Polytope of Type {4,8} with group SmallGroup(1344,11295)

Overview

Group: SmallGroup(1344,11295)
Rank: 3
Schläfli Type: {4,8}
Vertices, edges, …: 84, 336, 168
Order of s₀s₁s₂: 12
Order of s₀s₁s₂s₁: 8
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

2-fold

{4,8}*672d

4-fold

{4,8}*336b

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)^2*s1)^3> of order 2

84 facets

84 of {4}*8

42 vertex figures

42 of {8}*16

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

88 facets

80 of {4}*8
8 of {2}*4

44 vertex figures

4 of {4}*8
40 of {8}*16

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

56 facets

56 of {4}*8

28 vertex figures

28 of {8}*16

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

48 facets

36 of {4}*8
12 of {2}*4

24 vertex figures

6 of {4}*8
18 of {8}*16

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

44 facets

40 of {4}*8
4 of {2}*4

24 vertex figures

4 of {2}*4
20 of {8}*16

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

32 facets

24 of {4}*8
8 of {2}*4

16 vertex figures

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

P/N, where N=<(s1*s2)^4, s1*(s2*s1*s0)^2*s2*s1*s2> of order 8

26 facets

16 of {4}*8
10 of {2}*4

13 vertex figures

5 of {4}*8
8 of {8}*16

P/N, where N=<(s0*s1)^2, s0*(s2*s1)^3*s0*(s1*s2)^3> of order 12

16 facets

4 of {2}*4
12 of {4}*8

8 vertex figures

6 of {8}*16
2 of {4}*8

P/N, where N=<(s0*s1)^2, (s1*s2)^4, s0*(s1*s2)^3*s1*s0*s2> of order 24

10 facets

6 of {2}*4
4 of {4}*8

5 vertex figures

3 of {4}*8
2 of {8}*16

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.