Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,7,14}

Atlas Canonical Name {3,2,7,14}*1176

Overview

Group
SmallGroup(1176,237)
Rank
5
Schläfli Type
{3,2,7,14}
Vertices, edges, …
3, 3, 7, 49, 14
Order of s0s1s2s3s4
42
Order of s0s1s2s3s4s3s2s1
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 := (2,3);;
s1 := (1,2);;
s2 := ( 5,10)( 6, 9)( 7, 8)(11,46)(12,52)(13,51)(14,50)(15,49)(16,48)(17,47)(18,39)(19,45)(20,44)(21,43)(22,42)(23,41)(24,40)(25,32)(26,38)(27,37)(28,36)(29,35)(30,34)(31,33);;
s3 := ( 4,12)( 5,11)( 6,17)( 7,16)( 8,15)( 9,14)(10,13)(18,47)(19,46)(20,52)(21,51)(22,50)(23,49)(24,48)(25,40)(26,39)(27,45)(28,44)(29,43)(30,42)(31,41)(32,33)(34,38)(35,37);;
s4 := (11,46)(12,47)(13,48)(14,49)(15,50)(16,51)(17,52)(18,39)(19,40)(20,41)(21,42)(22,43)(23,44)(24,45)(25,32)(26,33)(27,34)(28,35)(29,36)(30,37)(31,38);;
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, 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(52)!(2,3);
s1 := Sym(52)!(1,2);
s2 := Sym(52)!( 5,10)( 6, 9)( 7, 8)(11,46)(12,52)(13,51)(14,50)(15,49)(16,48)(17,47)(18,39)(19,45)(20,44)(21,43)(22,42)(23,41)(24,40)(25,32)(26,38)(27,37)(28,36)(29,35)(30,34)(31,33);
s3 := Sym(52)!( 4,12)( 5,11)( 6,17)( 7,16)( 8,15)( 9,14)(10,13)(18,47)(19,46)(20,52)(21,51)(22,50)(23,49)(24,48)(25,40)(26,39)(27,45)(28,44)(29,43)(30,42)(31,41)(32,33)(34,38)(35,37);
s4 := Sym(52)!(11,46)(12,47)(13,48)(14,49)(15,50)(16,51)(17,52)(18,39)(19,40)(20,41)(21,42)(22,43)(23,44)(24,45)(25,32)(26,33)(27,34)(28,35)(29,36)(30,37)(31,38);
poly := sub<Sym(52)|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, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;