Overview
- Group
- SmallGroup(1920,240996)
- Rank
- 4
- Schläfli Type
- {6,6,4}
- Vertices, edges, …
- 16, 120, 80, 16
- Order of s0s1s2s3
- 5
- Order of s0s1s2s3s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Non-Orientable
Quotients maximal quotients in bold
No regular quotients.
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 8)( 6, 7)( 9,10);; s1 := (1,2)(4,6);; s2 := ( 2, 5)( 3, 8)( 6,10)( 7, 9);; s3 := ( 5, 9)( 8,10);; 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, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(10)!( 2, 3)( 5, 8)( 6, 7)( 9,10); s1 := Sym(10)!(1,2)(4,6); s2 := Sym(10)!( 2, 5)( 3, 8)( 6,10)( 7, 9); s3 := Sym(10)!( 5, 9)( 8,10); poly := sub<Sym(10)|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, s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1, s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1 >;
References
None.
to this polytope.