Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,6,4,2}

Atlas Canonical Name {6,6,4,2}*576c

Overview

Group
SmallGroup(576,8589)
Rank
5
Schläfli Type
{6,6,4,2}
Vertices, edges, …
6, 18, 12, 4, 2
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

9-fold

12-fold

18-fold

Covers minimal covers in bold

2-fold

3-fold

Representations

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