Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,15,4}

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

Overview

Group
SmallGroup(1920,240395)
Rank
4
Schläfli Type
{4,15,4}
Vertices, edges, …
16, 120, 120, 4
Order of s0s1s2s3
15
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

No regular quotients.

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=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 2

4 facets

8 vertex figures

P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 2

4 facets

8 vertex figures

P/N, where N=<(s1*s0*s1*s2)^2, s1*s0*s2*s1*s0*s1*s2*s1> of order 4

4 facets

4 vertex figures

P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 4

4 facets

4 vertex figures

Representations

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

References

None.

to this polytope.