Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,2,8,3}*384

Overview

Group
SmallGroup(384,20062)
Rank
5
Schläfli Type
{2,2,8,3}
Vertices, edges, …
2, 2, 16, 24, 6
Order of s0s1s2s3s4
12
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

4-fold

8-fold

Covers minimal covers in bold

2-fold

3-fold

5-fold

Representations

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