Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1152,153178)
Rank
6
Schläfli Type
{2,6,12,2,2}
Vertices, edges, …
2, 6, 36, 12, 2, 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 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)(64,65)(67,68)(70,71)(73,74);;
s2 := ( 3,40)( 4,39)( 5,41)( 6,46)( 7,45)( 8,47)( 9,43)(10,42)(11,44)(12,49)(13,48)(14,50)(15,55)(16,54)(17,56)(18,52)(19,51)(20,53)(21,67)(22,66)(23,68)(24,73)(25,72)(26,74)(27,70)(28,69)(29,71)(30,58)(31,57)(32,59)(33,64)(34,63)(35,65)(36,61)(37,60)(38,62);;
s3 := ( 3,60)( 4,61)( 5,62)( 6,57)( 7,58)( 8,59)( 9,63)(10,64)(11,65)(12,69)(13,70)(14,71)(15,66)(16,67)(17,68)(18,72)(19,73)(20,74)(21,42)(22,43)(23,44)(24,39)(25,40)(26,41)(27,45)(28,46)(29,47)(30,51)(31,52)(32,53)(33,48)(34,49)(35,50)(36,54)(37,55)(38,56);;
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*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)(64,65)(67,68)(70,71)(73,74);
s2 := Sym(78)!( 3,40)( 4,39)( 5,41)( 6,46)( 7,45)( 8,47)( 9,43)(10,42)(11,44)(12,49)(13,48)(14,50)(15,55)(16,54)(17,56)(18,52)(19,51)(20,53)(21,67)(22,66)(23,68)(24,73)(25,72)(26,74)(27,70)(28,69)(29,71)(30,58)(31,57)(32,59)(33,64)(34,63)(35,65)(36,61)(37,60)(38,62);
s3 := Sym(78)!( 3,60)( 4,61)( 5,62)( 6,57)( 7,58)( 8,59)( 9,63)(10,64)(11,65)(12,69)(13,70)(14,71)(15,66)(16,67)(17,68)(18,72)(19,73)(20,74)(21,42)(22,43)(23,44)(24,39)(25,40)(26,41)(27,45)(28,46)(29,47)(30,51)(31,52)(32,53)(33,48)(34,49)(35,50)(36,54)(37,55)(38,56);
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*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;