Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1152,153182)
Rank
6
Schläfli Type
{2,6,4,2,2}
Vertices, edges, …
2, 18, 36, 12, 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 := ( 3,30)( 4,32)( 5,31)( 6,36)( 7,38)( 8,37)( 9,33)(10,35)(11,34)(12,21)(13,23)(14,22)(15,27)(16,29)(17,28)(18,24)(19,26)(20,25)(39,66)(40,68)(41,67)(42,72)(43,74)(44,73)(45,69)(46,71)(47,70)(48,57)(49,59)(50,58)(51,63)(52,65)(53,64)(54,60)(55,62)(56,61);;
s2 := ( 3, 6)( 4, 7)( 5, 8)(12,15)(13,16)(14,17)(21,24)(22,25)(23,26)(30,33)(31,34)(32,35)(39,51)(40,52)(41,53)(42,48)(43,49)(44,50)(45,54)(46,55)(47,56)(57,69)(58,70)(59,71)(60,66)(61,67)(62,68)(63,72)(64,73)(65,74);;
s3 := ( 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);;
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, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(78)!(1,2);
s1 := Sym(78)!( 3,30)( 4,32)( 5,31)( 6,36)( 7,38)( 8,37)( 9,33)(10,35)(11,34)(12,21)(13,23)(14,22)(15,27)(16,29)(17,28)(18,24)(19,26)(20,25)(39,66)(40,68)(41,67)(42,72)(43,74)(44,73)(45,69)(46,71)(47,70)(48,57)(49,59)(50,58)(51,63)(52,65)(53,64)(54,60)(55,62)(56,61);
s2 := Sym(78)!( 3, 6)( 4, 7)( 5, 8)(12,15)(13,16)(14,17)(21,24)(22,25)(23,26)(30,33)(31,34)(32,35)(39,51)(40,52)(41,53)(42,48)(43,49)(44,50)(45,54)(46,55)(47,56)(57,69)(58,70)(59,71)(60,66)(61,67)(62,68)(63,72)(64,73)(65,74);
s3 := 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);
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, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;