Overview
- Group
- SmallGroup(1600,10271)
- Rank
- 6
- Schläfli Type
- {2,2,2,4,10}
- Vertices, edges, …
- 2, 2, 2, 10, 50, 25
- Order of s0s1s2s3s4s5
- 4
- Order of s0s1s2s3s4s5s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
No regular quotients.
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (3,4);; s2 := (5,6);; s3 := (13,16)(14,15);; s4 := ( 7,12)( 8,14)( 9,16)(10,13)(11,15);; s5 := ( 7, 8)( 9,11)(13,16)(14,15);; poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s3*s4*s3*s4*s3*s4*s3*s4,
s5*s3*s4*s5*s3*s4*s5*s3*s4*s5*s3*s4,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5,
s5*s3*s4*s3*s4*s5*s4*s3*s4*s5*s4*s3*s4*s5*s4*s3*s4*s5*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(16)!(1,2); s1 := Sym(16)!(3,4); s2 := Sym(16)!(5,6); s3 := Sym(16)!(13,16)(14,15); s4 := Sym(16)!( 7,12)( 8,14)( 9,16)(10,13)(11,15); s5 := Sym(16)!( 7, 8)( 9,11)(13,16)(14,15); poly := sub<Sym(16)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, s3*s4*s3*s4*s3*s4*s3*s4, s5*s3*s4*s5*s3*s4*s5*s3*s4*s5*s3*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, s5*s3*s4*s3*s4*s5*s4*s3*s4*s5*s4*s3*s4*s5*s4*s3*s4*s5*s4*s3*s4 >;