Polytope of Type {6,4,2,5} with group SmallGroup(960,11372)

Overview

Group: SmallGroup(960,11372)
Rank: 5
Schläfli Type: {6,4,2,5}
Vertices, edges, …: 12, 24, 8, 5, 5
Order of s₀s₁s₂s₃s₄: 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Orientable
Flat

Related Polytopes

Constructions

Facet of

{6,4,2,5,2} ·1920

Vertex figure of

{2,6,4,2,5} ·1920

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

{3,2,2,5}*120

12-fold

{2,2,2,5}*80

Covers minimal covers in bold

2-fold

Representations

Permutation Representation (GAP)

s0 := ( 8, 9)(11,12)(13,14)(15,16);;
s1 := ( 1, 2)( 3, 5)( 4,11)( 6, 8)( 7,15)( 9,12)(10,13)(14,16);;
s2 := ( 1, 7)( 2,10)( 3, 4)( 5, 6)( 8,14)( 9,13)(11,16)(12,15);;
s3 := (18,19)(20,21);;
s4 := (17,18)(19,20);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(21)!( 8, 9)(11,12)(13,14)(15,16);
s1 := Sym(21)!( 1, 2)( 3, 5)( 4,11)( 6, 8)( 7,15)( 9,12)(10,13)(14,16);
s2 := Sym(21)!( 1, 7)( 2,10)( 3, 4)( 5, 6)( 8,14)( 9,13)(11,16)(12,15);
s3 := Sym(21)!(18,19)(20,21);
s4 := Sym(21)!(17,18)(19,20);
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, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1 >;