Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,14,3}

Atlas Canonical Name {2,14,3}*1176

Overview

Group
SmallGroup(1176,225)
Rank
4
Schläfli Type
{2,14,3}
Vertices, edges, …
2, 98, 147, 21
Order of s0s1s2s3
6
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

49-fold

Covers minimal covers in bold

None in this atlas.

Representations

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