Overview
- Group
- SmallGroup(1728,47319)
- Rank
- 5
- Schläfli Type
- {6,6,2,12}
- Vertices, edges, …
- 6, 18, 6, 12, 12
- 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
8-fold
9-fold
12-fold
18-fold
24-fold
27-fold
36-fold
54-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,14)(12,13)(15,18)(16,17);; s1 := ( 1,15)( 2,11)( 3, 9)( 4,17)( 5, 7)( 6,16)( 8,13)(10,12)(14,18);; s2 := ( 5, 6)( 9,10)(11,12)(13,14)(15,16)(17,18);; s3 := (20,21)(22,23)(25,28)(26,27)(29,30);; s4 := (19,25)(20,22)(21,29)(23,26)(24,27)(28,30);; 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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(30)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,14)(12,13)(15,18)(16,17); s1 := Sym(30)!( 1,15)( 2,11)( 3, 9)( 4,17)( 5, 7)( 6,16)( 8,13)(10,12)(14,18); s2 := Sym(30)!( 5, 6)( 9,10)(11,12)(13,14)(15,16)(17,18); s3 := Sym(30)!(20,21)(22,23)(25,28)(26,27)(29,30); s4 := Sym(30)!(19,25)(20,22)(21,29)(23,26)(24,27)(28,30); poly := sub<Sym(30)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;