Overview
- Group
- SmallGroup(960,8239)
- Rank
- 4
- Schläfli Type
- {6,8,10}
- Vertices, edges, …
- 6, 24, 40, 10
- Order of s0s1s2s3
- 120
- Order of s0s1s2s3s2s1
- 2
- Also known as
- {{6,8|2},{8,10|2}}. if this polytope has another name.
Special Properties
- 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
16-fold
20-fold
24-fold
30-fold
40-fold
60-fold
Covers minimal covers in bold
2-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 6, 11)( 7, 12)( 8, 13)( 9, 14)( 10, 15)( 21, 26)( 22, 27)( 23, 28)( 24, 29)( 25, 30)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 56)( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 66, 71)( 67, 72)( 68, 73)( 69, 74)( 70, 75)( 81, 86)( 82, 87)( 83, 88)( 84, 89)( 85, 90)( 96,101)( 97,102)( 98,103)( 99,104)(100,105)(111,116)(112,117)(113,118)(114,119)(115,120);; s1 := ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5, 10)( 16, 21)( 17, 22)( 18, 23)( 19, 24)( 20, 25)( 31, 51)( 32, 52)( 33, 53)( 34, 54)( 35, 55)( 36, 46)( 37, 47)( 38, 48)( 39, 49)( 40, 50)( 41, 56)( 42, 57)( 43, 58)( 44, 59)( 45, 60)( 61, 96)( 62, 97)( 63, 98)( 64, 99)( 65,100)( 66, 91)( 67, 92)( 68, 93)( 69, 94)( 70, 95)( 71,101)( 72,102)( 73,103)( 74,104)( 75,105)( 76,111)( 77,112)( 78,113)( 79,114)( 80,115)( 81,106)( 82,107)( 83,108)( 84,109)( 85,110)( 86,116)( 87,117)( 88,118)( 89,119)( 90,120);; s2 := ( 1, 61)( 2, 65)( 3, 64)( 4, 63)( 5, 62)( 6, 66)( 7, 70)( 8, 69)( 9, 68)( 10, 67)( 11, 71)( 12, 75)( 13, 74)( 14, 73)( 15, 72)( 16, 76)( 17, 80)( 18, 79)( 19, 78)( 20, 77)( 21, 81)( 22, 85)( 23, 84)( 24, 83)( 25, 82)( 26, 86)( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31,106)( 32,110)( 33,109)( 34,108)( 35,107)( 36,111)( 37,115)( 38,114)( 39,113)( 40,112)( 41,116)( 42,120)( 43,119)( 44,118)( 45,117)( 46, 91)( 47, 95)( 48, 94)( 49, 93)( 50, 92)( 51, 96)( 52,100)( 53, 99)( 54, 98)( 55, 97)( 56,101)( 57,105)( 58,104)( 59,103)( 60,102);; s3 := ( 1, 2)( 3, 5)( 6, 7)( 8, 10)( 11, 12)( 13, 15)( 16, 17)( 18, 20)( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)( 38, 40)( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)( 58, 60)( 61, 62)( 63, 65)( 66, 67)( 68, 70)( 71, 72)( 73, 75)( 76, 77)( 78, 80)( 81, 82)( 83, 85)( 86, 87)( 88, 90)( 91, 92)( 93, 95)( 96, 97)( 98,100)(101,102)(103,105)(106,107)(108,110)(111,112)(113,115)(116,117)(118,120);; 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, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(120)!( 6, 11)( 7, 12)( 8, 13)( 9, 14)( 10, 15)( 21, 26)( 22, 27)( 23, 28)( 24, 29)( 25, 30)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 56)( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 66, 71)( 67, 72)( 68, 73)( 69, 74)( 70, 75)( 81, 86)( 82, 87)( 83, 88)( 84, 89)( 85, 90)( 96,101)( 97,102)( 98,103)( 99,104)(100,105)(111,116)(112,117)(113,118)(114,119)(115,120); s1 := Sym(120)!( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5, 10)( 16, 21)( 17, 22)( 18, 23)( 19, 24)( 20, 25)( 31, 51)( 32, 52)( 33, 53)( 34, 54)( 35, 55)( 36, 46)( 37, 47)( 38, 48)( 39, 49)( 40, 50)( 41, 56)( 42, 57)( 43, 58)( 44, 59)( 45, 60)( 61, 96)( 62, 97)( 63, 98)( 64, 99)( 65,100)( 66, 91)( 67, 92)( 68, 93)( 69, 94)( 70, 95)( 71,101)( 72,102)( 73,103)( 74,104)( 75,105)( 76,111)( 77,112)( 78,113)( 79,114)( 80,115)( 81,106)( 82,107)( 83,108)( 84,109)( 85,110)( 86,116)( 87,117)( 88,118)( 89,119)( 90,120); s2 := Sym(120)!( 1, 61)( 2, 65)( 3, 64)( 4, 63)( 5, 62)( 6, 66)( 7, 70)( 8, 69)( 9, 68)( 10, 67)( 11, 71)( 12, 75)( 13, 74)( 14, 73)( 15, 72)( 16, 76)( 17, 80)( 18, 79)( 19, 78)( 20, 77)( 21, 81)( 22, 85)( 23, 84)( 24, 83)( 25, 82)( 26, 86)( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31,106)( 32,110)( 33,109)( 34,108)( 35,107)( 36,111)( 37,115)( 38,114)( 39,113)( 40,112)( 41,116)( 42,120)( 43,119)( 44,118)( 45,117)( 46, 91)( 47, 95)( 48, 94)( 49, 93)( 50, 92)( 51, 96)( 52,100)( 53, 99)( 54, 98)( 55, 97)( 56,101)( 57,105)( 58,104)( 59,103)( 60,102); s3 := Sym(120)!( 1, 2)( 3, 5)( 6, 7)( 8, 10)( 11, 12)( 13, 15)( 16, 17)( 18, 20)( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)( 38, 40)( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)( 58, 60)( 61, 62)( 63, 65)( 66, 67)( 68, 70)( 71, 72)( 73, 75)( 76, 77)( 78, 80)( 81, 82)( 83, 85)( 86, 87)( 88, 90)( 91, 92)( 93, 95)( 96, 97)( 98,100)(101,102)(103,105)(106,107)(108,110)(111,112)(113,115)(116,117)(118,120); poly := sub<Sym(120)|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, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References
None.
to this polytope.