Overview
- Group
- SmallGroup(1728,47887)
- Rank
- 5
- Schläfli Type
- {2,2,6,4}
- Vertices, edges, …
- 2, 2, 54, 108, 36
- 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
3-fold
6-fold
9-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 := (3,4);; s2 := ( 6, 7)( 8,11)( 9,13)(10,12)(15,16)(17,20)(18,22)(19,21);; s3 := ( 5,18)( 6,17)( 7,19)( 8,21)( 9,20)(10,22)(11,15)(12,14)(13,16);; s4 := ( 8,11)( 9,12)(10,13);; 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, s1*s2*s1*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*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s2*s3*s2*s3*s4*s3*s2*s3*s4*s2*s3*s2*s3*s4*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(22)!(1,2); s1 := Sym(22)!(3,4); s2 := Sym(22)!( 6, 7)( 8,11)( 9,13)(10,12)(15,16)(17,20)(18,22)(19,21); s3 := Sym(22)!( 5,18)( 6,17)( 7,19)( 8,21)( 9,20)(10,22)(11,15)(12,14)(13,16); s4 := Sym(22)!( 8,11)( 9,12)(10,13); poly := sub<Sym(22)|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, s1*s2*s1*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*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s2*s3*s2*s3*s4*s3*s2*s3*s4*s2*s3*s2*s3*s4*s3 >;