Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1568,925)
Rank
6
Schläfli Type
{2,2,2,7,14}
Vertices, edges, …
2, 2, 2, 7, 49, 14
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 := (5,6);;
s3 := ( 8,13)( 9,12)(10,11)(14,49)(15,55)(16,54)(17,53)(18,52)(19,51)(20,50)(21,42)(22,48)(23,47)(24,46)(25,45)(26,44)(27,43)(28,35)(29,41)(30,40)(31,39)(32,38)(33,37)(34,36);;
s4 := ( 7,15)( 8,14)( 9,20)(10,19)(11,18)(12,17)(13,16)(21,50)(22,49)(23,55)(24,54)(25,53)(26,52)(27,51)(28,43)(29,42)(30,48)(31,47)(32,46)(33,45)(34,44)(35,36)(37,41)(38,40);;
s5 := (14,49)(15,50)(16,51)(17,52)(18,53)(19,54)(20,55)(21,42)(22,43)(23,44)(24,45)(25,46)(26,47)(27,48)(28,35)(29,36)(30,37)(31,38)(32,39)(33,40)(34,41);;
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, s2*s3*s2*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, s5*s3*s4*s5*s4*s5*s3*s4*s5*s4, 
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)!(5,6);
s3 := Sym(55)!( 8,13)( 9,12)(10,11)(14,49)(15,55)(16,54)(17,53)(18,52)(19,51)(20,50)(21,42)(22,48)(23,47)(24,46)(25,45)(26,44)(27,43)(28,35)(29,41)(30,40)(31,39)(32,38)(33,37)(34,36);
s4 := Sym(55)!( 7,15)( 8,14)( 9,20)(10,19)(11,18)(12,17)(13,16)(21,50)(22,49)(23,55)(24,54)(25,53)(26,52)(27,51)(28,43)(29,42)(30,48)(31,47)(32,46)(33,45)(34,44)(35,36)(37,41)(38,40);
s5 := Sym(55)!(14,49)(15,50)(16,51)(17,52)(18,53)(19,54)(20,55)(21,42)(22,43)(23,44)(24,45)(25,46)(26,47)(27,48)(28,35)(29,36)(30,37)(31,38)(32,39)(33,40)(34,41);
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, 
s2*s3*s2*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, s5*s3*s4*s5*s4*s5*s3*s4*s5*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;