Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,3}

Atlas Canonical Name {2,6,3}*1800

Overview

Group
SmallGroup(1800,586)
Rank
4
Schläfli Type
{2,6,3}
Vertices, edges, …
2, 150, 225, 75
Order of s0s1s2s3
30
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

25-fold

75-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 4,26)( 5,19)( 6,17)( 7,10)( 8,16)(11,25)(12,18)(13,24)(14,22)(20,23)(29,51)(30,44)(31,42)(32,35)(33,41)(36,50)(37,43)(38,49)(39,47)(45,48)(54,76)(55,69)(56,67)(57,60)(58,66)(61,75)(62,68)(63,74)(64,72)(70,73);;
s2 := ( 4, 7)( 5, 6)( 8,11)( 9,10)(13,14)(15,17)(18,22)(19,21)(23,25)(26,27)(28,53)(29,57)(30,56)(31,55)(32,54)(33,61)(34,60)(35,59)(36,58)(37,62)(38,64)(39,63)(40,67)(41,66)(42,65)(43,72)(44,71)(45,70)(46,69)(47,68)(48,75)(49,74)(50,73)(51,77)(52,76);;
s3 := ( 3,34)( 4,41)( 5,43)( 6,50)( 7,32)( 8,51)( 9,28)(10,35)(11,42)(12,44)(13,38)(14,45)(15,52)(16,29)(17,36)(18,30)(19,37)(20,39)(21,46)(22,48)(23,47)(24,49)(25,31)(26,33)(27,40)(53,59)(54,66)(55,68)(56,75)(58,76)(61,67)(62,69)(64,70)(65,77)(72,73);;
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, 
s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(77)!(1,2);
s1 := Sym(77)!( 4,26)( 5,19)( 6,17)( 7,10)( 8,16)(11,25)(12,18)(13,24)(14,22)(20,23)(29,51)(30,44)(31,42)(32,35)(33,41)(36,50)(37,43)(38,49)(39,47)(45,48)(54,76)(55,69)(56,67)(57,60)(58,66)(61,75)(62,68)(63,74)(64,72)(70,73);
s2 := Sym(77)!( 4, 7)( 5, 6)( 8,11)( 9,10)(13,14)(15,17)(18,22)(19,21)(23,25)(26,27)(28,53)(29,57)(30,56)(31,55)(32,54)(33,61)(34,60)(35,59)(36,58)(37,62)(38,64)(39,63)(40,67)(41,66)(42,65)(43,72)(44,71)(45,70)(46,69)(47,68)(48,75)(49,74)(50,73)(51,77)(52,76);
s3 := Sym(77)!( 3,34)( 4,41)( 5,43)( 6,50)( 7,32)( 8,51)( 9,28)(10,35)(11,42)(12,44)(13,38)(14,45)(15,52)(16,29)(17,36)(18,30)(19,37)(20,39)(21,46)(22,48)(23,47)(24,49)(25,31)(26,33)(27,40)(53,59)(54,66)(55,68)(56,75)(58,76)(61,67)(62,69)(64,70)(65,77)(72,73);
poly := sub<Sym(77)|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, s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2 >;