Polytope of Type {4,2,14}

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

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

Permutation Representation (Magma) :

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

to this polytope