Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,14,7}

Atlas Canonical Name {2,14,7}*392

Overview

Group
SmallGroup(392,41)
Rank
4
Schläfli Type
{2,14,7}
Vertices, edges, …
2, 14, 49, 7
Order of s0s1s2s3
14
Order of s0s1s2s3s2s1
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

2-fold

3-fold

4-fold

5-fold

Representations

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