Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {3,2,10,3}*1800

Overview

Group
SmallGroup(1800,575)
Rank
5
Schläfli Type
{3,2,10,3}
Vertices, edges, …
3, 3, 50, 75, 15
Order of s0s1s2s3s4
6
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

25-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 8)( 6, 7)( 9,24)(10,28)(11,27)(12,26)(13,25)(14,19)(15,23)(16,22)(17,21)(18,20);;
s3 := ( 4, 5)( 6, 8)( 9,13)(10,12)(14,16)(17,18)(20,23)(21,22)(24,27)(25,26);;
s4 := ( 5,11)( 6,18)( 7,20)( 8,27)( 9,21)(10,28)(13,14)(16,22)(17,24)(19,25);;
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*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s3*s4*s3, 
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(28)!(2,3);
s1 := Sym(28)!(1,2);
s2 := Sym(28)!( 5, 8)( 6, 7)( 9,24)(10,28)(11,27)(12,26)(13,25)(14,19)(15,23)(16,22)(17,21)(18,20);
s3 := Sym(28)!( 4, 5)( 6, 8)( 9,13)(10,12)(14,16)(17,18)(20,23)(21,22)(24,27)(25,26);
s4 := Sym(28)!( 5,11)( 6,18)( 7,20)( 8,27)( 9,21)(10,28)(13,14)(16,22)(17,24)(19,25);
poly := sub<Sym(28)|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*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;