Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,15,6}

Atlas Canonical Name {4,15,6}*1920

Overview

Group
SmallGroup(1920,238598)
Rank
4
Schläfli Type
{4,15,6}
Vertices, edges, …
8, 80, 120, 8
Order of s0s1s2s3
20
Order of s0s1s2s3s2s1
4
Also known as
if this polytope has a name.

Special Properties

  • Orientable
  • Flat

Quotients maximal quotients in bold

4-fold

5-fold

10-fold

20-fold

40-fold

48-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1)^2> of order 2

8 facets

4 vertex figures

Representations

Permutation Representation (GAP) 
s0 := ( 5, 6)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(21,22)(23,24)(25,27)(26,28)(29,32)(30,31)(37,38)(39,40)(41,43)(42,44)(45,48)(46,47)(53,54)(55,56)(57,59)(58,60)(61,64)(62,63)(69,70)(71,72)(73,75)(74,76)(77,80)(78,79);;
s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12)(15,16)(17,69)(18,70)(19,72)(20,71)(21,65)(22,66)(23,68)(24,67)(25,73)(26,74)(27,76)(28,75)(29,77)(30,78)(31,80)(32,79)(33,53)(34,54)(35,56)(36,55)(37,49)(38,50)(39,52)(40,51)(41,57)(42,58)(43,60)(44,59)(45,61)(46,62)(47,64)(48,63);;
s2 := ( 1,17)( 2,20)( 3,19)( 4,18)( 5,29)( 6,32)( 7,31)( 8,30)( 9,25)(10,28)(11,27)(12,26)(13,21)(14,24)(15,23)(16,22)(33,65)(34,68)(35,67)(36,66)(37,77)(38,80)(39,79)(40,78)(41,73)(42,76)(43,75)(44,74)(45,69)(46,72)(47,71)(48,70)(50,52)(53,61)(54,64)(55,63)(56,62)(58,60);;
s3 := ( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15)(19,20)(23,24)(25,29)(26,30)(27,32)(28,31)(35,36)(39,40)(41,45)(42,46)(43,48)(44,47)(51,52)(55,56)(57,61)(58,62)(59,64)(60,63)(67,68)(71,72)(73,77)(74,78)(75,80)(76,79);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s0*s1*s2*s1*s3*s0*s1*s2*s1*s0*s1*s2*s3*s0*s2, 
s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(80)!( 5, 6)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(21,22)(23,24)(25,27)(26,28)(29,32)(30,31)(37,38)(39,40)(41,43)(42,44)(45,48)(46,47)(53,54)(55,56)(57,59)(58,60)(61,64)(62,63)(69,70)(71,72)(73,75)(74,76)(77,80)(78,79);
s1 := Sym(80)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12)(15,16)(17,69)(18,70)(19,72)(20,71)(21,65)(22,66)(23,68)(24,67)(25,73)(26,74)(27,76)(28,75)(29,77)(30,78)(31,80)(32,79)(33,53)(34,54)(35,56)(36,55)(37,49)(38,50)(39,52)(40,51)(41,57)(42,58)(43,60)(44,59)(45,61)(46,62)(47,64)(48,63);
s2 := Sym(80)!( 1,17)( 2,20)( 3,19)( 4,18)( 5,29)( 6,32)( 7,31)( 8,30)( 9,25)(10,28)(11,27)(12,26)(13,21)(14,24)(15,23)(16,22)(33,65)(34,68)(35,67)(36,66)(37,77)(38,80)(39,79)(40,78)(41,73)(42,76)(43,75)(44,74)(45,69)(46,72)(47,71)(48,70)(50,52)(53,61)(54,64)(55,63)(56,62)(58,60);
s3 := Sym(80)!( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15)(19,20)(23,24)(25,29)(26,30)(27,32)(28,31)(35,36)(39,40)(41,45)(42,46)(43,48)(44,47)(51,52)(55,56)(57,61)(58,62)(59,64)(60,63)(67,68)(71,72)(73,77)(74,78)(75,80)(76,79);
poly := sub<Sym(80)|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, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s0*s1*s2*s1*s3*s0*s1*s2*s1*s0*s1*s2*s3*s0*s2, 
s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s1*s2*s1 >;

References

None.

to this polytope.