Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,6,2,2}

Atlas Canonical Name {2,4,6,2,2}*1152

Overview

Group
SmallGroup(1152,153182)
Rank
6
Schläfli Type
{2,4,6,2,2}
Vertices, edges, …
2, 12, 36, 18, 2, 2
Order of s0s1s2s3s4s5
4
Order of s0s1s2s3s4s5s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

9-fold

18-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)(33,36)(34,37)(35,38)(39,48)(40,49)(41,50)(42,54)(43,55)(44,56)(45,51)(46,52)(47,53)(57,66)(58,67)(59,68)(60,72)(61,73)(62,74)(63,69)(64,70)(65,71);;
s2 := ( 3,39)( 4,42)( 5,45)( 6,40)( 7,43)( 8,46)( 9,41)(10,44)(11,47)(12,48)(13,51)(14,54)(15,49)(16,52)(17,55)(18,50)(19,53)(20,56)(21,57)(22,60)(23,63)(24,58)(25,61)(26,64)(27,59)(28,62)(29,65)(30,66)(31,69)(32,72)(33,67)(34,70)(35,73)(36,68)(37,71)(38,74);;
s3 := ( 3,31)( 4,30)( 5,32)( 6,37)( 7,36)( 8,38)( 9,34)(10,33)(11,35)(12,22)(13,21)(14,23)(15,28)(16,27)(17,29)(18,25)(19,24)(20,26)(39,67)(40,66)(41,68)(42,73)(43,72)(44,74)(45,70)(46,69)(47,71)(48,58)(49,57)(50,59)(51,64)(52,63)(53,65)(54,61)(55,60)(56,62);;
s4 := (75,76);;
s5 := (77,78);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(78)!(1,2);
s1 := Sym(78)!( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)(33,36)(34,37)(35,38)(39,48)(40,49)(41,50)(42,54)(43,55)(44,56)(45,51)(46,52)(47,53)(57,66)(58,67)(59,68)(60,72)(61,73)(62,74)(63,69)(64,70)(65,71);
s2 := Sym(78)!( 3,39)( 4,42)( 5,45)( 6,40)( 7,43)( 8,46)( 9,41)(10,44)(11,47)(12,48)(13,51)(14,54)(15,49)(16,52)(17,55)(18,50)(19,53)(20,56)(21,57)(22,60)(23,63)(24,58)(25,61)(26,64)(27,59)(28,62)(29,65)(30,66)(31,69)(32,72)(33,67)(34,70)(35,73)(36,68)(37,71)(38,74);
s3 := Sym(78)!( 3,31)( 4,30)( 5,32)( 6,37)( 7,36)( 8,38)( 9,34)(10,33)(11,35)(12,22)(13,21)(14,23)(15,28)(16,27)(17,29)(18,25)(19,24)(20,26)(39,67)(40,66)(41,68)(42,73)(43,72)(44,74)(45,70)(46,69)(47,71)(48,58)(49,57)(50,59)(51,64)(52,63)(53,65)(54,61)(55,60)(56,62);
s4 := Sym(78)!(75,76);
s5 := Sym(78)!(77,78);
poly := sub<Sym(78)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;