Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,2,7,14}

Atlas Canonical Name {4,2,7,14}*1568

Overview

Group
SmallGroup(1568,858)
Rank
5
Schläfli Type
{4,2,7,14}
Vertices, edges, …
4, 4, 7, 49, 14
Order of s0s1s2s3s4
28
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

7-fold

14-fold

Covers minimal covers in bold

None in this atlas.

Representations

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