Polytope of Type {6,4} with group SmallGroup(1152,157849)

Overview

Group: SmallGroup(1152,157849)
Rank: 3
Schläfli Type: {6,4}
Vertices, edges, …: 144, 288, 96
Order of s₀s₁s₂: 8
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)^2*s0*s2*s1*s0*s1*(s2*s1*s0)^3*s1> of order 2

48 facets

48 of {6}*12

72 vertex figures

72 of {4}*8

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

48 facets

48 of {6}*12

72 vertex figures

72 of {4}*8

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

32 facets

32 of {6}*12

48 vertex figures

48 of {4}*8

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

24 facets

24 of {6}*12

36 vertex figures

36 of {4}*8

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

24 facets

24 of {6}*12

36 vertex figures

36 of {4}*8

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

24 facets

24 of {6}*12

36 vertex figures

36 of {4}*8

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

24 facets

24 of {6}*12

36 vertex figures

36 of {4}*8

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

24 facets

24 of {6}*12

36 vertex figures

36 of {4}*8

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

24 facets

24 of {6}*12

36 vertex figures

36 of {4}*8

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

24 facets

24 of {6}*12

36 vertex figures

36 of {4}*8

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

24 facets

24 of {6}*12

36 vertex figures

36 of {4}*8

P/N, where N=<(s0*s1)^3*s2*(s1*s0)^2*s1*s2, (s0*s1)^2*s0*s2*(s1*s0)^2*s1*s2*s1, (s0*s1*s2*s1)^2*s0*(s1*s2)^2> of order 8

12 facets

12 of {6}*12

18 vertex figures

18 of {4}*8

P/N, where N=<(s0*s1)^3*s2*(s1*s0)^2*s1*s2, (s0*s1*s2*s1)^2*s0*(s1*s2)^2, (s1*s0*s1*s2)^2*s1*s0*s2*s1*s2> of order 8

12 facets

12 of {6}*12

18 vertex figures

18 of {4}*8

P/N, where N=<s0*s1*s2*(s1*s0)^2*s1*s2*s1, (s1*s0)^2*(s2*s1*s0)^2*(s1*s2)^2> of order 8

12 facets

12 of {6}*12

18 vertex figures

18 of {4}*8

P/N, where N=<(s0*s1)^3*s2*(s1*s0)^2*s1*s2, (s0*s1)^2*s2*s1*s0*s1*s2*s1*s0*s2*s1> of order 8

12 facets

12 of {6}*12

18 vertex figures

18 of {4}*8

P/N, where N=<(s0*s1)^3*s2*(s1*s0)^2*s1*s2, (s0*s1*s2*s1)^2*s0*(s1*s2)^2, (s1*s0)^2*(s2*s1*s0)^2*s1*s2*s1> of order 8

12 facets

12 of {6}*12

18 vertex figures

18 of {4}*8

P/N, where N=<(s0*s1)^3*s2*(s1*s0)^2*s1*s2, (s0*s1*s2*s1)^2*s0*(s1*s2)^2, (s0*s1)^2*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 8

12 facets

12 of {6}*12

18 vertex figures

18 of {4}*8

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

8 facets

8 of {6}*12

12 vertex figures

12 of {4}*8

P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2, (s0*s1)^3*s2*(s1*s0)^2*s1*s2, (s0*s1)^2*s0*s2*(s1*s0)^2*s1*s2*s1> of order 16

6 facets

6 of {6}*12

9 vertex figures

9 of {4}*8

P/N, where N=<s0*(s1*s0*s2)^3*s1, (s0*s1)^3*s2*(s1*s0)^2*s1*s2, (s1*s0)^2*(s2*s1*s0)^2*s1*s2*s1> of order 16

6 facets

6 of {6}*12

9 vertex figures

9 of {4}*8

P/N, where N=<(s1*s0*s2)^3*s1*s2, (s0*s1)^3*s2*(s1*s0)^2*s1*s2, (s0*s1)^2*s0*s2*(s1*s0)^2*s1*s2*s1> of order 16

6 facets

6 of {6}*12

9 vertex figures

9 of {4}*8

P/N, where N=<(s1*s0*s2)^3*s1*s2, (s0*s1)^3*s2*(s1*s0)^2*s1*s2, (s0*s1)^2*s2*s1*s0*s1*s2*s1*s0*s2*s1> of order 16

6 facets

6 of {6}*12

9 vertex figures

9 of {4}*8

Representations

Permutation Representation (GAP)

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

References

None.

to this polytope.

Overview

Special Properties

Related Polytopes

Quotients maximal quotients in bold

Covers minimal covers in bold

Irregular Quotients of which this is a minimal cover

Representations

References

Twisty Puzzle