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

Overview

Group: SmallGroup(1152,157849)
Rank: 3
Schläfli Type: {8,12}
Vertices, edges, …: 48, 288, 72
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

{4,6}*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*s2*s1*s0*(s1*s2)^3*(s1*s0)^2*s1*s2> of order 2

36 facets

36 of {8}*16

28 vertex figures

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

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

24 facets

24 of {8}*16

20 vertex figures

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

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

18 facets

18 of {8}*16

18 vertex figures

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

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

6 facets

6 of {8}*16

10 vertex figures

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

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, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15);;
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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2, 
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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15);
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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2, 
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*s1*s2*s1*s2*s1*s2*s1*s2 >;

References

None.

to this polytope.