Part of the Atlas of Small Regular Polytopes

Polytope of Type {5,20,4}

Atlas Canonical Name {5,20,4}*1920

Overview

Group
SmallGroup(1920,240872)
Rank
4
Schläfli Type
{5,20,4}
Vertices, edges, …
12, 120, 96, 4
Order of s0s1s2s3
12
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP) 
s0 := ( 1,31)( 2,32)( 3,29)( 4,30)( 5,39)( 6,40)( 7,37)( 8,38)( 9,36)(10,35)(11,34)(12,33)(13,50)(14,49)(15,46)(16,45)(17,43)(18,44)(19,51)(20,52)(21,41)(22,42)(23,48)(24,47)(25,55)(26,56)(27,54)(28,53);;
s1 := ( 1,31)( 2,32)( 3,29)( 4,30)( 5,35)( 6,36)( 7,34)( 8,33)( 9,49)(10,50)(11,52)(12,51)(13,55)(14,56)(15,46)(16,45)(17,43)(18,44)(19,53)(20,54)(21,38)(22,37)(23,39)(24,40)(25,48)(26,47)(27,42)(28,41);;
s2 := ( 3, 4)( 7,10)( 8, 9)(11,12)(13,15)(14,16)(17,22)(18,21)(23,24)(25,28)(26,27)(29,30)(33,34)(35,37)(36,38)(41,44)(42,43)(45,49)(46,50)(47,48)(53,55)(54,56);;
s3 := ( 1, 3)( 2, 4)(29,31)(30,32);;
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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(56)!( 1,31)( 2,32)( 3,29)( 4,30)( 5,39)( 6,40)( 7,37)( 8,38)( 9,36)(10,35)(11,34)(12,33)(13,50)(14,49)(15,46)(16,45)(17,43)(18,44)(19,51)(20,52)(21,41)(22,42)(23,48)(24,47)(25,55)(26,56)(27,54)(28,53);
s1 := Sym(56)!( 1,31)( 2,32)( 3,29)( 4,30)( 5,35)( 6,36)( 7,34)( 8,33)( 9,49)(10,50)(11,52)(12,51)(13,55)(14,56)(15,46)(16,45)(17,43)(18,44)(19,53)(20,54)(21,38)(22,37)(23,39)(24,40)(25,48)(26,47)(27,42)(28,41);
s2 := Sym(56)!( 3, 4)( 7,10)( 8, 9)(11,12)(13,15)(14,16)(17,22)(18,21)(23,24)(25,28)(26,27)(29,30)(33,34)(35,37)(36,38)(41,44)(42,43)(45,49)(46,50)(47,48)(53,55)(54,56);
s3 := Sym(56)!( 1, 3)( 2, 4)(29,31)(30,32);
poly := sub<Sym(56)|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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 >;

References

None.

to this polytope.