Polytope of Type {2,12,4,2} with group SmallGroup(384,20049)

Overview

Group: SmallGroup(384,20049)
Rank: 5
Schläfli Type: {2,12,4,2}
Vertices, edges, …: 2, 12, 24, 4, 2
Order of s₀s₁s₂s₃s₄: 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Non-Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

2-fold

{2,6,4,2}*192c

4-fold

{2,3,4,2}*96

Covers minimal covers in bold

2-fold

3-fold

5-fold

Representations

Permutation Representation (GAP)

s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8,18)(10,14)(11,13)(12,26)(15,31)(16,34)(17,19)(20,36)(21,22)(23,39)(24,42)(25,32)(27,30)(28,46)(29,43)(33,45)(37,48)(38,40)(41,50)(44,47);;
s2 := ( 3,10)( 4, 6)( 5,21)( 7,11)( 8,45)( 9,13)(12,36)(14,22)(15,50)(16,44)(17,28)(18,27)(19,31)(20,25)(23,46)(24,35)(26,40)(29,49)(30,41)(32,39)(33,38)(34,43)(37,47)(42,48);;
s3 := ( 3,35)( 4,44)( 5,47)( 6,36)( 7,20)( 8,18)( 9,49)(10,45)(11,28)(12,31)(13,46)(14,33)(15,26)(16,19)(17,34)(21,50)(22,41)(23,39)(24,27)(25,43)(29,32)(30,42)(37,40)(38,48);;
s4 := (51,52);;
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, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s2*s1*s3*s2*s3*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(52)!(1,2);
s1 := Sym(52)!( 4, 5)( 6, 7)( 8,18)(10,14)(11,13)(12,26)(15,31)(16,34)(17,19)(20,36)(21,22)(23,39)(24,42)(25,32)(27,30)(28,46)(29,43)(33,45)(37,48)(38,40)(41,50)(44,47);
s2 := Sym(52)!( 3,10)( 4, 6)( 5,21)( 7,11)( 8,45)( 9,13)(12,36)(14,22)(15,50)(16,44)(17,28)(18,27)(19,31)(20,25)(23,46)(24,35)(26,40)(29,49)(30,41)(32,39)(33,38)(34,43)(37,47)(42,48);
s3 := Sym(52)!( 3,35)( 4,44)( 5,47)( 6,36)( 7,20)( 8,18)( 9,49)(10,45)(11,28)(12,31)(13,46)(14,33)(15,26)(16,19)(17,34)(21,50)(22,41)(23,39)(24,27)(25,43)(29,32)(30,42)(37,40)(38,48);
s4 := Sym(52)!(51,52);
poly := sub<Sym(52)|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, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*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 >;