Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,48,6}

Atlas Canonical Name {2,48,6}*1152b

Overview

Group
SmallGroup(1152,133451)
Rank
4
Schläfli Type
{2,48,6}
Vertices, edges, …
2, 48, 144, 6
Order of s0s1s2s3
48
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

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