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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,2,14}*1792a
if this polytope has a name.
Group : SmallGroup(1792,1035859)
Rank : 5
Schlafli Type : {8,4,2,14}
Number of vertices, edges, etc : 8, 16, 4, 14, 14
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 : {8,4,2,7}*896a, {4,4,2,14}*896, {8,2,2,14}*896
   4-fold quotients : {4,4,2,7}*448, {8,2,2,7}*448, {2,4,2,14}*448, {4,2,2,14}*448
   7-fold quotients : {8,4,2,2}*256a
   8-fold quotients : {2,4,2,7}*224, {4,2,2,7}*224, {2,2,2,14}*224
   14-fold quotients : {4,4,2,2}*128, {8,2,2,2}*128
   16-fold quotients : {2,2,2,7}*112
   28-fold quotients : {2,4,2,2}*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, 6)( 5, 8)( 9,11)(10,12)(13,15);;
s1 := ( 1, 2)( 3, 5)( 4, 7)( 6, 9)( 8,10)(11,13)(12,14)(15,16);;
s2 := ( 2, 4)( 3, 6)(10,13)(12,15);;
s3 := (19,20)(21,22)(23,24)(25,26)(27,28)(29,30);;
s4 := (17,21)(18,19)(20,25)(22,23)(24,29)(26,27)(28,30);;
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, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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(30)!( 2, 3)( 4, 6)( 5, 8)( 9,11)(10,12)(13,15);
s1 := Sym(30)!( 1, 2)( 3, 5)( 4, 7)( 6, 9)( 8,10)(11,13)(12,14)(15,16);
s2 := Sym(30)!( 2, 4)( 3, 6)(10,13)(12,15);
s3 := Sym(30)!(19,20)(21,22)(23,24)(25,26)(27,28)(29,30);
s4 := Sym(30)!(17,21)(18,19)(20,25)(22,23)(24,29)(26,27)(28,30);
poly := sub<Sym(30)|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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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