Overview
- Group
- SmallGroup(864,2455)
- Rank
- 4
- Schläfli Type
- {2,12,6}
- Vertices, edges, …
- 2, 36, 108, 18
- Order of s0s1s2s3
- 12
- 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
6-fold
9-fold
12-fold
18-fold
27-fold
36-fold
54-fold
Covers minimal covers in bold
2-fold
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 6, 9)( 7, 10)( 8, 11)( 12, 21)( 13, 22)( 14, 23)( 15, 27)( 16, 28)( 17, 29)( 18, 24)( 19, 25)( 20, 26)( 33, 36)( 34, 37)( 35, 38)( 39, 48)( 40, 49)( 41, 50)( 42, 54)( 43, 55)( 44, 56)( 45, 51)( 46, 52)( 47, 53)( 57, 84)( 58, 85)( 59, 86)( 60, 90)( 61, 91)( 62, 92)( 63, 87)( 64, 88)( 65, 89)( 66,102)( 67,103)( 68,104)( 69,108)( 70,109)( 71,110)( 72,105)( 73,106)( 74,107)( 75, 93)( 76, 94)( 77, 95)( 78, 99)( 79,100)( 80,101)( 81, 96)( 82, 97)( 83, 98);; s2 := ( 3, 79)( 4, 80)( 5, 78)( 6, 77)( 7, 75)( 8, 76)( 9, 81)( 10, 82)( 11, 83)( 12, 70)( 13, 71)( 14, 69)( 15, 68)( 16, 66)( 17, 67)( 18, 72)( 19, 73)( 20, 74)( 21, 61)( 22, 62)( 23, 60)( 24, 59)( 25, 57)( 26, 58)( 27, 63)( 28, 64)( 29, 65)( 30,106)( 31,107)( 32,105)( 33,104)( 34,102)( 35,103)( 36,108)( 37,109)( 38,110)( 39, 97)( 40, 98)( 41, 96)( 42, 95)( 43, 93)( 44, 94)( 45, 99)( 46,100)( 47,101)( 48, 88)( 49, 89)( 50, 87)( 51, 86)( 52, 84)( 53, 85)( 54, 90)( 55, 91)( 56, 92);; s3 := ( 4, 5)( 6, 9)( 7, 11)( 8, 10)( 13, 14)( 15, 18)( 16, 20)( 17, 19)( 22, 23)( 24, 27)( 25, 29)( 26, 28)( 31, 32)( 33, 36)( 34, 38)( 35, 37)( 40, 41)( 42, 45)( 43, 47)( 44, 46)( 49, 50)( 51, 54)( 52, 56)( 53, 55)( 58, 59)( 60, 63)( 61, 65)( 62, 64)( 67, 68)( 69, 72)( 70, 74)( 71, 73)( 76, 77)( 78, 81)( 79, 83)( 80, 82)( 85, 86)( 87, 90)( 88, 92)( 89, 91)( 94, 95)( 96, 99)( 97,101)( 98,100)(103,104)(105,108)(106,110)(107,109);; 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*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s3*s2*s3*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(110)!(1,2); s1 := Sym(110)!( 6, 9)( 7, 10)( 8, 11)( 12, 21)( 13, 22)( 14, 23)( 15, 27)( 16, 28)( 17, 29)( 18, 24)( 19, 25)( 20, 26)( 33, 36)( 34, 37)( 35, 38)( 39, 48)( 40, 49)( 41, 50)( 42, 54)( 43, 55)( 44, 56)( 45, 51)( 46, 52)( 47, 53)( 57, 84)( 58, 85)( 59, 86)( 60, 90)( 61, 91)( 62, 92)( 63, 87)( 64, 88)( 65, 89)( 66,102)( 67,103)( 68,104)( 69,108)( 70,109)( 71,110)( 72,105)( 73,106)( 74,107)( 75, 93)( 76, 94)( 77, 95)( 78, 99)( 79,100)( 80,101)( 81, 96)( 82, 97)( 83, 98); s2 := Sym(110)!( 3, 79)( 4, 80)( 5, 78)( 6, 77)( 7, 75)( 8, 76)( 9, 81)( 10, 82)( 11, 83)( 12, 70)( 13, 71)( 14, 69)( 15, 68)( 16, 66)( 17, 67)( 18, 72)( 19, 73)( 20, 74)( 21, 61)( 22, 62)( 23, 60)( 24, 59)( 25, 57)( 26, 58)( 27, 63)( 28, 64)( 29, 65)( 30,106)( 31,107)( 32,105)( 33,104)( 34,102)( 35,103)( 36,108)( 37,109)( 38,110)( 39, 97)( 40, 98)( 41, 96)( 42, 95)( 43, 93)( 44, 94)( 45, 99)( 46,100)( 47,101)( 48, 88)( 49, 89)( 50, 87)( 51, 86)( 52, 84)( 53, 85)( 54, 90)( 55, 91)( 56, 92); s3 := Sym(110)!( 4, 5)( 6, 9)( 7, 11)( 8, 10)( 13, 14)( 15, 18)( 16, 20)( 17, 19)( 22, 23)( 24, 27)( 25, 29)( 26, 28)( 31, 32)( 33, 36)( 34, 38)( 35, 37)( 40, 41)( 42, 45)( 43, 47)( 44, 46)( 49, 50)( 51, 54)( 52, 56)( 53, 55)( 58, 59)( 60, 63)( 61, 65)( 62, 64)( 67, 68)( 69, 72)( 70, 74)( 71, 73)( 76, 77)( 78, 81)( 79, 83)( 80, 82)( 85, 86)( 87, 90)( 88, 92)( 89, 91)( 94, 95)( 96, 99)( 97,101)( 98,100)(103,104)(105,108)(106,110)(107,109); poly := sub<Sym(110)|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*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s3*s2*s3*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 >;