Polytope of Type {10,3,4} with group SmallGroup(1440,5848)

Overview

Group: SmallGroup(1440,5848)
Rank: 4
Schläfli Type: {10,3,4}
Vertices, edges, …: 60, 90, 36, 4
Order of s₀s₁s₂s₃: 15
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Universal
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)^3*s1*s2> of order 3

4 facets

4 of 3-fold non-regular quotient of {10,3}*360

20 vertex figures

20 of {3,4}*24

P/N, where N=<(s1*s0)^2*s2*s1*s0*s1*s2> of order 5

4 facets

4 of 5-fold non-regular quotient of {10,3}*360

12 vertex figures

12 of {3,4}*24

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.