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