Polytope of Type {3,2,4,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,14}*672
if this polytope has a name.
Group : SmallGroup(672,1150)
Rank : 5
Schlafli Type : {3,2,4,14}
Number of vertices, edges, etc : 3, 3, 4, 28, 14
Order of s₀s₁s₂s₃s₄ : 84
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,4,14,2} of size 1344
Vertex Figure Of :
   {2,3,2,4,14} of size 1344
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,2,14}*336
   4-fold quotients : {3,2,2,7}*168
   7-fold quotients : {3,2,4,2}*96
   14-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,4,28}*1344, {3,2,8,14}*1344, {6,2,4,14}*1344
Permutation Representation (GAP) :

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