Polytope of Type {8,2,14,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,14,4}*1792
if this polytope has a name.
Group : SmallGroup(1792,1044755)
Rank : 5
Schlafli Type : {8,2,14,4}
Number of vertices, edges, etc : 8, 8, 14, 28, 4
Order of s₀s₁s₂s₃s₄ : 56
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {4,2,14,4}*896, {8,2,14,2}*896
   4-fold quotients : {8,2,7,2}*448, {2,2,14,4}*448, {4,2,14,2}*448
   7-fold quotients : {8,2,2,4}*256
   8-fold quotients : {4,2,7,2}*224, {2,2,14,2}*224
   14-fold quotients : {4,2,2,4}*128, {8,2,2,2}*128
   16-fold quotients : {2,2,7,2}*112
   28-fold quotients : {2,2,2,4}*64, {4,2,2,2}*64
   56-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (11,12)(14,15)(16,17)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)
(33,34)(35,36);;
s3 := ( 9,11)(10,19)(12,16)(13,14)(15,27)(17,23)(18,25)(20,21)(22,33)(26,31)
(28,29)(30,34)(32,35);;
s4 := ( 9,10)(11,14)(12,15)(13,18)(16,21)(17,22)(19,25)(20,26)(23,29)(24,30)
(27,31)(28,32)(33,35)(34,36);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*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(36)!(2,3)(4,5)(6,7);
s1 := Sym(36)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(36)!(11,12)(14,15)(16,17)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)
(31,32)(33,34)(35,36);
s3 := Sym(36)!( 9,11)(10,19)(12,16)(13,14)(15,27)(17,23)(18,25)(20,21)(22,33)
(26,31)(28,29)(30,34)(32,35);
s4 := Sym(36)!( 9,10)(11,14)(12,15)(13,18)(16,21)(17,22)(19,25)(20,26)(23,29)
(24,30)(27,31)(28,32)(33,35)(34,36);
poly := sub<Sym(36)|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, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*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 >;

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