Overview
- Group
- SmallGroup(1920,240558)
- Rank
- 4
- Schläfli Type
- {8,6,5}
- Vertices, edges, …
- 8, 96, 60, 20
- Order of s0s1s2s3
- 8
- Order of s0s1s2s3s2s1
- 2
- Also known as
- {{8,6|2},{6,5}4}. if this polytope has another name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
8-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 := ( 1,16)( 2, 9)( 3, 8)( 4,14)( 5,12)( 6,13)( 7,15)(10,11);; s1 := ( 1, 7)( 2, 6)( 3,15)( 4,10)( 5,13)( 8,14)( 9,11)(12,16)(18,21);; s2 := ( 1,16)( 2,14)( 3,13)( 4, 9)( 5,15)( 6, 8)( 7,12)(10,11)(17,20)(19,21);; s3 := ( 1,16)( 2,14)( 3,13)( 4, 9)( 5,15)( 6, 8)( 7,12)(10,11)(18,21)(19,20);; 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*s2*s1*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(21)!( 1,16)( 2, 9)( 3, 8)( 4,14)( 5,12)( 6,13)( 7,15)(10,11); s1 := Sym(21)!( 1, 7)( 2, 6)( 3,15)( 4,10)( 5,13)( 8,14)( 9,11)(12,16)(18,21); s2 := Sym(21)!( 1,16)( 2,14)( 3,13)( 4, 9)( 5,15)( 6, 8)( 7,12)(10,11)(17,20)(19,21); s3 := Sym(21)!( 1,16)( 2,14)( 3,13)( 4, 9)( 5,15)( 6, 8)( 7,12)(10,11)(18,21)(19,20); poly := sub<Sym(21)|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*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.