Overview
- Group
- SmallGroup(1280,141629)
- Rank
- 5
- Schläfli Type
- {5,2,8,4}
- Vertices, edges, …
- 5, 5, 16, 32, 8
- Order of s0s1s2s3s4
- 40
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
16-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3)(4,5);; s1 := (1,2)(3,4);; s2 := ( 6,14)( 7,15)( 8,16)( 9,17)(10,20)(11,21)(12,18)(13,19);; s3 := (10,12)(11,13)(14,18)(15,19)(16,20)(17,21);; s4 := (10,11)(12,13)(18,19)(20,21);; 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,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s4*s3*s4*s3*s2*s3*s2*s4*s3*s4*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(21)!(2,3)(4,5); s1 := Sym(21)!(1,2)(3,4); s2 := Sym(21)!( 6,14)( 7,15)( 8,16)( 9,17)(10,20)(11,21)(12,18)(13,19); s3 := Sym(21)!(10,12)(11,13)(14,18)(15,19)(16,20)(17,21); s4 := Sym(21)!(10,11)(12,13)(18,19)(20,21); poly := sub<Sym(21)|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, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s4*s3*s4*s3*s2*s3*s2*s4*s3*s4*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;