Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(576,8659)
Rank
5
Schläfli Type
{2,6,4,3}
Vertices, edges, …
2, 6, 24, 12, 6
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

3-fold

4-fold

6-fold

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