Polytope of Type {6,12} with group SmallGroup(1152,157478)

Overview

Group: SmallGroup(1152,157478)
Rank: 3
Schläfli Type: {6,12}
Vertices, edges, …: 48, 288, 96
Order of s₀s₁s₂: 6
Order of s₀s₁s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{6,6}*576d

32-fold

{6,3}*36

96-fold

{2,3}*12

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

48 facets

48 of {6}*12

24 vertex figures

24 of {12}*24

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

32 facets

32 of {6}*12

20 vertex figures

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

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

24 facets

24 of {6}*12

12 vertex figures

12 of {12}*24

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

24 facets

24 of {6}*12

12 vertex figures

12 of {12}*24

Representations

Permutation Representation (GAP)

s0 := ( 5, 8)( 6, 7)(11,13)(12,14)(19,24)(20,23);;
s1 := ( 1, 9)( 2,10)( 3,12)( 4,11)( 5,15)( 6,16)( 7,13)( 8,14)(19,20)(21,23)(22,24);;
s2 := ( 3, 4)( 5, 8)( 6, 7)( 9,22)(10,21)(11,23)(12,24)(13,20)(14,19)(15,18)(16,17);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, 
s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(24)!( 5, 8)( 6, 7)(11,13)(12,14)(19,24)(20,23);
s1 := Sym(24)!( 1, 9)( 2,10)( 3,12)( 4,11)( 5,15)( 6,16)( 7,13)( 8,14)(19,20)(21,23)(22,24);
s2 := Sym(24)!( 3, 4)( 5, 8)( 6, 7)( 9,22)(10,21)(11,23)(12,24)(13,20)(14,19)(15,18)(16,17);
poly := sub<Sym(24)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, 
s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1 >;

References

None.

to this polytope.