Polytope of Type {4,3,3,3} with group SmallGroup(1920,240996)

Overview

Group: SmallGroup(1920,240996)
Rank: 5
Schläfli Type: {4,3,3,3}
Vertices, edges, …: 16, 40, 40, 20, 5
Order of s₀s₁s₂s₃s₄: 5
Order of s₀s₁s₂s₃s₄s₃s₂s₁: 4
Also known as: hemi-5-cube, {4,3,3,3}₅. if this polytope has another name.

Special Properties

Projective
Locally Spherical
Non-Orientable
Flat

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2> of order 2

5 facets

2 of 2-fold non-regular quotient of {4,3,3}*384
3 of 2-fold non-regular quotient of {4,3,3}*384

8 vertex figures

8 of {3,3,3}*120

P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, (s0*s1)^2*s3*s2*s1*s0*s1*s2*s3> of order 4

5 facets

3 of 4-fold non-regular quotient of {4,3,3}*384
2 of 4-fold non-regular quotient of {4,3,3}*384

4 vertex figures

4 of {3,3,3}*120

Representations

Permutation Representation (GAP)

s0 := ( 2, 6)( 3, 7)( 5,10)( 8, 9);;
s1 := (1,2)(4,6);;
s2 := (2,3)(6,7);;
s3 := ( 3, 5)( 7,10);;
s4 := ( 5, 8)( 9,10);;
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, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s0*s2*s1*s0*s2*s1*s2*s3*s2*s1*s4*s0*s3*s2*s1*s0*s1*s2*s3*s4*s1*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(10)!( 2, 6)( 3, 7)( 5,10)( 8, 9);
s1 := Sym(10)!(1,2)(4,6);
s2 := Sym(10)!(2,3)(6,7);
s3 := Sym(10)!( 3, 5)( 7,10);
s4 := Sym(10)!( 5, 8)( 9,10);
poly := sub<Sym(10)|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, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s2*s1*s0*s2*s1*s2*s3*s2*s1*s4*s0*s3*s2*s1*s0*s1*s2*s3*s4*s1*s2*s3 >;

References

None.

to this polytope.