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

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

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

to this polytope