Polytope of Type {8,8} with group SmallGroup(1152,157849)

Overview

Group: SmallGroup(1152,157849)
Rank: 3
Schläfli Type: {8,8}
Vertices, edges, …: 72, 288, 72
Order of s₀s₁s₂: 6
Order of s₀s₁s₂s₁: 3
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Dual

Quotients maximal quotients in bold

16-fold

{4,4}*72

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)^4> of order 2

40 facets

8 of {4}*8
32 of {8}*16

40 vertex figures

32 of {8}*16
8 of {4}*8

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

24 facets

12 of {4}*8
12 of {8}*16

24 vertex figures

12 of {8}*16
12 of {4}*8

Representations

Permutation Representation (GAP)

s0 := ( 2, 5)( 3, 9)( 4,13)( 7,10)( 8,14)(12,15);;
s1 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,15)(10,16)(11,13)(12,14);;
s2 := ( 2,13)( 3, 9)( 4, 5)( 6,16)( 7,12)(10,15);;
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*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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(16)!( 2, 5)( 3, 9)( 4,13)( 7,10)( 8,14)(12,15);
s1 := Sym(16)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,15)(10,16)(11,13)(12,14);
s2 := Sym(16)!( 2,13)( 3, 9)( 4, 5)( 6,16)( 7,12)(10,15);
poly := sub<Sym(16)|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*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References

None.

to this polytope.