Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,12,6,2}

Atlas Canonical Name {2,2,12,6,2}*1152b

Overview

Group
SmallGroup(1152,153178)
Rank
6
Schläfli Type
{2,2,12,6,2}
Vertices, edges, …
2, 2, 12, 36, 6, 2
Order of s0s1s2s3s4s5
12
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

3-fold

6-fold

9-fold

12-fold

18-fold

Covers minimal covers in bold

None in this atlas.

Representations

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