Polytope of Type {3,6,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,2,2}*192
if this polytope has a name.
Group : SmallGroup(192,1537)
Rank : 5
Schlafli Type : {3,6,2,2}
Number of vertices, edges, etc : 4, 12, 8, 2, 2
Order of s₀s₁s₂s₃s₄ : 4
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,6,2,2,2} of size 384
   {3,6,2,2,3} of size 576
   {3,6,2,2,4} of size 768
   {3,6,2,2,5} of size 960
   {3,6,2,2,6} of size 1152
   {3,6,2,2,7} of size 1344
   {3,6,2,2,9} of size 1728
   {3,6,2,2,10} of size 1920
Vertex Figure Of :
   {2,3,6,2,2} of size 384
   {3,3,6,2,2} of size 960
   {6,3,6,2,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,3,2,2}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,6,2,4}*384, {3,6,4,2}*384, {3,12,2,2}*384, {6,6,2,2}*384
   3-fold covers : {3,6,2,2}*576, {3,6,2,6}*576, {3,6,6,2}*576
   4-fold covers : {3,6,4,4}*768, {3,6,2,2}*768, {3,6,4,2}*768b, {3,12,4,2}*768, {3,6,2,8}*768, {3,6,8,2}*768, {3,12,2,4}*768, {6,6,2,4}*768, {6,6,4,2}*768, {6,12,2,2}*768a, {12,6,2,2}*768a, {6,12,2,2}*768b, {12,6,2,2}*768b, {6,6,2,2}*768b
   5-fold covers : {3,6,2,10}*960, {3,6,10,2}*960, {15,6,2,2}*960
   6-fold covers : {3,6,2,12}*1152, {3,6,12,2}*1152, {3,6,4,6}*1152, {3,6,6,4}*1152a, {3,6,2,4}*1152, {3,12,2,2}*1152, {3,12,2,6}*1152, {3,12,6,2}*1152, {3,6,4,2}*1152a, {6,6,2,2}*1152a, {6,6,2,2}*1152b, {6,6,2,6}*1152, {6,6,6,2}*1152b
   7-fold covers : {3,6,2,14}*1344, {3,6,14,2}*1344, {21,6,2,2}*1344
   9-fold covers : {3,6,2,18}*1728, {3,6,18,2}*1728, {9,6,2,2}*1728, {3,6,2,2}*1728, {3,6,6,6}*1728b, {3,6,6,6}*1728c, {3,6,6,6}*1728d, {3,6,2,6}*1728, {3,6,6,2}*1728
   10-fold covers : {3,6,2,20}*1920, {3,6,20,2}*1920, {3,6,4,10}*1920, {3,6,10,4}*1920, {15,6,2,4}*1920, {15,12,2,2}*1920, {3,12,2,10}*1920, {3,12,10,2}*1920, {15,6,4,2}*1920, {6,6,2,10}*1920, {6,6,10,2}*1920, {6,30,2,2}*1920, {30,6,2,2}*1920
Permutation Representation (GAP) :

s0 := (1,4)(2,6);;
s1 := (3,4)(5,6);;
s2 := (1,4)(2,6)(3,5);;
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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(10)!(1,4)(2,6);
s1 := Sym(10)!(3,4)(5,6);
s2 := Sym(10)!(1,4)(2,6)(3,5);
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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

to this polytope