Polytope of Type {2,2,2,24} with group SmallGroup(384,19724)

Overview

Group: SmallGroup(384,19724)
Rank: 5
Schläfli Type: {2,2,2,24}
Vertices, edges, …: 2, 2, 2, 24, 24
Order of s₀s₁s₂s₃s₄: 24
Order of s₀s₁s₂s₃s₄s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Orientable
Flat

Related Polytopes

Constructions

Facet of

{2,2,2,24,2} ·768

Vertex figure of

Quotients maximal quotients in bold

2-fold

{2,2,2,12}*192

3-fold

{2,2,2,8}*128

4-fold

{2,2,2,6}*96

6-fold

{2,2,2,4}*64

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 := (5,6);;
s3 := ( 8, 9)(10,11)(12,15)(13,17)(14,16)(18,21)(19,23)(20,22)(25,28)(26,27)(29,30);;
s4 := ( 7,13)( 8,10)( 9,19)(11,14)(12,16)(15,25)(17,20)(18,22)(21,29)(23,26)(24,27)(28,30);;
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, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*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(30)!(1,2);
s1 := Sym(30)!(3,4);
s2 := Sym(30)!(5,6);
s3 := Sym(30)!( 8, 9)(10,11)(12,15)(13,17)(14,16)(18,21)(19,23)(20,22)(25,28)(26,27)(29,30);
s4 := Sym(30)!( 7,13)( 8,10)( 9,19)(11,14)(12,16)(15,25)(17,20)(18,22)(21,29)(23,26)(24,27)(28,30);
poly := sub<Sym(30)|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, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;