Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,6,15}

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

Overview

Group
SmallGroup(1920,238598)
Rank
4
Schläfli Type
{4,6,15}
Vertices, edges, …
8, 32, 120, 20
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

20 facets

  • 20 of 2-fold non-regular quotient of {4,6}*96

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

References

None.

to this polytope.