Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,8,6}

Atlas Canonical Name {2,6,8,6}*1152

Overview

Group
SmallGroup(1152,152548)
Rank
5
Schläfli Type
{2,6,8,6}
Vertices, edges, …
2, 6, 24, 24, 6
Order of s0s1s2s3s4
24
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

8-fold

9-fold

12-fold

16-fold

18-fold

24-fold

36-fold

Covers minimal covers in bold

None in this atlas.

Representations

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