Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,8,14}

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

Overview

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