Polytope of Type {2,2,4,12} with group SmallGroup(384,18267)

Overview

Group: SmallGroup(384,18267)
Rank: 5
Schläfli Type: {2,2,4,12}
Vertices, edges, …: 2, 2, 4, 24, 12
Order of s₀s₁s₂s₃s₄: 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Orientable
Flat

Related Polytopes

Constructions

Facet of

{2,2,4,12,2} ·768

Vertex figure of

Quotients maximal quotients in bold

2-fold

3-fold

{2,2,4,4}*128

4-fold

{2,2,2,6}*96

6-fold

8-fold

{2,2,2,3}*48

12-fold

{2,2,2,2}*32

Covers minimal covers in bold

2-fold

3-fold

5-fold

Representations

Permutation Representation (GAP)

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6,10)( 7,14)(12,19)(13,20)(15,23)(16,24);;
s3 := ( 5, 6)( 7,11)( 8,13)( 9,12)(10,18)(14,17)(15,22)(16,21)(19,28)(20,27)(23,26)(24,25);;
s4 := ( 5, 8)( 6,15)( 7,12)(10,23)(11,21)(13,16)(14,19)(17,25)(18,27)(20,24);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(28)!(1,2);
s1 := Sym(28)!(3,4);
s2 := Sym(28)!( 6,10)( 7,14)(12,19)(13,20)(15,23)(16,24);
s3 := Sym(28)!( 5, 6)( 7,11)( 8,13)( 9,12)(10,18)(14,17)(15,22)(16,21)(19,28)(20,27)(23,26)(24,25);
s4 := Sym(28)!( 5, 8)( 6,15)( 7,12)(10,23)(11,21)(13,16)(14,19)(17,25)(18,27)(20,24);
poly := sub<Sym(28)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;