Overview
- Group
- SmallGroup(864,2501)
- Rank
- 4
- Schläfli Type
- {2,18,12}
- Vertices, edges, …
- 2, 18, 108, 12
- Order of s0s1s2s3
- 36
- 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 := ( 4, 5)( 6, 9)( 7, 11)( 8, 10)( 12, 22)( 13, 21)( 14, 23)( 15, 28)( 16, 27)( 17, 29)( 18, 25)( 19, 24)( 20, 26)( 31, 32)( 33, 36)( 34, 38)( 35, 37)( 39, 49)( 40, 48)( 41, 50)( 42, 55)( 43, 54)( 44, 56)( 45, 52)( 46, 51)( 47, 53)( 58, 59)( 60, 63)( 61, 65)( 62, 64)( 66, 76)( 67, 75)( 68, 77)( 69, 82)( 70, 81)( 71, 83)( 72, 79)( 73, 78)( 74, 80)( 85, 86)( 87, 90)( 88, 92)( 89, 91)( 93,103)( 94,102)( 95,104)( 96,109)( 97,108)( 98,110)( 99,106)(100,105)(101,107);; s2 := ( 3, 69)( 4, 71)( 5, 70)( 6, 66)( 7, 68)( 8, 67)( 9, 72)( 10, 74)( 11, 73)( 12, 60)( 13, 62)( 14, 61)( 15, 57)( 16, 59)( 17, 58)( 18, 63)( 19, 65)( 20, 64)( 21, 79)( 22, 78)( 23, 80)( 24, 76)( 25, 75)( 26, 77)( 27, 82)( 28, 81)( 29, 83)( 30, 96)( 31, 98)( 32, 97)( 33, 93)( 34, 95)( 35, 94)( 36, 99)( 37,101)( 38,100)( 39, 87)( 40, 89)( 41, 88)( 42, 84)( 43, 86)( 44, 85)( 45, 90)( 46, 92)( 47, 91)( 48,106)( 49,105)( 50,107)( 51,103)( 52,102)( 53,104)( 54,109)( 55,108)( 56,110);; s3 := ( 6, 9)( 7, 10)( 8, 11)( 15, 18)( 16, 19)( 17, 20)( 24, 27)( 25, 28)( 26, 29)( 33, 36)( 34, 37)( 35, 38)( 42, 45)( 43, 46)( 44, 47)( 51, 54)( 52, 55)( 53, 56)( 57, 84)( 58, 85)( 59, 86)( 60, 90)( 61, 91)( 62, 92)( 63, 87)( 64, 88)( 65, 89)( 66, 93)( 67, 94)( 68, 95)( 69, 99)( 70,100)( 71,101)( 72, 96)( 73, 97)( 74, 98)( 75,102)( 76,103)( 77,104)( 78,108)( 79,109)( 80,110)( 81,105)( 82,106)( 83,107);; 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,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*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(110)!(1,2); s1 := Sym(110)!( 4, 5)( 6, 9)( 7, 11)( 8, 10)( 12, 22)( 13, 21)( 14, 23)( 15, 28)( 16, 27)( 17, 29)( 18, 25)( 19, 24)( 20, 26)( 31, 32)( 33, 36)( 34, 38)( 35, 37)( 39, 49)( 40, 48)( 41, 50)( 42, 55)( 43, 54)( 44, 56)( 45, 52)( 46, 51)( 47, 53)( 58, 59)( 60, 63)( 61, 65)( 62, 64)( 66, 76)( 67, 75)( 68, 77)( 69, 82)( 70, 81)( 71, 83)( 72, 79)( 73, 78)( 74, 80)( 85, 86)( 87, 90)( 88, 92)( 89, 91)( 93,103)( 94,102)( 95,104)( 96,109)( 97,108)( 98,110)( 99,106)(100,105)(101,107); s2 := Sym(110)!( 3, 69)( 4, 71)( 5, 70)( 6, 66)( 7, 68)( 8, 67)( 9, 72)( 10, 74)( 11, 73)( 12, 60)( 13, 62)( 14, 61)( 15, 57)( 16, 59)( 17, 58)( 18, 63)( 19, 65)( 20, 64)( 21, 79)( 22, 78)( 23, 80)( 24, 76)( 25, 75)( 26, 77)( 27, 82)( 28, 81)( 29, 83)( 30, 96)( 31, 98)( 32, 97)( 33, 93)( 34, 95)( 35, 94)( 36, 99)( 37,101)( 38,100)( 39, 87)( 40, 89)( 41, 88)( 42, 84)( 43, 86)( 44, 85)( 45, 90)( 46, 92)( 47, 91)( 48,106)( 49,105)( 50,107)( 51,103)( 52,102)( 53,104)( 54,109)( 55,108)( 56,110); s3 := Sym(110)!( 6, 9)( 7, 10)( 8, 11)( 15, 18)( 16, 19)( 17, 20)( 24, 27)( 25, 28)( 26, 29)( 33, 36)( 34, 37)( 35, 38)( 42, 45)( 43, 46)( 44, 47)( 51, 54)( 52, 55)( 53, 56)( 57, 84)( 58, 85)( 59, 86)( 60, 90)( 61, 91)( 62, 92)( 63, 87)( 64, 88)( 65, 89)( 66, 93)( 67, 94)( 68, 95)( 69, 99)( 70,100)( 71,101)( 72, 96)( 73, 97)( 74, 98)( 75,102)( 76,103)( 77,104)( 78,108)( 79,109)( 80,110)( 81,105)( 82,106)( 83,107); 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, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*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 >;