Polytope of Type {8,3} with group SmallGroup(1008,881)

Overview

Group: SmallGroup(1008,881)
Rank: 3
Schläfli Type: {8,3}
Vertices, edges, …: 168, 252, 63
Order of s₀s₁s₂: 21
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

3-fold

{8,3}*336b

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

21 facets

21 of {8}*16

56 vertex figures

56 of {3}*6

P/N, where N=<s0*s1*s2*(s1*s0)^2*s2*s1> of order 7

9 facets

9 of {8}*16

24 vertex figures

24 of {3}*6

P/N, where N=<s0*s1*s2*(s1*s0)^2*s2*s1, (s0*s1)^4*s2*s1*s0*s1*s2> of order 21

3 facets

3 of {8}*16

8 vertex figures

8 of {3}*6

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.