Polytope of Type {4,8} with group SmallGroup(1440,5843)

Overview

Group: SmallGroup(1440,5843)
Rank: 3
Schläfli Type: {4,8}
Vertices, edges, …: 90, 360, 180
Order of s₀s₁s₂: 10
Order of s₀s₁s₂s₁: 10
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{4,8}*720

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

92 facets

88 of {4}*8
4 of {2}*4

46 vertex figures

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

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

60 facets

60 of {4}*8

30 vertex figures

30 of {8}*16

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

48 facets

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

24 vertex figures

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

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

32 facets

4 of {2}*4
28 of {4}*8

16 vertex figures

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

P/N, where N=<s0*s2*s1*s0*s1*s2*s1*s0*(s2*s1)^2, s0*s1*s0*s2*s1*s0*s1*(s2*s1*s0)^2*s2> of order 9

20 facets

20 of {4}*8

10 vertex figures

10 of {8}*16

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

16 facets

14 of {4}*8
2 of {2}*4

8 vertex figures

7 of {8}*16
1 of {4}*8

P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*s1*s2*s1*s0*(s2*s1)^2, s0*s2*s1*s0*(s2*s1)^2*s0*s1*s2*s1> of order 18

12 facets

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

6 vertex figures

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

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.