Polytope of Type {12,5} with group SmallGroup(1920,241004)

Overview

Group: SmallGroup(1920,241004)
Rank: 3
Schläfli Type: {12,5}
Vertices, edges, …: 192, 480, 80
Order of s₀s₁s₂: 5
Order of s₀s₁s₂s₁: 5
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

{6,5}*960

32-fold

{3,5}*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=<((s1*s0)^2*s1*s2)^2> of order 2

40 facets

40 of {12}*24

96 vertex figures

96 of {5}*10

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

28 facets

26 of {12}*24
2 of {4}*8

64 vertex figures

64 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, 3)( 2,17)( 4, 7)( 5,27)( 6,14)( 8,24)( 9,20)(10,12)(11,19)(13,32)(15,21)(16,26)(23,29)(25,28);;
s2 := ( 1, 2)( 3,31)( 4,20)( 5,16)( 6,10)( 7,32)( 8,23)( 9,19)(11,15)(13,21)(14,30)(18,29)(22,27)(25,28);;
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*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1 ];;
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, 3)( 2,17)( 4, 7)( 5,27)( 6,14)( 8,24)( 9,20)(10,12)(11,19)(13,32)(15,21)(16,26)(23,29)(25,28);
s2 := Sym(32)!( 1, 2)( 3,31)( 4,20)( 5,16)( 6,10)( 7,32)( 8,23)( 9,19)(11,15)(13,21)(14,30)(18,29)(22,27)(25,28);
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*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1 >;

References

None.

to this polytope.