Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,3,6}

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

Overview

Group
SmallGroup(1800,586)
Rank
4
Schläfli Type
{2,3,6}
Vertices, edges, …
2, 75, 225, 150
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 := ( 4,10)( 5,17)( 6,19)( 7,26)( 8,20)( 9,27)(12,13)(15,21)(16,23)(18,24)(28,53)(29,60)(30,67)(31,69)(32,76)(33,70)(34,77)(35,54)(36,61)(37,63)(38,62)(39,64)(40,71)(41,73)(42,55)(43,74)(44,56)(45,58)(46,65)(47,72)(48,66)(49,68)(50,75)(51,57)(52,59);;
s2 := ( 3,28)( 4,32)( 5,31)( 6,30)( 7,29)( 8,36)( 9,35)(10,34)(11,33)(12,37)(13,39)(14,38)(15,42)(16,41)(17,40)(18,47)(19,46)(20,45)(21,44)(22,43)(23,50)(24,49)(25,48)(26,52)(27,51)(54,57)(55,56)(58,61)(59,60)(63,64)(65,67)(68,72)(69,71)(73,75)(76,77);;
s3 := ( 3,14)( 4,12)( 6,23)( 7,21)( 8,27)( 9,20)(10,13)(15,26)(16,19)(22,25)(28,39)(29,37)(31,48)(32,46)(33,52)(34,45)(35,38)(40,51)(41,44)(47,50)(53,64)(54,62)(56,73)(57,71)(58,77)(59,70)(60,63)(65,76)(66,69)(72,75);;
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*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(77)!(1,2);
s1 := Sym(77)!( 4,10)( 5,17)( 6,19)( 7,26)( 8,20)( 9,27)(12,13)(15,21)(16,23)(18,24)(28,53)(29,60)(30,67)(31,69)(32,76)(33,70)(34,77)(35,54)(36,61)(37,63)(38,62)(39,64)(40,71)(41,73)(42,55)(43,74)(44,56)(45,58)(46,65)(47,72)(48,66)(49,68)(50,75)(51,57)(52,59);
s2 := Sym(77)!( 3,28)( 4,32)( 5,31)( 6,30)( 7,29)( 8,36)( 9,35)(10,34)(11,33)(12,37)(13,39)(14,38)(15,42)(16,41)(17,40)(18,47)(19,46)(20,45)(21,44)(22,43)(23,50)(24,49)(25,48)(26,52)(27,51)(54,57)(55,56)(58,61)(59,60)(63,64)(65,67)(68,72)(69,71)(73,75)(76,77);
s3 := Sym(77)!( 3,14)( 4,12)( 6,23)( 7,21)( 8,27)( 9,20)(10,13)(15,26)(16,19)(22,25)(28,39)(29,37)(31,48)(32,46)(33,52)(34,45)(35,38)(40,51)(41,44)(47,50)(53,64)(54,62)(56,73)(57,71)(58,77)(59,70)(60,63)(65,76)(66,69)(72,75);
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, s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 >;