Overview
- Group
- SmallGroup(1920,236178)
- Rank
- 8
- Schläfli Type
- {2,4,2,5,2,3,2}
- Vertices, edges, …
- 2, 4, 4, 5, 5, 3, 3, 2
- Order of s0s1s2s3s4s5s6s7
- 60
- Order of s0s1s2s3s4s5s6s7s6s5s4s3s2s1
- 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
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (4,5);; s2 := (3,4)(5,6);; s3 := ( 8, 9)(10,11);; s4 := ( 7, 8)( 9,10);; s5 := (13,14);; s6 := (12,13);; s7 := (15,16);; poly := Group([s0,s1,s2,s3,s4,s5,s6,s7]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4","s5","s6","s7");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;; s6 := F.7;; s7 := F.8;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s6*s6, s7*s7, s0*s1*s0*s1, s0*s2*s0*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, s4*s5*s4*s5, s0*s6*s0*s6,
s1*s6*s1*s6, s2*s6*s2*s6, s3*s6*s3*s6,
s4*s6*s4*s6, s0*s7*s0*s7, s1*s7*s1*s7,
s2*s7*s2*s7, s3*s7*s3*s7, s4*s7*s4*s7,
s5*s7*s5*s7, s6*s7*s6*s7, s5*s6*s5*s6*s5*s6,
s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(16)!(1,2); s1 := Sym(16)!(4,5); s2 := Sym(16)!(3,4)(5,6); s3 := Sym(16)!( 8, 9)(10,11); s4 := Sym(16)!( 7, 8)( 9,10); s5 := Sym(16)!(13,14); s6 := Sym(16)!(12,13); s7 := Sym(16)!(15,16); poly := sub<Sym(16)|s0,s1,s2,s3,s4,s5,s6,s7>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4,s5,s6,s7> := Group< s0,s1,s2,s3,s4,s5,s6,s7 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, s6*s6, s7*s7, s0*s1*s0*s1, s0*s2*s0*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, s4*s5*s4*s5, s0*s6*s0*s6, s1*s6*s1*s6, s2*s6*s2*s6, s3*s6*s3*s6, s4*s6*s4*s6, s0*s7*s0*s7, s1*s7*s1*s7, s2*s7*s2*s7, s3*s7*s3*s7, s4*s7*s4*s7, s5*s7*s5*s7, s6*s7*s6*s7, s5*s6*s5*s6*s5*s6, s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;