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

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

s0 := ( 3, 4)( 6, 7)( 9,10)(11,12);;
s1 := ( 1, 3)( 2, 9)( 5, 6)( 7,10)( 8,11);;
s2 := ( 1, 2)( 3, 6)( 4, 7)( 5, 8)( 9,11)(10,12);;
s3 := (13,14);;
s4 := (15,16);;
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, 
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(16)!( 3, 4)( 6, 7)( 9,10)(11,12);
s1 := Sym(16)!( 1, 3)( 2, 9)( 5, 6)( 7,10)( 8,11);
s2 := Sym(16)!( 1, 2)( 3, 6)( 4, 7)( 5, 8)( 9,11)(10,12);
s3 := Sym(16)!(13,14);
s4 := Sym(16)!(15,16);
poly := sub<Sym(16)|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, 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, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope