Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,60}

Atlas Canonical Name {4,60}*480a

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(480,847)
Rank
3
Schläfli Type
{4,60}
Vertices, edges, …
4, 120, 60
Order of s0s1s2
60
Order of s0s1s2s1
2
Also known as
{4,60|2}. if this polytope has another name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • 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

3-fold

4-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.

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