Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,60,4}

Atlas Canonical Name {2,60,4}*960a

Overview

Group
SmallGroup(960,10441)
Rank
4
Schläfli Type
{2,60,4}
Vertices, edges, …
2, 60, 120, 4
Order of s0s1s2s3
60
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

5-fold

6-fold

8-fold

10-fold

12-fold

15-fold

20-fold

24-fold

30-fold

40-fold

60-fold

Covers minimal covers in bold

2-fold

Representations

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