Polytope of Type {4,14,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,14,2,2}*448
if this polytope has a name.
Group : SmallGroup(448,1369)
Rank : 5
Schlafli Type : {4,14,2,2}
Number of vertices, edges, etc : 4, 28, 14, 2, 2
Order of s₀s₁s₂s₃s₄ : 28
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,14,2,2,2} of size 896
   {4,14,2,2,3} of size 1344
   {4,14,2,2,4} of size 1792
Vertex Figure Of :
   {2,4,14,2,2} of size 896
   {4,4,14,2,2} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,14,2,2}*224
   4-fold quotients : {2,7,2,2}*112
   7-fold quotients : {4,2,2,2}*64
   14-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,28,2,2}*896, {4,14,4,2}*896, {4,14,2,4}*896, {8,14,2,2}*896
   3-fold covers : {12,14,2,2}*1344, {4,14,2,6}*1344, {4,14,6,2}*1344, {4,42,2,2}*1344a
   4-fold covers : {4,28,4,2}*1792, {4,14,4,4}*1792, {4,28,2,4}*1792, {8,28,2,2}*1792a, {4,56,2,2}*1792a, {8,28,2,2}*1792b, {4,56,2,2}*1792b, {4,28,2,2}*1792, {4,14,2,8}*1792, {8,14,2,4}*1792, {4,14,8,2}*1792, {8,14,4,2}*1792, {16,14,2,2}*1792
Permutation Representation (GAP) :

s0 := ( 2, 5)( 6,11)( 7,12)(13,19)(14,20)(21,25)(22,26);;
s1 := ( 1, 2)( 3, 7)( 4, 6)( 5,10)( 8,14)( 9,13)(11,18)(12,17)(15,22)(16,21)
(19,24)(20,23)(25,28)(26,27);;
s2 := ( 1, 3)( 2, 6)( 4, 8)( 5,11)( 7,13)( 9,15)(10,17)(12,19)(14,21)(18,23)
(20,25)(24,27);;
s3 := (29,30);;
s4 := (31,32);;
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*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(32)!( 2, 5)( 6,11)( 7,12)(13,19)(14,20)(21,25)(22,26);
s1 := Sym(32)!( 1, 2)( 3, 7)( 4, 6)( 5,10)( 8,14)( 9,13)(11,18)(12,17)(15,22)
(16,21)(19,24)(20,23)(25,28)(26,27);
s2 := Sym(32)!( 1, 3)( 2, 6)( 4, 8)( 5,11)( 7,13)( 9,15)(10,17)(12,19)(14,21)
(18,23)(20,25)(24,27);
s3 := Sym(32)!(29,30);
s4 := Sym(32)!(31,32);
poly := sub<Sym(32)|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*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope