Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,6,6}

Atlas Canonical Name {2,4,6,6}*1152a

Overview

Group
SmallGroup(1152,157863)
Rank
5
Schläfli Type
{2,4,6,6}
Vertices, edges, …
2, 8, 24, 36, 6
Order of s0s1s2s3s4
6
Order of s0s1s2s3s4s3s2s1
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

12-fold

24-fold

36-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (  3, 77)(  4, 78)(  5, 75)(  6, 76)(  7, 81)(  8, 82)(  9, 79)( 10, 80)( 11, 85)( 12, 86)( 13, 83)( 14, 84)( 15, 89)( 16, 90)( 17, 87)( 18, 88)( 19, 93)( 20, 94)( 21, 91)( 22, 92)( 23, 97)( 24, 98)( 25, 95)( 26, 96)( 27,101)( 28,102)( 29, 99)( 30,100)( 31,105)( 32,106)( 33,103)( 34,104)( 35,109)( 36,110)( 37,107)( 38,108)( 39,113)( 40,114)( 41,111)( 42,112)( 43,117)( 44,118)( 45,115)( 46,116)( 47,121)( 48,122)( 49,119)( 50,120)( 51,125)( 52,126)( 53,123)( 54,124)( 55,129)( 56,130)( 57,127)( 58,128)( 59,133)( 60,134)( 61,131)( 62,132)( 63,137)( 64,138)( 65,135)( 66,136)( 67,141)( 68,142)( 69,139)( 70,140)( 71,145)( 72,146)( 73,143)( 74,144);;
s2 := (  4,  5)(  8,  9)( 12, 13)( 15, 27)( 16, 29)( 17, 28)( 18, 30)( 19, 31)( 20, 33)( 21, 32)( 22, 34)( 23, 35)( 24, 37)( 25, 36)( 26, 38)( 40, 41)( 44, 45)( 48, 49)( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 67)( 56, 69)( 57, 68)( 58, 70)( 59, 71)( 60, 73)( 61, 72)( 62, 74)( 76, 77)( 80, 81)( 84, 85)( 87, 99)( 88,101)( 89,100)( 90,102)( 91,103)( 92,105)( 93,104)( 94,106)( 95,107)( 96,109)( 97,108)( 98,110)(112,113)(116,117)(120,121)(123,135)(124,137)(125,136)(126,138)(127,139)(128,141)(129,140)(130,142)(131,143)(132,145)(133,144)(134,146);;
s3 := (  3, 27)(  4, 30)(  5, 29)(  6, 28)(  7, 35)(  8, 38)(  9, 37)( 10, 36)( 11, 31)( 12, 34)( 13, 33)( 14, 32)( 16, 18)( 19, 23)( 20, 26)( 21, 25)( 22, 24)( 39, 63)( 40, 66)( 41, 65)( 42, 64)( 43, 71)( 44, 74)( 45, 73)( 46, 72)( 47, 67)( 48, 70)( 49, 69)( 50, 68)( 52, 54)( 55, 59)( 56, 62)( 57, 61)( 58, 60)( 75, 99)( 76,102)( 77,101)( 78,100)( 79,107)( 80,110)( 81,109)( 82,108)( 83,103)( 84,106)( 85,105)( 86,104)( 88, 90)( 91, 95)( 92, 98)( 93, 97)( 94, 96)(111,135)(112,138)(113,137)(114,136)(115,143)(116,146)(117,145)(118,144)(119,139)(120,142)(121,141)(122,140)(124,126)(127,131)(128,134)(129,133)(130,132);;
s4 := (  3, 43)(  4, 44)(  5, 45)(  6, 46)(  7, 39)(  8, 40)(  9, 41)( 10, 42)( 11, 47)( 12, 48)( 13, 49)( 14, 50)( 15, 55)( 16, 56)( 17, 57)( 18, 58)( 19, 51)( 20, 52)( 21, 53)( 22, 54)( 23, 59)( 24, 60)( 25, 61)( 26, 62)( 27, 67)( 28, 68)( 29, 69)( 30, 70)( 31, 63)( 32, 64)( 33, 65)( 34, 66)( 35, 71)( 36, 72)( 37, 73)( 38, 74)( 75,115)( 76,116)( 77,117)( 78,118)( 79,111)( 80,112)( 81,113)( 82,114)( 83,119)( 84,120)( 85,121)( 86,122)( 87,127)( 88,128)( 89,129)( 90,130)( 91,123)( 92,124)( 93,125)( 94,126)( 95,131)( 96,132)( 97,133)( 98,134)( 99,139)(100,140)(101,141)(102,142)(103,135)(104,136)(105,137)(106,138)(107,143)(108,144)(109,145)(110,146);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s4*s3*s2*s3*s4*s3, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(146)!(1,2);
