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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,2,2}*192c
if this polytope has a name.
Group : SmallGroup(192,1537)
Rank : 5
Schlafli Type : {4,6,2,2}
Number of vertices, edges, etc : 4, 12, 6, 2, 2
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,6,2,2,2} of size 384
   {4,6,2,2,3} of size 576
   {4,6,2,2,4} of size 768
   {4,6,2,2,5} of size 960
   {4,6,2,2,6} of size 1152
   {4,6,2,2,7} of size 1344
   {4,6,2,2,9} of size 1728
   {4,6,2,2,10} of size 1920
Vertex Figure Of :
   {2,4,6,2,2} of size 384
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,3,2,2}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12,2,2}*384b, {4,12,2,2}*384c, {4,6,2,4}*384c, {4,6,4,2}*384c, {4,6,2,2}*384
   3-fold covers : {4,18,2,2}*576b, {4,6,2,6}*576c, {4,6,6,2}*576d, {4,6,6,2}*576e
   4-fold covers : {4,12,4,2}*768d, {4,12,4,2}*768e, {4,6,4,4}*768b, {4,12,2,4}*768b, {4,12,2,4}*768c, {4,6,2,2}*768a, {4,24,2,2}*768c, {4,24,2,2}*768d, {4,6,2,8}*768c, {4,6,8,2}*768b, {4,12,2,2}*768b, {4,6,2,2}*768b, {4,6,2,4}*768, {4,6,4,2}*768b, {4,12,2,2}*768c, {8,6,2,2}*768b, {8,6,2,2}*768c, {4,6,4,2}*768c
   5-fold covers : {4,6,2,10}*960c, {4,6,10,2}*960b, {4,30,2,2}*960b
   6-fold covers : {4,36,2,2}*1152b, {4,36,2,2}*1152c, {4,18,2,4}*1152b, {4,18,4,2}*1152c, {4,18,2,2}*1152, {4,12,2,6}*1152b, {4,12,2,6}*1152c, {4,12,6,2}*1152d, {4,12,6,2}*1152e, {4,12,6,2}*1152f, {4,12,6,2}*1152g, {4,6,2,12}*1152c, {4,6,12,2}*1152d, {4,6,4,6}*1152b, {4,6,6,4}*1152e, {4,6,6,4}*1152f, {4,6,12,2}*1152e, {4,6,2,6}*1152, {4,6,6,2}*1152a, {4,6,6,2}*1152b, {12,6,2,2}*1152a, {12,6,2,2}*1152b
   7-fold covers : {4,6,2,14}*1344c, {4,6,14,2}*1344b, {4,42,2,2}*1344b
   9-fold covers : {4,54,2,2}*1728b, {4,6,2,18}*1728c, {4,6,18,2}*1728c, {4,18,2,6}*1728b, {4,18,6,2}*1728c, {4,18,6,2}*1728d, {4,6,6,6}*1728b, {4,6,6,2}*1728d, {4,6,6,2}*1728e, {4,6,6,6}*1728j, {4,6,6,6}*1728k, {4,6,6,6}*1728l, {4,6,6,6}*1728m, {4,6,6,2}*1728i
   10-fold covers : {4,12,2,10}*1920b, {4,12,2,10}*1920c, {4,12,10,2}*1920b, {4,12,10,2}*1920c, {4,6,2,20}*1920c, {4,6,20,2}*1920b, {4,6,4,10}*1920b, {4,6,10,4}*1920b, {4,60,2,2}*1920b, {4,60,2,2}*1920c, {4,30,2,4}*1920b, {4,30,4,2}*1920c, {4,6,2,10}*1920, {4,6,10,2}*1920a, {20,6,2,2}*1920a, {4,30,2,2}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope