Polytope of Type {6,48} with group SmallGroup(1920,240469)

Overview

Group: SmallGroup(1920,240469)
Rank: 3
Schläfli Type: {6,48}
Vertices, edges, …: 20, 480, 160
Order of s₀s₁s₂: 48
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

{6,24}*960a

4-fold

{6,12}*480a

8-fold

{6,6}*240a

16-fold

{6,6}*120

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

80 facets

80 of {6}*12

10 vertex figures

10 of {48}*96

Representations

Permutation Representation (GAP)

s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37);;
s1 := ( 1, 2)( 6,22)( 7,23)( 8,25)( 9,24)(10,28)(11,29)(12,26)(13,27)(14,34)(15,35)(16,37)(17,36)(18,30)(19,31)(20,33)(21,32);;
s2 := ( 2, 4)( 3, 5)( 6,14)( 7,15)( 8,17)( 9,16)(10,20)(11,21)(12,18)(13,19)(22,30)(23,31)(24,33)(25,32)(26,36)(27,37)(28,34)(29,35);;
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*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2, 
s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(37)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37);
s1 := Sym(37)!( 1, 2)( 6,22)( 7,23)( 8,25)( 9,24)(10,28)(11,29)(12,26)(13,27)(14,34)(15,35)(16,37)(17,36)(18,30)(19,31)(20,33)(21,32);
s2 := Sym(37)!( 2, 4)( 3, 5)( 6,14)( 7,15)( 8,17)( 9,16)(10,20)(11,21)(12,18)(13,19)(22,30)(23,31)(24,33)(25,32)(26,36)(27,37)(28,34)(29,35);
poly := sub<Sym(37)|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*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2, 
s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1 >;

References

None.

to this polytope.