Overview
- Group
- SmallGroup(1728,30882)
- Rank
- 5
- Schläfli Type
- {2,12,6,2}
- Vertices, edges, …
- 2, 36, 108, 18, 2
- Order of s0s1s2s3s4
- 12
- Order of s0s1s2s3s4s3s2s1
- 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
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 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)( 57, 84)( 58, 86)( 59, 85)( 60, 90)( 61, 92)( 62, 91)( 63, 87)( 64, 89)( 65, 88)( 66, 93)( 67, 95)( 68, 94)( 69, 99)( 70,101)( 71,100)( 72, 96)( 73, 98)( 74, 97)( 75,102)( 76,104)( 77,103)( 78,108)( 79,110)( 80,109)( 81,105)( 82,107)( 83,106);; s2 := ( 3, 60)( 4, 61)( 5, 62)( 6, 57)( 7, 58)( 8, 59)( 9, 63)( 10, 64)( 11, 65)( 12, 78)( 13, 79)( 14, 80)( 15, 75)( 16, 76)( 17, 77)( 18, 81)( 19, 82)( 20, 83)( 21, 69)( 22, 70)( 23, 71)( 24, 66)( 25, 67)( 26, 68)( 27, 72)( 28, 73)( 29, 74)( 30, 87)( 31, 88)( 32, 89)( 33, 84)( 34, 85)( 35, 86)( 36, 90)( 37, 91)( 38, 92)( 39,105)( 40,106)( 41,107)( 42,102)( 43,103)( 44,104)( 45,108)( 46,109)( 47,110)( 48, 96)( 49, 97)( 50, 98)( 51, 93)( 52, 94)( 53, 95)( 54, 99)( 55,100)( 56,101);; s3 := ( 3, 12)( 4, 13)( 5, 14)( 6, 20)( 7, 18)( 8, 19)( 9, 16)( 10, 17)( 11, 15)( 24, 29)( 25, 27)( 26, 28)( 30, 39)( 31, 40)( 32, 41)( 33, 47)( 34, 45)( 35, 46)( 36, 43)( 37, 44)( 38, 42)( 51, 56)( 52, 54)( 53, 55)( 57, 66)( 58, 67)( 59, 68)( 60, 74)( 61, 72)( 62, 73)( 63, 70)( 64, 71)( 65, 69)( 78, 83)( 79, 81)( 80, 82)( 84, 93)( 85, 94)( 86, 95)( 87,101)( 88, 99)( 89,100)( 90, 97)( 91, 98)( 92, 96)(105,110)(106,108)(107,109);; s4 := (111,112);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2,
s1*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(112)!(1,2); s1 := Sym(112)!( 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)( 57, 84)( 58, 86)( 59, 85)( 60, 90)( 61, 92)( 62, 91)( 63, 87)( 64, 89)( 65, 88)( 66, 93)( 67, 95)( 68, 94)( 69, 99)( 70,101)( 71,100)( 72, 96)( 73, 98)( 74, 97)( 75,102)( 76,104)( 77,103)( 78,108)( 79,110)( 80,109)( 81,105)( 82,107)( 83,106); s2 := Sym(112)!( 3, 60)( 4, 61)( 5, 62)( 6, 57)( 7, 58)( 8, 59)( 9, 63)( 10, 64)( 11, 65)( 12, 78)( 13, 79)( 14, 80)( 15, 75)( 16, 76)( 17, 77)( 18, 81)( 19, 82)( 20, 83)( 21, 69)( 22, 70)( 23, 71)( 24, 66)( 25, 67)( 26, 68)( 27, 72)( 28, 73)( 29, 74)( 30, 87)( 31, 88)( 32, 89)( 33, 84)( 34, 85)( 35, 86)( 36, 90)( 37, 91)( 38, 92)( 39,105)( 40,106)( 41,107)( 42,102)( 43,103)( 44,104)( 45,108)( 46,109)( 47,110)( 48, 96)( 49, 97)( 50, 98)( 51, 93)( 52, 94)( 53, 95)( 54, 99)( 55,100)( 56,101); s3 := Sym(112)!( 3, 12)( 4, 13)( 5, 14)( 6, 20)( 7, 18)( 8, 19)( 9, 16)( 10, 17)( 11, 15)( 24, 29)( 25, 27)( 26, 28)( 30, 39)( 31, 40)( 32, 41)( 33, 47)( 34, 45)( 35, 46)( 36, 43)( 37, 44)( 38, 42)( 51, 56)( 52, 54)( 53, 55)( 57, 66)( 58, 67)( 59, 68)( 60, 74)( 61, 72)( 62, 73)( 63, 70)( 64, 71)( 65, 69)( 78, 83)( 79, 81)( 80, 82)( 84, 93)( 85, 94)( 86, 95)( 87,101)( 88, 99)( 89,100)( 90, 97)( 91, 98)( 92, 96)(105,110)(106,108)(107,109); s4 := Sym(112)!(111,112); poly := sub<Sym(112)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2, s1*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2 >;