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

Overview

Group: SmallGroup(1920,241004)
Rank: 3
Schläfli Type: {5,12}
Vertices, edges, …: 80, 480, 192
Order of s₀s₁s₂: 10
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

{5,6}*960

32-fold

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

96 facets

96 of {5}*10

40 vertex figures

40 of {12}*24

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

64 facets

64 of {5}*10

28 vertex figures

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

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

References

None.

to this polytope.