Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,6,2}

Atlas Canonical Name {3,6,2}*1176

Overview

Group
SmallGroup(1176,225)
Rank
4
Schläfli Type
{3,6,2}
Vertices, edges, …
49, 147, 98, 2
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

No regular quotients.

Covers minimal covers in bold

None in this atlas.

Representations

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