Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,10,6,3}

Atlas Canonical Name {2,2,10,6,3}*1440

Overview

Group
SmallGroup(1440,5924)
Rank
6
Schläfli Type
{2,2,10,6,3}
Vertices, edges, …
2, 2, 10, 30, 9, 3
Order of s0s1s2s3s4s5
30
Order of s0s1s2s3s4s5s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

5-fold

6-fold

15-fold

Covers minimal covers in bold

None in this atlas.

Representations

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