Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,14,8}

Atlas Canonical Name {2,14,8}*1568a

Overview

Group
SmallGroup(1568,917)
Rank
4
Schläfli Type
{2,14,8}
Vertices, edges, …
2, 49, 196, 28
Order of s0s1s2s3
8
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

No regular quotients.

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