Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,15,4}

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

Overview

Group
SmallGroup(1920,238598)
Rank
4
Schläfli Type
{6,15,4}
Vertices, edges, …
8, 120, 80, 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=<(s2*s3)^2> of order 2

4 facets

8 vertex figures

Representations

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

References

None.

to this polytope.