Overview
- Group
- SmallGroup(896,19315)
- Rank
- 7
- Schläfli Type
- {7,2,2,2,2,4}
- Vertices, edges, …
- 7, 7, 2, 2, 2, 4, 4
- Order of s0s1s2s3s4s5s6
- 28
- Order of s0s1s2s3s4s5s6s5s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
Covers minimal covers in bold
2-fold
Representations
Permutation Representation (GAP)
s0 := (2,3)(4,5)(6,7);; s1 := (1,2)(3,4)(5,6);; s2 := (8,9);; s3 := (10,11);; s4 := (12,13);; s5 := (15,16);; s6 := (14,15)(16,17);; poly := Group([s0,s1,s2,s3,s4,s5,s6]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4","s5","s6");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;; s6 := F.7;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s6*s6, 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, s3*s4*s3*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s4*s5*s4*s5, s0*s6*s0*s6,
s1*s6*s1*s6, s2*s6*s2*s6, s3*s6*s3*s6,
s4*s6*s4*s6, s5*s6*s5*s6*s5*s6*s5*s6,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(17)!(2,3)(4,5)(6,7); s1 := Sym(17)!(1,2)(3,4)(5,6); s2 := Sym(17)!(8,9); s3 := Sym(17)!(10,11); s4 := Sym(17)!(12,13); s5 := Sym(17)!(15,16); s6 := Sym(17)!(14,15)(16,17); poly := sub<Sym(17)|s0,s1,s2,s3,s4,s5,s6>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4,s5,s6> := Group< s0,s1,s2,s3,s4,s5,s6 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, s6*s6, 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, s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, s0*s6*s0*s6, s1*s6*s1*s6, s2*s6*s2*s6, s3*s6*s3*s6, s4*s6*s4*s6, s5*s6*s5*s6*s5*s6*s5*s6, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;