Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1152,152548)
Rank
5
Schläfli Type
{2,8,6,6}
Vertices, edges, …
2, 8, 24, 18, 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

9-fold

12-fold

18-fold

24-fold

36-fold

Covers minimal covers in bold

None in this atlas.

Representations

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