Polytope of Type {7,2,10,5}

Atlas Canonical Name {7,2,10,5}*1680b

Overview

Group: SmallGroup(1680,931)
Rank: 5
Schläfli Type: {7,2,10,5}
Vertices, edges, …: 7, 7, 12, 30, 6
Order of s₀s₁s₂s₃s₄: 21
Order of s₀s₁s₂s₃s₄s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Non-Orientable
Flat

Quotients maximal quotients in bold

2-fold

{7,2,5,5}*840

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP)

s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := ( 8,10)( 9,15)(11,19)(12,14)(13,16)(17,18);;
s3 := (10,12)(11,18)(13,19)(14,16);;
s4 := ( 9,16)(11,19)(12,14)(13,15);;
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, 
s2*s3*s4*s2*s3*s4*s2*s3*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(19)!(2,3)(4,5)(6,7);
s1 := Sym(19)!(1,2)(3,4)(5,6);
s2 := Sym(19)!( 8,10)( 9,15)(11,19)(12,14)(13,16)(17,18);
s3 := Sym(19)!(10,12)(11,18)(13,19)(14,16);
s4 := Sym(19)!( 9,16)(11,19)(12,14)(13,15);
poly := sub<Sym(19)|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, s2*s3*s4*s2*s3*s4*s2*s3*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;