Overview
- Group
- SmallGroup(1440,5842)
- Rank
- 5
- Schläfli Type
- {3,3,3,6}
- Vertices, edges, …
- 6, 15, 20, 30, 12
- Order of s0s1s2s3s4
- 6
- Order of s0s1s2s3s4s3s2s1
- 6
- Also known as
- {{3,3},{3,3},{3,6}4}. if this polytope has another name.
Special Properties
- Universal
- Orientable
Quotients maximal quotients in bold
2-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := (3,5);; s1 := (5,6);; s2 := (4,6);; s3 := (2,4);; s4 := (1,2)(7,8);; 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, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3,
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(8)!(3,5); s1 := Sym(8)!(5,6); s2 := Sym(8)!(4,6); s3 := Sym(8)!(2,4); s4 := Sym(8)!(1,2)(7,8); poly := sub<Sym(8)|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, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3 >;
References
None.
to this polytope.