Polytope of Type {4,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,14}*392
if this polytope has a name.
Group : SmallGroup(392,37)
Rank : 3
Schlafli Type : {4,14}
Number of vertices, edges, etc : 14, 98, 49
Order of s₀s₁s₂ : 4
Order of s₀s₁s₂s₁ : 14
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {4,14,2} of size 784
Vertex Figure Of :
   {2,4,14} of size 784
   {4,4,14} of size 1568
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,14}*784
   3-fold covers : {12,14}*1176
   4-fold covers : {8,14}*1568a, {4,28}*1568
   5-fold covers : {20,14}*1960
Permutation Representation (GAP) :

s0 := ( 8,43)( 9,44)(10,45)(11,46)(12,47)(13,48)(14,49)(15,36)(16,37)(17,38)
(18,39)(19,40)(20,41)(21,42)(22,29)(23,30)(24,31)(25,32)(26,33)(27,34)
(28,35);;
s1 := ( 2, 8)( 3,15)( 4,22)( 5,29)( 6,36)( 7,43)(10,16)(11,23)(12,30)(13,37)
(14,44)(18,24)(19,31)(20,38)(21,45)(26,32)(27,39)(28,46)(34,40)(35,47)
(42,48);;
s2 := ( 1, 2)( 3, 7)( 4, 6)( 8,44)( 9,43)(10,49)(11,48)(12,47)(13,46)(14,45)
(15,37)(16,36)(17,42)(18,41)(19,40)(20,39)(21,38)(22,30)(23,29)(24,35)(25,34)
(26,33)(27,32)(28,31);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(49)!( 8,43)( 9,44)(10,45)(11,46)(12,47)(13,48)(14,49)(15,36)(16,37)
(17,38)(18,39)(19,40)(20,41)(21,42)(22,29)(23,30)(24,31)(25,32)(26,33)(27,34)
(28,35);
s1 := Sym(49)!( 2, 8)( 3,15)( 4,22)( 5,29)( 6,36)( 7,43)(10,16)(11,23)(12,30)
(13,37)(14,44)(18,24)(19,31)(20,38)(21,45)(26,32)(27,39)(28,46)(34,40)(35,47)
(42,48);
s2 := Sym(49)!( 1, 2)( 3, 7)( 4, 6)( 8,44)( 9,43)(10,49)(11,48)(12,47)(13,46)
(14,45)(15,37)(16,36)(17,42)(18,41)(19,40)(20,39)(21,38)(22,30)(23,29)(24,35)
(25,34)(26,33)(27,32)(28,31);
poly := sub<Sym(49)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope