Polytope of Type {12,8} with group SmallGroup(1152,157849)

Overview

Group: SmallGroup(1152,157849)
Rank: 3
Schläfli Type: {12,8}
Vertices, edges, …: 72, 288, 48
Order of s₀s₁s₂: 4
Order of s₀s₁s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

16-fold

{6,4}*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)^6> of order 2

28 facets

8 of {6}*12
20 of {12}*24

36 vertex figures

36 of {8}*16

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

20 facets

6 of {4}*8
14 of {12}*24

24 vertex figures

24 of {8}*16

P/N, where N=<(s0*s1)^6, s0*(s1*s2)^2*(s1*s0)^3*s1*s2*s1*s0*s1*s2> of order 4

18 facets

12 of {6}*12
6 of {12}*24

18 vertex figures

18 of {8}*16

P/N, where N=<(s0*s1)^4, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 12

10 facets

6 of {4}*8
4 of {6}*12

6 vertex figures

6 of {8}*16

Representations

Permutation Representation (GAP)

s0 := ( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15);;
s1 := ( 1, 3)( 2, 4)( 5,15)( 6,16)( 7,13)( 8,14)( 9,11)(10,12);;
s2 := ( 2, 5)( 3,13)( 4, 9)( 7,14)( 8,10)(11,16);;
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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*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 ];;
poly := F / rels;;

Permutation Representation (Magma)

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

References

None.

to this polytope.