Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(576,8340)
Rank
5
Schläfli Type
{3,8,2,3}
Vertices, edges, …
6, 24, 16, 3, 3
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)( 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);;
s1 := ( 1, 4)( 2,13)( 3, 9)( 6,42)( 7,41)( 8,25)(10,14)(11,47)(12,48)(15,40)(16,39)(17,24)(18,21)(19,20)(22,23)(27,44)(28,46)(29,33)(30,36)(31,32)(34,35)(37,38);;
s2 := ( 1,44)( 2,40)( 3,39)( 4,47)( 5,33)( 6,34)( 7,31)( 8,46)( 9,42)(10,24)(11,22)(12,19)(13,41)(14,21)(15,35)(16,32)(17,45)(18,43)(20,27)(23,28)(25,48)(26,36)(29,38)(30,37);;
s3 := (50,51);;
s4 := (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*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, 
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(51)!( 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);
s1 := Sym(51)!( 1, 4)( 2,13)( 3, 9)( 6,42)( 7,41)( 8,25)(10,14)(11,47)(12,48)(15,40)(16,39)(17,24)(18,21)(19,20)(22,23)(27,44)(28,46)(29,33)(30,36)(31,32)(34,35)(37,38);
s2 := Sym(51)!( 1,44)( 2,40)( 3,39)( 4,47)( 5,33)( 6,34)( 7,31)( 8,46)( 9,42)(10,24)(11,22)(12,19)(13,41)(14,21)(15,35)(16,32)(17,45)(18,43)(20,27)(23,28)(25,48)(26,36)(29,38)(30,37);
s3 := Sym(51)!(50,51);
s4 := Sym(51)!(49,50);
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, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*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*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1 >;