Part of the Atlas of Small Regular Polytopes

Polytope of Type {14,8,2}

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

Overview

Group
SmallGroup(1568,917)
Rank
4
Schläfli Type
{14,8,2}
Vertices, edges, …
49, 196, 28, 2
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 := ( 2, 7)( 3, 6)( 4, 5)( 8,43)( 9,49)(10,48)(11,47)(12,46)(13,45)(14,44)(15,36)(16,42)(17,41)(18,40)(19,39)(20,38)(21,37)(22,29)(23,35)(24,34)(25,33)(26,32)(27,31)(28,30);;
s1 := ( 1, 2)( 3, 7)( 4, 6)( 8,14)( 9,13)(10,12)(15,19)(16,18)(20,21)(22,24)(25,28)(26,27)(30,35)(31,34)(32,33)(36,41)(37,40)(38,39)(43,46)(44,45)(47,49);;
s2 := ( 2,46)( 3,42)( 4,31)( 5,27)( 6,16)( 7,12)( 8,30)( 9,26)(10,15)(13,45)(14,41)(17,44)(18,40)(19,29)(20,25)(22,39)(23,35)(28,43)(32,49)(33,38)(36,48);;
s3 := (50,51);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(51)!( 2, 7)( 3, 6)( 4, 5)( 8,43)( 9,49)(10,48)(11,47)(12,46)(13,45)(14,44)(15,36)(16,42)(17,41)(18,40)(19,39)(20,38)(21,37)(22,29)(23,35)(24,34)(25,33)(26,32)(27,31)(28,30);
s1 := Sym(51)!( 1, 2)( 3, 7)( 4, 6)( 8,14)( 9,13)(10,12)(15,19)(16,18)(20,21)(22,24)(25,28)(26,27)(30,35)(31,34)(32,33)(36,41)(37,40)(38,39)(43,46)(44,45)(47,49);
s2 := Sym(51)!( 2,46)( 3,42)( 4,31)( 5,27)( 6,16)( 7,12)( 8,30)( 9,26)(10,15)(13,45)(14,41)(17,44)(18,40)(19,29)(20,25)(22,39)(23,35)(28,43)(32,49)(33,38)(36,48);
s3 := Sym(51)!(50,51);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0 >;