s1 := Sym(146)!(  3, 77)(  4, 78)(  5, 75)(  6, 76)(  7, 81)(  8, 82)(  9, 79)( 10, 80)( 11, 85)( 12, 86)( 13, 83)( 14, 84)( 15, 89)( 16, 90)( 17, 87)( 18, 88)( 19, 93)( 20, 94)( 21, 91)( 22, 92)( 23, 97)( 24, 98)( 25, 95)( 26, 96)( 27,101)( 28,102)( 29, 99)( 30,100)( 31,105)( 32,106)( 33,103)( 34,104)( 35,109)( 36,110)( 37,107)( 38,108)( 39,113)( 40,114)( 41,111)( 42,112)( 43,117)( 44,118)( 45,115)( 46,116)( 47,121)( 48,122)( 49,119)( 50,120)( 51,125)( 52,126)( 53,123)( 54,124)( 55,129)( 56,130)( 57,127)( 58,128)( 59,133)( 60,134)( 61,131)( 62,132)( 63,137)( 64,138)( 65,135)( 66,136)( 67,141)( 68,142)( 69,139)( 70,140)( 71,145)( 72,146)( 73,143)( 74,144);
s2 := Sym(146)!(  4,  5)(  8,  9)( 12, 13)( 15, 27)( 16, 29)( 17, 28)( 18, 30)( 19, 31)( 20, 33)( 21, 32)( 22, 34)( 23, 35)( 24, 37)( 25, 36)( 26, 38)( 40, 41)( 44, 45)( 48, 49)( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 67)( 56, 69)( 57, 68)( 58, 70)( 59, 71)( 60, 73)( 61, 72)( 62, 74)( 76, 77)( 80, 81)( 84, 85)( 87, 99)( 88,101)( 89,100)( 90,102)( 91,103)( 92,105)( 93,104)( 94,106)( 95,107)( 96,109)( 97,108)( 98,110)(112,113)(116,117)(120,121)(123,135)(124,137)(125,136)(126,138)(127,139)(128,141)(129,140)(130,142)(131,143)(132,145)(133,144)(134,146);
s3 := Sym(146)!(  3, 27)(  4, 30)(  5, 29)(  6, 28)(  7, 35)(  8, 38)(  9, 37)( 10, 36)( 11, 31)( 12, 34)( 13, 33)( 14, 32)( 16, 18)( 19, 23)( 20, 26)( 21, 25)( 22, 24)( 39, 63)( 40, 66)( 41, 65)( 42, 64)( 43, 71)( 44, 74)( 45, 73)( 46, 72)( 47, 67)( 48, 70)( 49, 69)( 50, 68)( 52, 54)( 55, 59)( 56, 62)( 57, 61)( 58, 60)( 75, 99)( 76,102)( 77,101)( 78,100)( 79,107)( 80,110)( 81,109)( 82,108)( 83,103)( 84,106)( 85,105)( 86,104)( 88, 90)( 91, 95)( 92, 98)( 93, 97)( 94, 96)(111,135)(112,138)(113,137)(114,136)(115,143)(116,146)(117,145)(118,144)(119,139)(120,142)(121,141)(122,140)(124,126)(127,131)(128,134)(129,133)(130,132);
s4 := Sym(146)!(  3, 43)(  4, 44)(  5, 45)(  6, 46)(  7, 39)(  8, 40)(  9, 41)( 10, 42)( 11, 47)( 12, 48)( 13, 49)( 14, 50)( 15, 55)( 16, 56)( 17, 57)( 18, 58)( 19, 51)( 20, 52)( 21, 53)( 22, 54)( 23, 59)( 24, 60)( 25, 61)( 26, 62)( 27, 67)( 28, 68)( 29, 69)( 30, 70)( 31, 63)( 32, 64)( 33, 65)( 34, 66)( 35, 71)( 36, 72)( 37, 73)( 38, 74)( 75,115)( 76,116)( 77,117)( 78,118)( 79,111)( 80,112)( 81,113)( 82,114)( 83,119)( 84,120)( 85,121)( 86,122)( 87,127)( 88,128)( 89,129)( 90,130)( 91,123)( 92,124)( 93,125)( 94,126)( 95,131)( 96,132)( 97,133)( 98,134)( 99,139)(100,140)(101,141)(102,142)(103,135)(104,136)(105,137)(106,138)(107,143)(108,144)(109,145)(110,146);
poly := sub<Sym(146)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s4*s3*s2*s3*s4*s3, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;