Polytope of Type {8,6,2} with group SmallGroup(192,1313)

Overview

Group: SmallGroup(192,1313)
Rank: 4
Schläfli Type: {8,6,2}
Vertices, edges, …: 8, 24, 6, 2
Order of s₀s₁s₂s₃: 24
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

2-fold

{4,6,2}*96a

3-fold

{8,2,2}*64

4-fold

{2,6,2}*48

6-fold

{4,2,2}*32

8-fold

{2,3,2}*24

12-fold

{2,2,2}*16

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

9-fold

10-fold

Representations

Permutation Representation (GAP)

s0 := ( 2, 5)( 6, 9)( 7,10)( 8,11)(12,15)(13,16)(14,17)(18,21)(19,22);;
s1 := ( 1, 2)( 3, 7)( 4, 6)( 5, 8)( 9,13)(10,12)(11,14)(15,19)(16,18)(17,20)(21,24)(22,23);;
s2 := ( 1, 3)( 2, 6)( 5, 9)( 8,12)(11,15)(14,18)(17,21)(20,23);;
s3 := (25,26);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*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 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(26)!( 2, 5)( 6, 9)( 7,10)( 8,11)(12,15)(13,16)(14,17)(18,21)(19,22);
s1 := Sym(26)!( 1, 2)( 3, 7)( 4, 6)( 5, 8)( 9,13)(10,12)(11,14)(15,19)(16,18)(17,20)(21,24)(22,23);
s2 := Sym(26)!( 1, 3)( 2, 6)( 5, 9)( 8,12)(11,15)(14,18)(17,21)(20,23);
s3 := Sym(26)!(25,26);
poly := sub<Sym(26)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*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 >;