Polytope of Type {10,6,4} with group SmallGroup(1920,240592)

Overview

Group: SmallGroup(1920,240592)
Rank: 4
Schläfli Type: {10,6,4}
Vertices, edges, …: 40, 120, 48, 4
Order of s₀s₁s₂s₃: 4
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

{5,6,2}*240a

60-fold

{2,2,4}*32

120-fold

{2,2,2}*16

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

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

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

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

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References