Polytope of Type {16,4,5} with group SmallGroup(1920,240469)

Overview

Group: SmallGroup(1920,240469)
Rank: 4
Schläfli Type: {16,4,5}
Vertices, edges, …: 16, 96, 30, 15
Order of s₀s₁s₂s₃: 48
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Universal
Non-Orientable
Flat

Quotients maximal quotients in bold

2-fold

{8,4,5}*960

4-fold

{4,4,5}*480

8-fold

{2,4,5}*240

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := ( 6,14)( 7,15)( 8,17)( 9,16)(10,20)(11,21)(12,18)(13,19)(22,30)(23,31)(24,33)(25,32)(26,36)(27,37)(28,34)(29,35);;
s1 := ( 4, 5)( 6,22)( 7,23)( 8,25)( 9,24)(10,28)(11,29)(12,26)(13,27)(14,34)(15,35)(16,37)(17,36)(18,30)(19,31)(20,33)(21,32);;
s2 := (2,4)(3,5);;
s3 := (1,2)(4,5);;
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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(37)!( 6,14)( 7,15)( 8,17)( 9,16)(10,20)(11,21)(12,18)(13,19)(22,30)(23,31)(24,33)(25,32)(26,36)(27,37)(28,34)(29,35);
s1 := Sym(37)!( 4, 5)( 6,22)( 7,23)( 8,25)( 9,24)(10,28)(11,29)(12,26)(13,27)(14,34)(15,35)(16,37)(17,36)(18,30)(19,31)(20,33)(21,32);
s2 := Sym(37)!(2,4)(3,5);
s3 := Sym(37)!(1,2)(4,5);
poly := sub<Sym(37)|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, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References