Polytope of Type {14,2,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,2,4}*224
if this polytope has a name.
Group : SmallGroup(224,178)
Rank : 4
Schlafli Type : {14,2,4}
Number of vertices, edges, etc : 14, 14, 4, 4
Order of s₀s₁s₂s₃ : 28
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {14,2,4,2} of size 448
   {14,2,4,3} of size 672
   {14,2,4,4} of size 896
   {14,2,4,6} of size 1344
   {14,2,4,3} of size 1344
   {14,2,4,6} of size 1344
   {14,2,4,6} of size 1344
   {14,2,4,8} of size 1792
   {14,2,4,8} of size 1792
   {14,2,4,4} of size 1792
Vertex Figure Of :
   {2,14,2,4} of size 448
   {4,14,2,4} of size 896
   {6,14,2,4} of size 1344
   {7,14,2,4} of size 1568
   {8,14,2,4} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {7,2,4}*112, {14,2,2}*112
   4-fold quotients : {7,2,2}*56
   7-fold quotients : {2,2,4}*32
   14-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {28,2,4}*448, {14,4,4}*448, {14,2,8}*448
   3-fold covers : {14,2,12}*672, {14,6,4}*672a, {42,2,4}*672
   4-fold covers : {28,4,4}*896, {56,2,4}*896, {28,2,8}*896, {14,4,8}*896a, {14,8,4}*896a, {14,4,8}*896b, {14,8,4}*896b, {14,4,4}*896, {14,2,16}*896
   5-fold covers : {14,2,20}*1120, {14,10,4}*1120, {70,2,4}*1120
   6-fold covers : {28,2,12}*1344, {28,6,4}*1344a, {14,4,12}*1344, {14,12,4}*1344a, {14,2,24}*1344, {14,6,8}*1344, {84,2,4}*1344, {42,4,4}*1344, {42,2,8}*1344
   7-fold covers : {98,2,4}*1568, {14,2,28}*1568, {14,14,4}*1568a, {14,14,4}*1568c
   8-fold covers : {14,4,8}*1792a, {14,8,4}*1792a, {14,8,8}*1792a, {14,8,8}*1792b, {14,8,8}*1792c, {14,8,8}*1792d, {56,2,8}*1792, {28,4,8}*1792a, {56,4,4}*1792a, {28,4,8}*1792b, {56,4,4}*1792b, {28,8,4}*1792a, {28,4,4}*1792a, {28,4,4}*1792b, {28,8,4}*1792b, {28,8,4}*1792c, {28,8,4}*1792d, {14,4,16}*1792a, {14,16,4}*1792a, {14,4,16}*1792b, {14,16,4}*1792b, {14,4,4}*1792, {14,4,8}*1792b, {14,8,4}*1792b, {28,2,16}*1792, {112,2,4}*1792, {14,2,32}*1792
Permutation Representation (GAP) :

s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,14);;
s2 := (16,17);;
s3 := (15,16)(17,18);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope