Part of the Atlas of Small Regular Polytopes

Polytope of Type {5,2,4,6,4}

Atlas Canonical Name {5,2,4,6,4}*1920a

Overview

Group
SmallGroup(1920,208116)
Rank
6
Schläfli Type
{5,2,4,6,4}
Vertices, edges, …
5, 5, 4, 12, 12, 4
Order of s0s1s2s3s4s5
60
Order of s0s1s2s3s4s5s4s3s2s1
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

12-fold

Covers minimal covers in bold

None in this atlas.

Representations

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