Polytope of Type {10,5} with group SmallGroup(1920,241004)

Overview

Group: SmallGroup(1920,241004)
Rank: 3
Schläfli Type: {10,5}
Vertices, edges, …: 192, 480, 96
Order of s₀s₁s₂: 12
Order of s₀s₁s₂s₁: 12
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

{5,5}*960

32-fold

{5,5}*60

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

48 facets

48 of {10}*20

96 vertex figures

96 of {5}*10

Representations

Permutation Representation (GAP)

s0 := ( 3, 4)( 5,15)( 7, 8)( 9,30)(11,16)(12,17)(13,25)(14,19)(18,29)(20,31)(21,28)(22,27)(23,32)(24,26);;
s1 := ( 1, 6)( 2,14)( 3,10)( 4,23)( 5,19)( 8,21)( 9,17)(12,20)(13,16)(15,32)(24,25)(26,28)(27,30)(29,31);;
s2 := ( 1, 2)( 3,20)( 4,31)( 5,11)( 6,10)( 7,23)( 8,32)( 9,14)(12,17)(13,28)(15,16)(19,30)(21,25)(24,26);;
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*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(32)!( 3, 4)( 5,15)( 7, 8)( 9,30)(11,16)(12,17)(13,25)(14,19)(18,29)(20,31)(21,28)(22,27)(23,32)(24,26);
s1 := Sym(32)!( 1, 6)( 2,14)( 3,10)( 4,23)( 5,19)( 8,21)( 9,17)(12,20)(13,16)(15,32)(24,25)(26,28)(27,30)(29,31);
s2 := Sym(32)!( 1, 2)( 3,20)( 4,31)( 5,11)( 6,10)( 7,23)( 8,32)( 9,14)(12,17)(13,28)(15,16)(19,30)(21,25)(24,26);
poly := sub<Sym(32)|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*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2 >;

References

None.

to this polytope.