Overview
- Group
- SmallGroup(256,16894)
- Rank
- 4
- Schläfli Type
- {4,8,4}
- Vertices, edges, …
- 4, 16, 16, 4
- Order of s0s1s2s3
- 8
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
16-fold
Covers minimal covers in bold
2-fold
3-fold
5-fold
7-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 5, 6)( 7, 8)(13,14)(15,16);; s1 := ( 5, 6)( 7, 8)( 9,13)(10,14)(11,15)(12,16);; s2 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,14)( 6,13)( 7,16)( 8,15);; s3 := ( 9,11)(10,12)(13,15)(14,16);; 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, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(16)!( 5, 6)( 7, 8)(13,14)(15,16); s1 := Sym(16)!( 5, 6)( 7, 8)( 9,13)(10,14)(11,15)(12,16); s2 := Sym(16)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,14)( 6,13)( 7,16)( 8,15); s3 := Sym(16)!( 9,11)(10,12)(13,15)(14,16); poly := sub<Sym(16)|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, s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;
References
None.
to this polytope.