Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,3,4}

Atlas Canonical Name {2,6,3,4}*576

Overview

Group
SmallGroup(576,8659)
Rank
5
Schläfli Type
{2,6,3,4}
Vertices, edges, …
2, 6, 18, 12, 8
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

Covers minimal covers in bold

2-fold

3-fold

Representations

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