Polytope of Type {2,6,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,14}*1176
if this polytope has a name.
Group : SmallGroup(1176,225)
Rank : 4
Schlafli Type : {2,6,14}
Number of vertices, edges, etc : 2, 21, 147, 49
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4,24)( 5,45)( 6,17)( 7,38)( 8,10)( 9,31)(11,29)(12,50)(13,22)(14,43)
(16,36)(18,27)(19,48)(21,41)(23,34)(26,46)(28,39)(30,32)(33,51)(35,44)
(40,49);;
s2 := ( 4,10)( 5,17)( 6,24)( 7,31)( 8,38)( 9,45)(12,18)(13,25)(14,32)(15,39)
(16,46)(20,26)(21,33)(22,40)(23,47)(28,34)(29,41)(30,48)(36,42)(37,49)
(44,50);;
s3 := ( 3,25)( 4,24)( 5,30)( 6,29)( 7,28)( 8,27)( 9,26)(10,18)(11,17)(12,23)
(13,22)(14,21)(15,20)(16,19)(31,46)(32,45)(33,51)(34,50)(35,49)(36,48)(37,47)
(38,39)(40,44)(41,43);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s1*s2*s3*s1*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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(51)!(1,2);
s1 := Sym(51)!( 4,24)( 5,45)( 6,17)( 7,38)( 8,10)( 9,31)(11,29)(12,50)(13,22)
(14,43)(16,36)(18,27)(19,48)(21,41)(23,34)(26,46)(28,39)(30,32)(33,51)(35,44)
(40,49);
s2 := Sym(51)!( 4,10)( 5,17)( 6,24)( 7,31)( 8,38)( 9,45)(12,18)(13,25)(14,32)
(15,39)(16,46)(20,26)(21,33)(22,40)(23,47)(28,34)(29,41)(30,48)(36,42)(37,49)
(44,50);
s3 := Sym(51)!( 3,25)( 4,24)( 5,30)( 6,29)( 7,28)( 8,27)( 9,26)(10,18)(11,17)
(12,23)(13,22)(14,21)(15,20)(16,19)(31,46)(32,45)(33,51)(34,50)(35,49)(36,48)
(37,47)(38,39)(40,44)(41,43);
poly := sub<Sym(51)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s1*s2*s3*s1*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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