Polytope of Type {6,16} with group SmallGroup(192,469)

Overview

Group: SmallGroup(192,469)
Rank: 3
Schläfli Type: {6,16}
Vertices, edges, …: 6, 48, 16
Order of s₀s₁s₂: 48
Order of s₀s₁s₂s₁: 2
Also known as: {6,16|2}. if this polytope has another name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

2-fold

{6,8}*96

3-fold

{2,16}*64

4-fold

{6,4}*48a

6-fold

{2,8}*32

8-fold

{6,2}*24

12-fold

{2,4}*16

16-fold

{3,2}*12

24-fold

{2,2}*8

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

9-fold

10-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48);;
s1 := ( 1, 2)( 4, 5)( 7,11)( 8,10)( 9,12)(13,20)(14,19)(15,21)(16,23)(17,22)(18,24)(25,44)(26,43)(27,45)(28,47)(29,46)(30,48)(31,38)(32,37)(33,39)(34,41)(35,40)(36,42);;
s2 := ( 1,25)( 2,26)( 3,27)( 4,28)( 5,29)( 6,30)( 7,34)( 8,35)( 9,36)(10,31)(11,32)(12,33)(13,43)(14,44)(15,45)(16,46)(17,47)(18,48)(19,37)(20,38)(21,39)(22,40)(23,41)(24,42);;
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*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(48)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48);
s1 := Sym(48)!( 1, 2)( 4, 5)( 7,11)( 8,10)( 9,12)(13,20)(14,19)(15,21)(16,23)(17,22)(18,24)(25,44)(26,43)(27,45)(28,47)(29,46)(30,48)(31,38)(32,37)(33,39)(34,41)(35,40)(36,42);
s2 := Sym(48)!( 1,25)( 2,26)( 3,27)( 4,28)( 5,29)( 6,30)( 7,34)( 8,35)( 9,36)(10,31)(11,32)(12,33)(13,43)(14,44)(15,45)(16,46)(17,47)(18,48)(19,37)(20,38)(21,39)(22,40)(23,41)(24,42);
poly := sub<Sym(48)|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*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References