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

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

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

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