Polytope of Type {2,2,2,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,14}*224
if this polytope has a name.
Group : SmallGroup(224,196)
Rank : 5
Schlafli Type : {2,2,2,14}
Number of vertices, edges, etc : 2, 2, 2, 14, 14
Order of s₀s₁s₂s₃s₄ : 14
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,2,14,2} of size 448
   {2,2,2,14,4} of size 896
   {2,2,2,14,6} of size 1344
   {2,2,2,14,7} of size 1568
   {2,2,2,14,8} of size 1792
Vertex Figure Of :
   {2,2,2,2,14} of size 448
   {3,2,2,2,14} of size 672
   {4,2,2,2,14} of size 896
   {5,2,2,2,14} of size 1120
   {6,2,2,2,14} of size 1344
   {7,2,2,2,14} of size 1568
   {8,2,2,2,14} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,2,7}*112
   7-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,2,28}*448, {2,2,4,14}*448, {2,4,2,14}*448, {4,2,2,14}*448
   3-fold covers : {2,2,6,14}*672, {2,6,2,14}*672, {6,2,2,14}*672, {2,2,2,42}*672
   4-fold covers : {2,2,4,28}*896, {2,4,2,28}*896, {4,2,2,28}*896, {2,4,4,14}*896, {4,4,2,14}*896, {4,2,4,14}*896, {2,2,2,56}*896, {2,2,8,14}*896, {2,8,2,14}*896, {8,2,2,14}*896
   5-fold covers : {2,2,10,14}*1120, {2,10,2,14}*1120, {10,2,2,14}*1120, {2,2,2,70}*1120
   6-fold covers : {2,2,12,14}*1344, {2,12,2,14}*1344, {12,2,2,14}*1344, {2,2,6,28}*1344a, {2,6,2,28}*1344, {6,2,2,28}*1344, {2,4,6,14}*1344a, {2,6,4,14}*1344, {4,2,6,14}*1344, {4,6,2,14}*1344a, {6,2,4,14}*1344, {6,4,2,14}*1344a, {2,2,2,84}*1344, {2,2,4,42}*1344a, {2,4,2,42}*1344, {4,2,2,42}*1344
   7-fold covers : {2,2,2,98}*1568, {2,2,14,14}*1568a, {2,2,14,14}*1568b, {2,14,2,14}*1568, {14,2,2,14}*1568
   8-fold covers : {4,4,4,14}*1792, {2,4,4,28}*1792, {4,4,2,28}*1792, {4,2,4,28}*1792, {2,4,8,14}*1792a, {2,8,4,14}*1792a, {4,8,2,14}*1792a, {8,4,2,14}*1792a, {2,2,8,28}*1792a, {2,2,4,56}*1792a, {2,4,8,14}*1792b, {2,8,4,14}*1792b, {4,8,2,14}*1792b, {8,4,2,14}*1792b, {2,2,8,28}*1792b, {2,2,4,56}*1792b, {2,4,4,14}*1792, {4,4,2,14}*1792, {2,2,4,28}*1792, {4,2,8,14}*1792, {8,2,4,14}*1792, {2,8,2,28}*1792, {8,2,2,28}*1792, {2,4,2,56}*1792, {4,2,2,56}*1792, {2,2,16,14}*1792, {2,16,2,14}*1792, {16,2,2,14}*1792, {2,2,2,112}*1792
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20);;
s4 := ( 7,11)( 8, 9)(10,15)(12,13)(14,19)(16,17)(18,20);;
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*s1*s0*s1, 
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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(20)!(1,2);
s1 := Sym(20)!(3,4);
s2 := Sym(20)!(5,6);
s3 := Sym(20)!( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20);
s4 := Sym(20)!( 7,11)( 8, 9)(10,15)(12,13)(14,19)(16,17)(18,20);
poly := sub<Sym(20)|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*s1*s0*s1, 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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope