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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,2,2,2}*192
if this polytope has a name.
Group : SmallGroup(192,1542)
Rank : 6
Schlafli Type : {2,6,2,2,2}
Number of vertices, edges, etc : 2, 6, 6, 2, 2, 2
Order of s0s1s2s3s4s5 : 6
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,2,2,2,2} of size 384
   {2,6,2,2,2,3} of size 576
   {2,6,2,2,2,4} of size 768
   {2,6,2,2,2,5} of size 960
   {2,6,2,2,2,6} of size 1152
   {2,6,2,2,2,7} of size 1344
   {2,6,2,2,2,9} of size 1728
   {2,6,2,2,2,10} of size 1920
Vertex Figure Of :
   {2,2,6,2,2,2} of size 384
   {3,2,6,2,2,2} of size 576
   {4,2,6,2,2,2} of size 768
   {5,2,6,2,2,2} of size 960
   {6,2,6,2,2,2} of size 1152
   {7,2,6,2,2,2} of size 1344
   {9,2,6,2,2,2} of size 1728
   {10,2,6,2,2,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,3,2,2,2}*96
   3-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,12,2,2,2}*384, {2,6,2,2,4}*384, {2,6,2,4,2}*384, {2,6,4,2,2}*384a, {4,6,2,2,2}*384a
   3-fold covers : {2,18,2,2,2}*576, {2,6,2,2,6}*576, {2,6,2,6,2}*576, {2,6,6,2,2}*576a, {2,6,6,2,2}*576c, {6,6,2,2,2}*576a, {6,6,2,2,2}*576b
   4-fold covers : {2,6,2,4,4}*768, {2,6,4,4,2}*768, {2,12,4,2,2}*768a, {4,12,2,2,2}*768a, {2,6,4,2,4}*768a, {4,6,2,2,4}*768a, {4,6,2,4,2}*768a, {4,6,4,2,2}*768a, {2,12,2,2,4}*768, {2,12,2,4,2}*768, {2,6,2,2,8}*768, {2,6,2,8,2}*768, {2,6,8,2,2}*768, {8,6,2,2,2}*768, {2,24,2,2,2}*768, {2,6,4,2,2}*768, {4,6,2,2,2}*768
   5-fold covers : {2,6,2,2,10}*960, {2,6,2,10,2}*960, {2,6,10,2,2}*960, {10,6,2,2,2}*960, {2,30,2,2,2}*960
   6-fold covers : {2,18,2,2,4}*1152, {2,18,2,4,2}*1152, {2,18,4,2,2}*1152a, {4,18,2,2,2}*1152a, {2,36,2,2,2}*1152, {2,6,2,4,6}*1152a, {2,6,2,6,4}*1152a, {2,6,4,2,6}*1152a, {2,6,4,6,2}*1152, {2,6,6,2,4}*1152a, {2,6,6,2,4}*1152c, {2,6,6,4,2}*1152a, {4,6,2,2,6}*1152a, {4,6,2,6,2}*1152a, {4,6,6,2,2}*1152a, {4,6,6,2,2}*1152b, {6,6,2,2,4}*1152a, {6,6,2,2,4}*1152b, {6,6,2,4,2}*1152a, {6,6,2,4,2}*1152b, {6,6,4,2,2}*1152a, {6,6,4,2,2}*1152b, {2,6,6,4,2}*1152c, {2,6,12,2,2}*1152a, {12,6,2,2,2}*1152a, {2,6,2,2,12}*1152, {2,6,2,12,2}*1152, {2,6,12,2,2}*1152b, {2,12,2,2,6}*1152, {2,12,2,6,2}*1152, {2,12,6,2,2}*1152b, {2,12,6,2,2}*1152c, {6,12,2,2,2}*1152b, {6,12,2,2,2}*1152c, {12,6,2,2,2}*1152b
   7-fold covers : {2,6,2,2,14}*1344, {2,6,2,14,2}*1344, {2,6,14,2,2}*1344, {14,6,2,2,2}*1344, {2,42,2,2,2}*1344
   9-fold covers : {2,54,2,2,2}*1728, {2,6,2,2,18}*1728, {2,6,2,18,2}*1728, {2,6,18,2,2}*1728a, {2,18,2,2,6}*1728, {2,18,2,6,2}*1728, {2,18,6,2,2}*1728a, {2,18,6,2,2}*1728b, {6,18,2,2,2}*1728a, {6,18,2,2,2}*1728b, {18,6,2,2,2}*1728a, {2,6,6,2,2}*1728b, {2,6,6,2,2}*1728c, {2,6,6,6,2}*1728a, {6,6,2,2,2}*1728a, {6,6,2,2,2}*1728b, {2,6,2,6,6}*1728a, {2,6,2,6,6}*1728b, {2,6,2,6,6}*1728c, {2,6,6,2,2}*1728d, {2,6,6,2,6}*1728a, {2,6,6,2,6}*1728c, {2,6,6,6,2}*1728b, {2,6,6,6,2}*1728c, {2,6,6,6,2}*1728e, {2,6,6,6,2}*1728g, {6,6,2,2,2}*1728d, {6,6,2,2,6}*1728a, {6,6,2,2,6}*1728b, {6,6,2,6,2}*1728a, {6,6,2,6,2}*1728b, {6,6,6,2,2}*1728b, {6,6,6,2,2}*1728d, {6,6,6,2,2}*1728e, {6,6,6,2,2}*1728f
   10-fold covers : {2,30,2,2,4}*1920, {2,30,2,4,2}*1920, {2,30,4,2,2}*1920a, {4,30,2,2,2}*1920a, {2,60,2,2,2}*1920, {2,6,2,4,10}*1920, {2,6,2,10,4}*1920, {2,6,4,2,10}*1920a, {2,6,4,10,2}*1920, {2,6,10,2,4}*1920, {2,6,10,4,2}*1920, {4,6,2,2,10}*1920a, {4,6,2,10,2}*1920a, {4,6,10,2,2}*1920a, {10,6,2,2,4}*1920, {10,6,2,4,2}*1920, {10,6,4,2,2}*1920a, {2,12,2,2,10}*1920, {2,12,2,10,2}*1920, {2,12,10,2,2}*1920, {10,12,2,2,2}*1920, {2,6,2,2,20}*1920, {2,6,2,20,2}*1920, {2,6,20,2,2}*1920a, {20,6,2,2,2}*1920a
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (5,6)(7,8);;
s2 := (3,7)(4,5)(6,8);;
s3 := ( 9,10);;
s4 := (11,12);;
s5 := (13,14);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, 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*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(14)!(1,2);
s1 := Sym(14)!(5,6)(7,8);
s2 := Sym(14)!(3,7)(4,5)(6,8);
s3 := Sym(14)!( 9,10);
s4 := Sym(14)!(11,12);
s5 := Sym(14)!(13,14);
poly := sub<Sym(14)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, 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*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

to this polytope