Polytope of Type {4,10} with group SmallGroup(1440,5843)

Overview

Group: SmallGroup(1440,5843)
Rank: 3
Schläfli Type: {4,10}
Vertices, edges, …: 72, 360, 180
Order of s₀s₁s₂: 10
Order of s₀s₁s₂s₁: 8
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

2-fold

{4,10}*720

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*s0*(s2*s1)^3*s0*(s1*s2)^2*s1> of order 2

90 facets

90 of {4}*8

37 vertex figures

35 of {10}*20
2 of {5}*10

Representations

Permutation Representation (GAP)

s0 := ( 2, 8)( 3, 6)( 4, 9)( 7,10);;
s1 := ( 1, 2)( 4, 9)( 5, 8)( 6,10)(11,12);;
s2 := ( 1, 5)( 2, 3)( 4, 7)( 6, 8)( 9,10);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP)

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

Permutation Representation (Magma)

s0 := Sym(12)!( 2, 8)( 3, 6)( 4, 9)( 7,10);
s1 := Sym(12)!( 1, 2)( 4, 9)( 5, 8)( 6,10)(11,12);
s2 := Sym(12)!( 1, 5)( 2, 3)( 4, 7)( 6, 8)( 9,10);
poly := sub<Sym(12)|s0,s1,s2>;

Finitely Presented Group Representation (Magma)

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

References

None.

to this polytope.