( 91,107)( 92,106)(111,129)(112,131)(113,130)(114,135)(115,137)(116,136)(117,132)(118,134)(119,133)(120,138)(121,140)(122,139)(123,144)(124,146)(125,145)(126,141)(127,143)(128,142);;
s2 := (  3, 79)(  4, 78)(  5, 80)(  6, 76)(  7, 75)(  8, 77)(  9, 82)( 10, 81)( 11, 83)( 12, 88)( 13, 87)( 14, 89)( 15, 85)( 16, 84)( 17, 86)( 18, 91)( 19, 90)( 20, 92)( 21, 97)( 22, 96)( 23, 98)( 24, 94)( 25, 93)( 26, 95)( 27,100)( 28, 99)( 29,101)( 30,106)( 31,105)( 32,107)( 33,103)( 34,102)( 35,104)( 36,109)( 37,108)( 38,110)( 39,124)( 40,123)( 41,125)( 42,121)( 43,120)( 44,122)( 45,127)( 46,126)( 47,128)( 48,115)( 49,114)( 50,116)( 51,112)( 52,111)( 53,113)( 54,118)( 55,117)( 56,119)( 57,142)( 58,141)( 59,143)( 60,139)( 61,138)( 62,140)( 63,145)( 64,144)( 65,146)( 66,133)( 67,132)( 68,134)( 69,130)( 70,129)( 71,131)( 72,136)( 73,135)( 74,137);;
s3 := (  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);;
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, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(146)!(1,2);
s1 := Sym(146)!(  4,  5)(  6,  9)(  7, 11)(  8, 10)( 13, 14)( 15, 18)( 16, 20)( 17, 19)( 22, 23)( 24, 27)( 25, 29)( 26, 28)( 31, 32)( 33, 36)( 34, 38)( 35, 37)( 40, 41)( 42, 45)( 43, 47)( 44, 46)( 49, 50)( 51, 54)( 52, 56)( 53, 55)( 58, 59)( 60, 63)( 61, 65)( 62, 64)( 67, 68)( 69, 72)( 70, 74)( 71, 73)( 75, 93)( 76, 95)( 77, 94)( 78, 99)( 79,101)( 80,100)( 81, 96)( 82, 98)( 83, 97)( 84,102)( 85,104)( 86,103)( 87,108)( 88,110)( 89,109)( 90,105)( 91,107)( 92,106)(111,129)(112,131)(113,130)(114,135)(115,137)(116,136)(117,132)(118,134)(119,133)(120,138)(121,140)(122,139)(123,144)(124,146)(125,145)(126,141)(127,143)(128,142);
s2 := Sym(146)!(  3, 79)(  4, 78)(  5, 80)(  6, 76)(  7, 75)(  8, 77)(  9, 82)( 10, 81)( 11, 83)( 12, 88)( 13, 87)( 14, 89)( 15, 85)( 16, 84)( 17, 86)( 18, 91)( 19, 90)( 20, 92)( 21, 97)( 22, 96)( 23, 98)( 24, 94)( 25, 93)( 26, 95)( 27,100)( 28, 99)( 29,101)( 30,106)( 31,105)( 32,107)( 33,103)( 34,102)( 35,104)( 36,109)( 37,108)( 38,110)( 39,124)( 40,123)( 41,125)( 42,121)( 43,120)( 44,122)( 45,127)( 46,126)( 47,128)( 48,115)( 49,114)( 50,116)( 51,112)( 52,111)( 53,113)( 54,118)( 55,117)( 56,119)( 57,142)( 58,141)( 59,143)( 60,139)( 61,138)( 62,140)( 63,145)( 64,144)( 65,146)( 66,133)( 67,132)( 68,134)( 69,130)( 70,129)( 71,131)( 72,136)( 73,135)( 74,137);
s3 := 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);
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, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2 >;