Polytope of Type {10,8} with group SmallGroup(1440,5843)

Overview

Group: SmallGroup(1440,5843)
Rank: 3
Schläfli Type: {10,8}
Vertices, edges, …: 90, 360, 72
Order of s₀s₁s₂: 3
Order of s₀s₁s₂s₁: 10
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

{10,8}*720b

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*s2*s1)^4*s0*s1*s2> of order 2

36 facets

36 of {10}*20

46 vertex figures

44 of {8}*16
2 of {4}*8

P/N, where N=<s0*s2*(s1*s0)^2*(s1*s2)^2*s1*s0*s1*s2*s1*s0*s2, s0*(s2*s1)^3*(s0*s1)^2*s2*s1*s0*(s1*s2)^2> of order 4

18 facets

18 of {10}*20

24 vertex figures

21 of {8}*16
3 of {4}*8

Representations

Permutation Representation (GAP)

s0 := ( 1, 3)( 2, 6)( 4, 9)( 5, 7)( 8,10);;
s1 := ( 3, 7)( 4, 6)( 5, 8)( 9,10)(11,12);;
s2 := ( 1, 3)( 2, 5)( 4, 8)( 6, 7)( 9,10)(11,12);;
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*s2*s0*s1*s2*s0*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

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

References

None.

to this polytope.