Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,15,4}

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

Overview

Group
SmallGroup(1920,240395)
Rank
4
Schläfli Type
{4,15,4}
Vertices, edges, …
4, 120, 120, 16
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*s3*s2*s1*(s2*s3)^2> of order 2

8 facets

4 vertex figures

P/N, where N=<(s2*s1*s2*s3)^2> of order 2

8 facets

4 vertex figures

P/N, where N=<s2*s1*s2*s3*s2*s1*s3*s2, s1*s2*s3*s2*s1*(s2*s3)^2> of order 4

4 facets

4 vertex figures

P/N, where N=<(s2*s1*s2*s3)^2, s1*s2*s3*s2*s1*(s2*s3)^2> of order 4

4 facets

4 vertex figures

Representations

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