Part of the Atlas of Small Regular Polytopes

Polytope of Type {5,2,8,3,2}

Atlas Canonical Name {5,2,8,3,2}*1920

Overview

Group
SmallGroup(1920,240195)
Rank
6
Schläfli Type
{5,2,8,3,2}
Vertices, edges, …
5, 5, 16, 24, 6, 2
Order of s0s1s2s3s4s5
60
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 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 6,16)( 7,12)( 8,11)( 9,32)(10,34)(13,17)(14,21)(15,23)(18,20)(19,22)(24,49)(25,53)(26,48)(27,51)(28,52)(29,50)(30,33)(31,35)(36,44)(37,46)(38,42)(39,45)(40,47)(41,43);;
s3 := ( 7, 8)( 9,10)(11,24)(12,27)(14,19)(15,18)(16,36)(17,39)(20,42)(21,43)(22,28)(23,25)(26,47)(29,46)(30,31)(32,48)(33,50)(34,37)(35,40)(38,52)(41,53)(44,45);;
s4 := ( 6,10)( 7,19)( 8,15)(11,23)(12,22)(13,31)(14,18)(16,34)(17,35)(20,21)(24,26)(25,47)(27,29)(28,46)(36,38)(37,52)(39,41)(40,53)(42,44)(43,45)(48,49)(50,51);;
s5 := (54,55);;
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, 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*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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(55)!(2,3)(4,5);
s1 := Sym(55)!(1,2)(3,4);
s2 := Sym(55)!( 6,16)( 7,12)( 8,11)( 9,32)(10,34)(13,17)(14,21)(15,23)(18,20)(19,22)(24,49)(25,53)(26,48)(27,51)(28,52)(29,50)(30,33)(31,35)(36,44)(37,46)(38,42)(39,45)(40,47)(41,43);
s3 := Sym(55)!( 7, 8)( 9,10)(11,24)(12,27)(14,19)(15,18)(16,36)(17,39)(20,42)(21,43)(22,28)(23,25)(26,47)(29,46)(30,31)(32,48)(33,50)(34,37)(35,40)(38,52)(41,53)(44,45);
s4 := Sym(55)!( 6,10)( 7,19)( 8,15)(11,23)(12,22)(13,31)(14,18)(16,34)(17,35)(20,21)(24,26)(25,47)(27,29)(28,46)(36,38)(37,52)(39,41)(40,53)(42,44)(43,45)(48,49)(50,51);
s5 := Sym(55)!(54,55);
poly := sub<Sym(55)|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, 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*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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 >;