Polytope of Type {6,2,2,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,2,4}*192
if this polytope has a name.
Group : SmallGroup(192,1514)
Rank : 5
Schlafli Type : {6,2,2,4}
Number of vertices, edges, etc : 6, 6, 2, 4, 4
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,2,2,4,2} of size 384
   {6,2,2,4,3} of size 576
   {6,2,2,4,4} of size 768
   {6,2,2,4,6} of size 1152
   {6,2,2,4,3} of size 1152
   {6,2,2,4,6} of size 1152
   {6,2,2,4,6} of size 1152
   {6,2,2,4,9} of size 1728
   {6,2,2,4,4} of size 1728
   {6,2,2,4,6} of size 1728
   {6,2,2,4,10} of size 1920
Vertex Figure Of :
   {2,6,2,2,4} of size 384
   {3,6,2,2,4} of size 576
   {4,6,2,2,4} of size 768
   {3,6,2,2,4} of size 768
   {4,6,2,2,4} of size 768
   {4,6,2,2,4} of size 768
   {4,6,2,2,4} of size 1152
   {6,6,2,2,4} of size 1152
   {6,6,2,2,4} of size 1152
   {6,6,2,2,4} of size 1152
   {9,6,2,2,4} of size 1728
   {3,6,2,2,4} of size 1728
   {6,6,2,2,4} of size 1728
   {10,6,2,2,4} of size 1920
   {4,6,2,2,4} of size 1920
   {5,6,2,2,4} of size 1920
   {6,6,2,2,4} of size 1920
   {5,6,2,2,4} of size 1920
   {5,6,2,2,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,2,4}*96, {6,2,2,2}*96
   3-fold quotients : {2,2,2,4}*64
   4-fold quotients : {3,2,2,2}*48
   6-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,2,2,4}*384, {6,2,4,4}*384, {6,4,2,4}*384a, {6,2,2,8}*384
   3-fold covers : {18,2,2,4}*576, {6,2,2,12}*576, {6,2,6,4}*576a, {6,6,2,4}*576a, {6,6,2,4}*576c
   4-fold covers : {6,4,4,4}*768, {12,2,4,4}*768, {12,4,2,4}*768a, {6,2,4,8}*768a, {6,2,8,4}*768a, {6,2,4,8}*768b, {6,2,8,4}*768b, {6,2,4,4}*768, {6,4,2,8}*768a, {6,8,2,4}*768, {12,2,2,8}*768, {24,2,2,4}*768, {6,2,2,16}*768, {6,4,2,4}*768
   5-fold covers : {6,2,2,20}*960, {6,2,10,4}*960, {6,10,2,4}*960, {30,2,2,4}*960
   6-fold covers : {18,2,4,4}*1152, {6,6,4,4}*1152b, {6,6,4,4}*1152c, {6,2,4,12}*1152a, {6,2,12,4}*1152a, {18,4,2,4}*1152a, {36,2,2,4}*1152, {6,4,6,4}*1152a, {6,12,2,4}*1152a, {6,4,2,12}*1152a, {6,12,2,4}*1152b, {12,2,6,4}*1152a, {12,6,2,4}*1152b, {12,6,2,4}*1152c, {12,2,2,12}*1152, {18,2,2,8}*1152, {6,2,6,8}*1152, {6,6,2,8}*1152a, {6,6,2,8}*1152c, {6,2,2,24}*1152
   7-fold covers : {6,2,2,28}*1344, {6,2,14,4}*1344, {6,14,2,4}*1344, {42,2,2,4}*1344
   9-fold covers : {54,2,2,4}*1728, {18,2,2,12}*1728, {6,2,2,36}*1728, {6,2,18,4}*1728a, {6,18,2,4}*1728a, {18,2,6,4}*1728a, {18,6,2,4}*1728a, {18,6,2,4}*1728b, {6,6,6,4}*1728a, {6,6,2,4}*1728b, {6,6,2,4}*1728c, {6,2,6,12}*1728a, {6,2,6,12}*1728b, {6,6,2,12}*1728a, {6,6,2,12}*1728c, {6,6,6,4}*1728d, {6,6,6,4}*1728e, {6,6,2,4}*1728d, {6,6,6,4}*1728g, {6,2,6,12}*1728c, {6,6,6,4}*1728i, {6,2,6,4}*1728
   10-fold covers : {30,2,4,4}*1920, {6,10,4,4}*1920, {6,2,4,20}*1920, {6,2,20,4}*1920, {30,4,2,4}*1920a, {60,2,2,4}*1920, {6,4,10,4}*1920, {12,2,10,4}*1920, {12,10,2,4}*1920, {6,4,2,20}*1920a, {6,20,2,4}*1920a, {12,2,2,20}*1920, {30,2,2,8}*1920, {6,2,10,8}*1920, {6,10,2,8}*1920, {6,2,2,40}*1920
Permutation Representation (GAP) :

s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := (7,8);;
s3 := (10,11);;
s4 := ( 9,10)(11,12);;
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*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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(12)!(3,4)(5,6);
s1 := Sym(12)!(1,5)(2,3)(4,6);
s2 := Sym(12)!(7,8);
s3 := Sym(12)!(10,11);
s4 := Sym(12)!( 9,10)(11,12);
poly := sub<Sym(12)|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*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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope