Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,6,3}

Atlas Canonical Name {6,6,3}*288

Overview

Group
SmallGroup(288,1028)
Rank
4
Schläfli Type
{6,6,3}
Vertices, edges, …
6, 24, 12, 4
Order of s0s1s2s3
12
Order of s0s1s2s3s2s1
2
Also known as
{{6,6|2},{6,3}4}. if this polytope has another name.

Special Properties

  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

6-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.