Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {6,2,6,12}*1728c

Overview

Group
SmallGroup(1728,47409)
Rank
5
Schläfli Type
{6,2,6,12}
Vertices, edges, …
6, 6, 6, 36, 12
Order of s0s1s2s3s4
12
Order of s0s1s2s3s4s3s2s1
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

4-fold

6-fold

8-fold

9-fold

12-fold

18-fold

24-fold

27-fold

36-fold

54-fold

Covers minimal covers in bold

None in this atlas.

Representations

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