Part of the Atlas of Small Regular Polytopes

Polytope of Type {20,10,2}

Atlas Canonical Name {20,10,2}*1920b

Overview

Group
SmallGroup(1920,240988)
Rank
4
Schläfli Type
{20,10,2}
Vertices, edges, …
48, 240, 24, 2
Order of s0s1s2s3
12
Order of s0s1s2s3s2s1
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

16-fold

120-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := ( 2,45)( 3,41)( 4,17)( 5,19)( 7,30)( 8,48)( 9,36)(10,47)(11,23)(12,34)(13,22)(14,40)(15,39)(20,26)(21,29)(24,38)(25,37)(27,46)(28,31)(35,42);;
s1 := ( 1, 4)( 2,13)( 3, 8)( 5,16)( 6,17)( 7,43)( 9,30)(10,35)(11,27)(12,22)(14,24)(15,25)(18,19)(20,46)(21,28)(23,33)(26,29)(31,40)(32,39)(34,42)(36,38)(37,47)(41,44)(45,48);;
s2 := ( 1,33)( 2, 8)( 3,40)( 4,31)( 5,34)( 6,43)( 7,35)( 9,24)(10,25)(11,22)(12,19)(13,23)(14,41)(15,21)(16,44)(17,28)(18,32)(20,46)(26,27)(29,39)(30,42)(36,38)(37,47)(45,48)(49,50);;
s3 := (51,52);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(52)!( 2,45)( 3,41)( 4,17)( 5,19)( 7,30)( 8,48)( 9,36)(10,47)(11,23)(12,34)(13,22)(14,40)(15,39)(20,26)(21,29)(24,38)(25,37)(27,46)(28,31)(35,42);
s1 := Sym(52)!( 1, 4)( 2,13)( 3, 8)( 5,16)( 6,17)( 7,43)( 9,30)(10,35)(11,27)(12,22)(14,24)(15,25)(18,19)(20,46)(21,28)(23,33)(26,29)(31,40)(32,39)(34,42)(36,38)(37,47)(41,44)(45,48);
s2 := Sym(52)!( 1,33)( 2, 8)( 3,40)( 4,31)( 5,34)( 6,43)( 7,35)( 9,24)(10,25)(11,22)(12,19)(13,23)(14,41)(15,21)(16,44)(17,28)(18,32)(20,46)(26,27)(29,39)(30,42)(36,38)(37,47)(45,48)(49,50);
s3 := Sym(52)!(51,52);
poly := sub<Sym(52)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1 >;