Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,2,4,30}

Atlas Canonical Name {2,2,2,4,30}*1920c

Overview

Group
SmallGroup(1920,240411)
Rank
6
Schläfli Type
{2,2,2,4,30}
Vertices, edges, …
2, 2, 2, 4, 60, 30
Order of s0s1s2s3s4s5
30
Order of s0s1s2s3s4s5s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

5-fold

10-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := (  7, 68)(  8, 67)(  9, 70)( 10, 69)( 11, 72)( 12, 71)( 13, 74)( 14, 73)( 15, 76)( 16, 75)( 17, 78)( 18, 77)( 19, 80)( 20, 79)( 21, 82)( 22, 81)( 23, 84)( 24, 83)( 25, 86)( 26, 85)( 27, 88)( 28, 87)( 29, 90)( 30, 89)( 31, 92)( 32, 91)( 33, 94)( 34, 93)( 35, 96)( 36, 95)( 37, 98)( 38, 97)( 39,100)( 40, 99)( 41,102)( 42,101)( 43,104)( 44,103)( 45,106)( 46,105)( 47,108)( 48,107)( 49,110)( 50,109)( 51,112)( 52,111)( 53,114)( 54,113)( 55,116)( 56,115)( 57,118)( 58,117)( 59,120)( 60,119)( 61,122)( 62,121)( 63,124)( 64,123)( 65,126)( 66,125);;
s4 := (  8,  9)( 11, 23)( 12, 25)( 13, 24)( 14, 26)( 15, 19)( 16, 21)( 17, 20)( 18, 22)( 27, 47)( 28, 49)( 29, 48)( 30, 50)( 31, 63)( 32, 65)( 33, 64)( 34, 66)( 35, 59)( 36, 61)( 37, 60)( 38, 62)( 39, 55)( 40, 57)( 41, 56)( 42, 58)( 43, 51)( 44, 53)( 45, 52)( 46, 54)( 68, 69)( 71, 83)( 72, 85)( 73, 84)( 74, 86)( 75, 79)( 76, 81)( 77, 80)( 78, 82)( 87,107)( 88,109)( 89,108)( 90,110)( 91,123)( 92,125)( 93,124)( 94,126)( 95,119)( 96,121)( 97,120)( 98,122)( 99,115)(100,117)(101,116)(102,118)(103,111)(104,113)(105,112)(106,114);;
s5 := (  7, 91)(  8, 92)(  9, 94)( 10, 93)( 11, 87)( 12, 88)( 13, 90)( 14, 89)( 15,103)( 16,104)( 17,106)( 18,105)( 19, 99)( 20,100)( 21,102)( 22,101)( 23, 95)( 24, 96)( 25, 98)( 26, 97)( 27, 71)( 28, 72)( 29, 74)( 30, 73)( 31, 67)( 32, 68)( 33, 70)( 34, 69)( 35, 83)( 36, 84)( 37, 86)( 38, 85)( 39, 79)( 40, 80)( 41, 82)( 42, 81)( 43, 75)( 44, 76)( 45, 78)( 46, 77)( 47,111)( 48,112)( 49,114)( 50,113)( 51,107)( 52,108)( 53,110)( 54,109)( 55,123)( 56,124)( 57,126)( 58,125)( 59,119)( 60,120)( 61,122)( 62,121)( 63,115)( 64,116)( 65,118)( 66,117);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s5*s4*s3*s4*s5*s4*s5*s4, 
s5*s4*s3*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s3*s5*s4*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(126)!(1,2);
s1 := Sym(126)!(3,4);
s2 := Sym(126)!(5,6);
s3 := Sym(126)!(  7, 68)(  8, 67)(  9, 70)( 10, 69)( 11, 72)( 12, 71)( 13, 74)( 14, 73)( 15, 76)( 16, 75)( 17, 78)( 18, 77)( 19, 80)( 20, 79)( 21, 82)( 22, 81)( 23, 84)( 24, 83)( 25, 86)( 26, 85)( 27, 88)( 28, 87)( 29, 90)( 30, 89)( 31, 92)( 32, 91)( 33, 94)( 34, 93)( 35, 96)( 36, 95)( 37, 98)( 38, 97)( 39,100)( 40, 99)( 41,102)( 42,101)( 43,104)( 44,103)( 45,106)( 46,105)( 47,108)( 48,107)( 49,110)( 50,109)( 51,112)( 52,111)( 53,114)( 54,113)( 55,116)( 56,115)( 57,118)( 58,117)( 59,120)( 60,119)( 61,122)( 62,121)( 63,124)( 64,123)( 65,126)( 66,125);
s4 := Sym(126)!(  8,  9)( 11, 23)( 12, 25)( 13, 24)( 14, 26)( 15, 19)( 16, 21)( 17, 20)( 18, 22)( 27, 47)( 28, 49)( 29, 48)( 30, 50)( 31, 63)( 32, 65)( 33, 64)( 34, 66)( 35, 59)( 36, 61)( 37, 60)( 38, 62)( 39, 55)( 40, 57)( 41, 56)( 42, 58)( 43, 51)( 44, 53)( 45, 52)( 46, 54)( 68, 69)( 71, 83)( 72, 85)( 73, 84)( 74, 86)( 75, 79)( 76, 81)( 77, 80)( 78, 82)( 87,107)( 88,109)( 89,108)( 90,110)( 91,123)( 92,125)( 93,124)( 94,126)( 95,119)( 96,121)( 97,120)( 98,122)( 99,115)(100,117)(101,116)(102,118)(103,111)(104,113)(105,112)(106,114);
s5 := Sym(126)!(  7, 91)(  8, 92)(  9, 94)( 10, 93)( 11, 87)( 12, 88)( 13, 90)( 14, 89)( 15,103)( 16,104)( 17,106)( 18,105)( 19, 99)( 20,100)( 21,102)( 22,101)( 23, 95)( 24, 96)( 25, 98)( 26, 97)( 27, 71)( 28, 72)( 29, 74)( 30, 73)( 31, 67)( 32, 68)( 33, 70)( 34, 69)( 35, 83)( 36, 84)( 37, 86)( 38, 85)( 39, 79)( 40, 80)( 41, 82)( 42, 81)( 43, 75)( 44, 76)( 45, 78)( 46, 77)( 47,111)( 48,112)( 49,114)( 50,113)( 51,107)( 52,108)( 53,110)( 54,109)( 55,123)( 56,124)( 57,126)( 58,125)( 59,119)( 60,120)( 61,122)( 62,121)( 63,115)( 64,116)( 65,118)( 66,117);
poly := sub<Sym(126)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s5*s4*s3*s4*s5*s4*s5*s4, 
s5*s4*s3*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s3*s5*s4*s3 >;