Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {3,2,8,3}*576

Overview

Group
SmallGroup(576,8340)
Rank
5
Schläfli Type
{3,2,8,3}
Vertices, edges, …
3, 3, 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

Representations

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