Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,14,7,2}

Atlas Canonical Name {2,2,14,7,2}*1568

Overview

Group
SmallGroup(1568,925)
Rank
6
Schläfli Type
{2,2,14,7,2}
Vertices, edges, …
2, 2, 14, 49, 7, 2
Order of s0s1s2s3s4s5
14
Order of s0s1s2s3s4s5s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

7-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (3,4);;
s2 := (12,47)(13,48)(14,49)(15,50)(16,51)(17,52)(18,53)(19,40)(20,41)(21,42)(22,43)(23,44)(24,45)(25,46)(26,33)(27,34)(28,35)(29,36)(30,37)(31,38)(32,39);;
s3 := ( 5,12)( 6,18)( 7,17)( 8,16)( 9,15)(10,14)(11,13)(19,47)(20,53)(21,52)(22,51)(23,50)(24,49)(25,48)(26,40)(27,46)(28,45)(29,44)(30,43)(31,42)(32,41)(34,39)(35,38)(36,37);;
s4 := ( 5, 6)( 7,11)( 8,10)(12,48)(13,47)(14,53)(15,52)(16,51)(17,50)(18,49)(19,41)(20,40)(21,46)(22,45)(23,44)(24,43)(25,42)(26,34)(27,33)(28,39)(29,38)(30,37)(31,36)(32,35);;
s5 := (54,55);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(55)!(1,2);
s1 := Sym(55)!(3,4);
s2 := Sym(55)!(12,47)(13,48)(14,49)(15,50)(16,51)(17,52)(18,53)(19,40)(20,41)(21,42)(22,43)(23,44)(24,45)(25,46)(26,33)(27,34)(28,35)(29,36)(30,37)(31,38)(32,39);
s3 := Sym(55)!( 5,12)( 6,18)( 7,17)( 8,16)( 9,15)(10,14)(11,13)(19,47)(20,53)(21,52)(22,51)(23,50)(24,49)(25,48)(26,40)(27,46)(28,45)(29,44)(30,43)(31,42)(32,41)(34,39)(35,38)(36,37);
s4 := Sym(55)!( 5, 6)( 7,11)( 8,10)(12,48)(13,47)(14,53)(15,52)(16,51)(17,50)(18,49)(19,41)(20,40)(21,46)(22,45)(23,44)(24,43)(25,42)(26,34)(27,33)(28,39)(29,38)(30,37)(31,36)(32,35);
s5 := Sym(55)!(54,55);
poly := sub<Sym(55)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;