Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,3,2,2,3}

Atlas Canonical Name {8,3,2,2,3}*1152

Overview

Group
SmallGroup(1152,157603)
Rank
6
Schläfli Type
{8,3,2,2,3}
Vertices, edges, …
16, 24, 6, 2, 3, 3
Order of s0s1s2s3s4s5
12
Order of s0s1s2s3s4s5s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := ( 1,11)( 2, 7)( 3, 6)( 4,27)( 5,29)( 8,12)( 9,16)(10,18)(13,15)(14,17)(19,44)(20,48)(21,43)(22,46)(23,47)(24,45)(25,28)(26,30)(31,39)(32,41)(33,37)(34,40)(35,42)(36,38);;
s1 := ( 2, 3)( 4, 5)( 6,19)( 7,22)( 9,14)(10,13)(11,31)(12,34)(15,37)(16,38)(17,23)(18,20)(21,42)(24,41)(25,26)(27,43)(28,45)(29,32)(30,35)(33,47)(36,48)(39,40);;
s2 := ( 1, 5)( 2,14)( 3,10)( 6,18)( 7,17)( 8,26)( 9,13)(11,29)(12,30)(15,16)(19,21)(20,42)(22,24)(23,41)(31,33)(32,47)(34,36)(35,48)(37,39)(38,40)(43,44)(45,46);;
s3 := (49,50);;
s4 := (52,53);;
s5 := (51,52);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s1*s2*s1*s2*s1*s2, s4*s5*s4*s5*s4*s5, 
s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(53)!( 1,11)( 2, 7)( 3, 6)( 4,27)( 5,29)( 8,12)( 9,16)(10,18)(13,15)(14,17)(19,44)(20,48)(21,43)(22,46)(23,47)(24,45)(25,28)(26,30)(31,39)(32,41)(33,37)(34,40)(35,42)(36,38);
s1 := Sym(53)!( 2, 3)( 4, 5)( 6,19)( 7,22)( 9,14)(10,13)(11,31)(12,34)(15,37)(16,38)(17,23)(18,20)(21,42)(24,41)(25,26)(27,43)(28,45)(29,32)(30,35)(33,47)(36,48)(39,40);
s2 := Sym(53)!( 1, 5)( 2,14)( 3,10)( 6,18)( 7,17)( 8,26)( 9,13)(11,29)(12,30)(15,16)(19,21)(20,42)(22,24)(23,41)(31,33)(32,47)(34,36)(35,48)(37,39)(38,40)(43,44)(45,46);
s3 := Sym(53)!(49,50);
s4 := Sym(53)!(52,53);
s5 := Sym(53)!(51,52);
poly := sub<Sym(53)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s1*s2*s1*s2*s1*s2, s4*s5*s4*s5*s4*s5, 
s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;