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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,2,14,4}*1792
if this polytope has a name.
Group : SmallGroup(1792,1076474)
Rank : 6
Schlafli Type : {2,4,2,14,4}
Number of vertices, edges, etc : 2, 4, 4, 14, 28, 4
Order of s₀s₁s₂s₃s₄s₅ : 28
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,2,14,4}*896, {2,4,2,14,2}*896
   4-fold quotients : {2,4,2,7,2}*448, {2,2,2,14,2}*448
   7-fold quotients : {2,4,2,2,4}*256
   8-fold quotients : {2,2,2,7,2}*224
   14-fold quotients : {2,2,2,2,4}*128, {2,4,2,2,2}*128
   28-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (4,5);;
s2 := (3,4)(5,6);;
s3 := ( 9,10)(12,13)(14,15)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)
(31,32)(33,34);;
s4 := ( 7, 9)( 8,17)(10,14)(11,12)(13,25)(15,21)(16,23)(18,19)(20,31)(24,29)
(26,27)(28,32)(30,33);;
s5 := ( 7, 8)( 9,12)(10,13)(11,16)(14,19)(15,20)(17,23)(18,24)(21,27)(22,28)
(25,29)(26,30)(31,33)(32,34);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, 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, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5, 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)!(4,5);
s2 := Sym(34)!(3,4)(5,6);
s3 := Sym(34)!( 9,10)(12,13)(14,15)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)
(29,30)(31,32)(33,34);
s4 := Sym(34)!( 7, 9)( 8,17)(10,14)(11,12)(13,25)(15,21)(16,23)(18,19)(20,31)
(24,29)(26,27)(28,32)(30,33);
s5 := Sym(34)!( 7, 8)( 9,12)(10,13)(11,16)(14,19)(15,20)(17,23)(18,24)(21,27)
(22,28)(25,29)(26,30)(31,33)(32,34);
poly := sub<Sym(34)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, 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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5, 
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 >;

to this polytope