Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,14,2}

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

Overview

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