Polytope of Type {6,10} with group SmallGroup(720,771)

Overview

Group: SmallGroup(720,771)
Rank: 3
Schläfli Type: {6,10}
Vertices, edges, …: 36, 180, 60
Order of s₀s₁s₂: 30
Order of s₀s₁s₂s₁: 10
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

{3,10}*360

3-fold

{6,10}*240e

6-fold

12-fold

{3,5}*60

Covers minimal covers in bold

2-fold

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)^4*s1*s0*s2*s1> of order 2

30 facets

30 of {6}*12

24 vertex figures

12 of {10}*20
12 of {5}*10

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

20 facets

20 of {6}*12

12 vertex figures

12 of {10}*20

P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^2> of order 5

12 facets

12 of {6}*12

12 vertex figures

6 of {10}*20
6 of {2}*4

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.