Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1728,47409)
Rank
5
Schläfli Type
{6,2,12,6}
Vertices, edges, …
6, 6, 12, 36, 6
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 := ( 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);;
s3 := ( 7,62)( 8,61)( 9,63)(10,68)(11,67)(12,69)(13,65)(14,64)(15,66)(16,71)(17,70)(18,72)(19,77)(20,76)(21,78)(22,74)(23,73)(24,75)(25,44)(26,43)(27,45)(28,50)(29,49)(30,51)(31,47)(32,46)(33,48)(34,53)(35,52)(36,54)(37,59)(38,58)(39,60)(40,56)(41,55)(42,57);;
s4 := ( 7,46)( 8,48)( 9,47)(10,43)(11,45)(12,44)(13,49)(14,51)(15,50)(16,55)(17,57)(18,56)(19,52)(20,54)(21,53)(22,58)(23,60)(24,59)(25,64)(26,66)(27,65)(28,61)(29,63)(30,62)(31,67)(32,69)(33,68)(34,73)(35,75)(36,74)(37,70)(38,72)(39,71)(40,76)(41,78)(42,77);;
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, 
s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
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)!( 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);
s3 := Sym(78)!( 7,62)( 8,61)( 9,63)(10,68)(11,67)(12,69)(13,65)(14,64)(15,66)(16,71)(17,70)(18,72)(19,77)(20,76)(21,78)(22,74)(23,73)(24,75)(25,44)(26,43)(27,45)(28,50)(29,49)(30,51)(31,47)(32,46)(33,48)(34,53)(35,52)(36,54)(37,59)(38,58)(39,60)(40,56)(41,55)(42,57);
s4 := Sym(78)!( 7,46)( 8,48)( 9,47)(10,43)(11,45)(12,44)(13,49)(14,51)(15,50)(16,55)(17,57)(18,56)(19,52)(20,54)(21,53)(22,58)(23,60)(24,59)(25,64)(26,66)(27,65)(28,61)(29,63)(30,62)(31,67)(32,69)(33,68)(34,73)(35,75)(36,74)(37,70)(38,72)(39,71)(40,76)(41,78)(42,77);
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, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;