Polytope of Type {6,5} with group SmallGroup(1200,941)

Overview

Group: SmallGroup(1200,941)
Rank: 3
Schläfli Type: {6,5}
Vertices, edges, …: 120, 300, 100
Order of s₀s₁s₂: 20
Order of s₀s₁s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

5-fold

{6,5}*240a

10-fold

{6,5}*120a

60-fold

{2,5}*20

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)^3*(s2*s1)^2*s0*(s1*s2)^2> of order 2

50 facets

50 of {6}*12

60 vertex figures

60 of {5}*10

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

50 facets

50 of {6}*12

60 vertex figures

60 of {5}*10

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

40 facets

10 of {2}*4
30 of {6}*12

40 vertex figures

40 of {5}*10

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

25 facets

25 of {6}*12

30 vertex figures

30 of {5}*10

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

25 facets

25 of {6}*12

30 vertex figures

30 of {5}*10

P/N, where N=<s0*s1*(s2*s1*s0)^3*s2*s1*s2> of order 5

20 facets

20 of {6}*12

24 vertex figures

24 of {5}*10

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

20 facets

5 of {2}*4
15 of {6}*12

20 vertex figures

20 of {5}*10

P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s2, s0*(s2*s1)^2*s0*(s1*s2)^2> of order 10

10 facets

10 of {6}*12

12 vertex figures

12 of {5}*10

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

15 facets

10 of {2}*4
5 of {6}*12

10 vertex figures

10 of {5}*10

P/N, where N=<s0*s1*s2*(s1*s0)^2*s2*s1, (s1*s0)^2*s2*s1*s0*s1*s2> of order 20

5 facets

5 of {6}*12

6 vertex figures

6 of {5}*10

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.