Part of the Atlas of Small Regular Polytopes

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

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

Overview

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