Polytope of Type {5,4,4} with group SmallGroup(960,10882)

Overview

Group: SmallGroup(960,10882)
Rank: 4
Schläfli Type: {5,4,4}
Vertices, edges, …: 30, 60, 48, 4
Order of s₀s₁s₂s₃: 12
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: {{5,4}₆,{4,4|2}}. if this polytope has another name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

4-fold

{5,4,2}*240

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

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

4 facets

4 of 2-fold non-regular quotient of {5,4}*240

16 vertex figures

14 of {4,4}*32
2 of {2,4}*16

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

4 facets

4 of 4-fold non-regular quotient of {5,4}*240

9 vertex figures

6 of {4,4}*32
3 of {2,4}*16

Representations

Permutation Representation (GAP)

s0 := ( 6, 7)( 8, 9)(10,11);;
s1 := ( 5, 6)( 7, 8)(10,11);;
s2 := (3,4)(6,7);;
s3 := (1,3)(2,4);;
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*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(11)!( 6, 7)( 8, 9)(10,11);
s1 := Sym(11)!( 5, 6)( 7, 8)(10,11);
s2 := Sym(11)!(3,4)(6,7);
s3 := Sym(11)!(1,3)(2,4);
poly := sub<Sym(11)|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*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References

None.

to this polytope.