Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1440,5924)
Rank
6
Schläfli Type
{2,10,6,3,2}
Vertices, edges, …
2, 10, 30, 9, 3, 2
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 := ( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)(25,26)(29,32)(30,31)(34,37)(35,36)(39,42)(40,41)(44,47)(45,46);;
s2 := ( 3, 4)( 5, 7)( 8,14)( 9,13)(10,17)(11,16)(12,15)(18,19)(20,22)(23,29)(24,28)(25,32)(26,31)(27,30)(33,34)(35,37)(38,44)(39,43)(40,47)(41,46)(42,45);;
s3 := ( 3, 8)( 4, 9)( 5,10)( 6,11)( 7,12)(18,38)(19,39)(20,40)(21,41)(22,42)(23,33)(24,34)(25,35)(26,36)(27,37)(28,43)(29,44)(30,45)(31,46)(32,47);;
s4 := ( 3,18)( 4,19)( 5,20)( 6,21)( 7,22)( 8,28)( 9,29)(10,30)(11,31)(12,32)(13,23)(14,24)(15,25)(16,26)(17,27)(38,43)(39,44)(40,45)(41,46)(42,47);;
s5 := (48,49);;
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, 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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(49)!(1,2);
s1 := Sym(49)!( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)(25,26)(29,32)(30,31)(34,37)(35,36)(39,42)(40,41)(44,47)(45,46);
s2 := Sym(49)!( 3, 4)( 5, 7)( 8,14)( 9,13)(10,17)(11,16)(12,15)(18,19)(20,22)(23,29)(24,28)(25,32)(26,31)(27,30)(33,34)(35,37)(38,44)(39,43)(40,47)(41,46)(42,45);
s3 := Sym(49)!( 3, 8)( 4, 9)( 5,10)( 6,11)( 7,12)(18,38)(19,39)(20,40)(21,41)(22,42)(23,33)(24,34)(25,35)(26,36)(27,37)(28,43)(29,44)(30,45)(31,46)(32,47);
s4 := Sym(49)!( 3,18)( 4,19)( 5,20)( 6,21)( 7,22)( 8,28)( 9,29)(10,30)(11,31)(12,32)(13,23)(14,24)(15,25)(16,26)(17,27)(38,43)(39,44)(40,45)(41,46)(42,47);
s5 := Sym(49)!(48,49);
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, 
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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;