Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,14}

Atlas Canonical Name {2,6,14}*1176

Overview

Group
SmallGroup(1176,225)
Rank
4
Schläfli Type
{2,6,14}
Vertices, edges, …
2, 21, 147, 49
Order of s0s1s2s3
6
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

None in this atlas.

Representations

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