Overview
- Group
- SmallGroup(1680,931)
- Rank
- 4
- Schläfli Type
- {5,10,14}
- Vertices, edges, …
- 6, 30, 84, 14
- Order of s0s1s2s3
- 42
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
7-fold
14-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 := ( 9,10)(11,12);; s1 := ( 8, 9)(10,11);; s2 := ( 2, 3)( 4, 5)( 6, 7)( 9,11)(10,12);; s3 := ( 1, 2)( 3, 4)( 5, 6)(13,14);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(14)!( 9,10)(11,12); s1 := Sym(14)!( 8, 9)(10,11); s2 := Sym(14)!( 2, 3)( 4, 5)( 6, 7)( 9,11)(10,12); s3 := Sym(14)!( 1, 2)( 3, 4)( 5, 6)(13,14); poly := sub<Sym(14)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References
None.
to this polytope.