Polytope of Type {2,2,28,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,28,2}*448
if this polytope has a name.
Group : SmallGroup(448,1367)
Rank : 5
Schlafli Type : {2,2,28,2}
Number of vertices, edges, etc : 2, 2, 28, 28, 2
Order of s₀s₁s₂s₃s₄ : 28
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,28,2,2} of size 896
   {2,2,28,2,3} of size 1344
   {2,2,28,2,4} of size 1792
Vertex Figure Of :
   {2,2,2,28,2} of size 896
   {3,2,2,28,2} of size 1344
   {4,2,2,28,2} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,14,2}*224
   4-fold quotients : {2,2,7,2}*112
   7-fold quotients : {2,2,4,2}*64
   14-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,28,4}*896, {2,4,28,2}*896, {4,2,28,2}*896, {2,2,56,2}*896
   3-fold covers : {2,2,28,6}*1344a, {2,6,28,2}*1344a, {6,2,28,2}*1344, {2,2,84,2}*1344
   4-fold covers : {4,4,28,2}*1792, {2,4,28,4}*1792, {4,2,28,4}*1792, {2,2,28,8}*1792a, {2,8,28,2}*1792a, {2,2,56,4}*1792a, {2,4,56,2}*1792a, {2,2,28,8}*1792b, {2,8,28,2}*1792b, {2,2,56,4}*1792b, {2,4,56,2}*1792b, {2,2,28,4}*1792, {2,4,28,2}*1792, {8,2,28,2}*1792, {4,2,56,2}*1792, {2,2,112,2}*1792
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 8, 9)(11,14)(12,13)(15,16)(17,18)(19,22)(20,21)(23,24)(25,26)
(27,30)(28,29)(31,32);;
s3 := ( 5,11)( 6, 8)( 7,17)( 9,19)(10,13)(12,15)(14,25)(16,27)(18,21)(20,23)
(22,31)(24,28)(26,29)(30,32);;
s4 := (33,34);;
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, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, 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*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(34)!(1,2);
s1 := Sym(34)!(3,4);
s2 := Sym(34)!( 6, 7)( 8, 9)(11,14)(12,13)(15,16)(17,18)(19,22)(20,21)(23,24)
(25,26)(27,30)(28,29)(31,32);
s3 := Sym(34)!( 5,11)( 6, 8)( 7,17)( 9,19)(10,13)(12,15)(14,25)(16,27)(18,21)
(20,23)(22,31)(24,28)(26,29)(30,32);
s4 := Sym(34)!(33,34);
poly := sub<Sym(34)|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, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, 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*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