Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,12,2,3}

Atlas Canonical Name {6,12,2,3}*1728a

Overview

Group
SmallGroup(1728,47874)
Rank
5
Schläfli Type
{6,12,2,3}
Vertices, edges, …
12, 72, 24, 3, 3
Order of s0s1s2s3s4
6
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

12-fold

24-fold

36-fold

Covers minimal covers in bold

None in this atlas.

Representations

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