Overview
- Group
- SmallGroup(960,10441)
- Rank
- 4
- Schläfli Type
- {60,4,2}
- Vertices, edges, …
- 60, 120, 4, 2
- 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 := ( 2, 5)( 3, 4)( 6, 11)( 7, 15)( 8, 14)( 9, 13)( 10, 12)( 17, 20)( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 32, 35)( 33, 34)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 47, 50)( 48, 49)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 91)( 62, 95)( 63, 94)( 64, 93)( 65, 92)( 66,101)( 67,105)( 68,104)( 69,103)( 70,102)( 71, 96)( 72,100)( 73, 99)( 74, 98)( 75, 97)( 76,106)( 77,110)( 78,109)( 79,108)( 80,107)( 81,116)( 82,120)( 83,119)( 84,118)( 85,117)( 86,111)( 87,115)( 88,114)( 89,113)( 90,112);; s1 := ( 1, 67)( 2, 66)( 3, 70)( 4, 69)( 5, 68)( 6, 62)( 7, 61)( 8, 65)( 9, 64)( 10, 63)( 11, 72)( 12, 71)( 13, 75)( 14, 74)( 15, 73)( 16, 82)( 17, 81)( 18, 85)( 19, 84)( 20, 83)( 21, 77)( 22, 76)( 23, 80)( 24, 79)( 25, 78)( 26, 87)( 27, 86)( 28, 90)( 29, 89)( 30, 88)( 31, 97)( 32, 96)( 33,100)( 34, 99)( 35, 98)( 36, 92)( 37, 91)( 38, 95)( 39, 94)( 40, 93)( 41,102)( 42,101)( 43,105)( 44,104)( 45,103)( 46,112)( 47,111)( 48,115)( 49,114)( 50,113)( 51,107)( 52,106)( 53,110)( 54,109)( 55,108)( 56,117)( 57,116)( 58,120)( 59,119)( 60,118);; s2 := ( 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);; s3 := (121,122);; 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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(122)!( 2, 5)( 3, 4)( 6, 11)( 7, 15)( 8, 14)( 9, 13)( 10, 12)( 17, 20)( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 32, 35)( 33, 34)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 47, 50)( 48, 49)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 91)( 62, 95)( 63, 94)( 64, 93)( 65, 92)( 66,101)( 67,105)( 68,104)( 69,103)( 70,102)( 71, 96)( 72,100)( 73, 99)( 74, 98)( 75, 97)( 76,106)( 77,110)( 78,109)( 79,108)( 80,107)( 81,116)( 82,120)( 83,119)( 84,118)( 85,117)( 86,111)( 87,115)( 88,114)( 89,113)( 90,112); s1 := Sym(122)!( 1, 67)( 2, 66)( 3, 70)( 4, 69)( 5, 68)( 6, 62)( 7, 61)( 8, 65)( 9, 64)( 10, 63)( 11, 72)( 12, 71)( 13, 75)( 14, 74)( 15, 73)( 16, 82)( 17, 81)( 18, 85)( 19, 84)( 20, 83)( 21, 77)( 22, 76)( 23, 80)( 24, 79)( 25, 78)( 26, 87)( 27, 86)( 28, 90)( 29, 89)( 30, 88)( 31, 97)( 32, 96)( 33,100)( 34, 99)( 35, 98)( 36, 92)( 37, 91)( 38, 95)( 39, 94)( 40, 93)( 41,102)( 42,101)( 43,105)( 44,104)( 45,103)( 46,112)( 47,111)( 48,115)( 49,114)( 50,113)( 51,107)( 52,106)( 53,110)( 54,109)( 55,108)( 56,117)( 57,116)( 58,120)( 59,119)( 60,118); s2 := Sym(122)!( 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); s3 := Sym(122)!(121,122); 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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;