Polytope of Type {20,6} with group SmallGroup(1920,240872)

Overview

Group: SmallGroup(1920,240872)
Rank: 3
Schläfli Type: {20,6}
Vertices, edges, …: 160, 480, 48
Order of s₀s₁s₂: 20
Order of s₀s₁s₂s₁: 20
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie

Related Polytopes

Constructions

Facet of

None in this Atlas.

Vertex figure of

None in this Atlas.

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

32-fold

{5,3}*60

120-fold

{4,2}*16

240-fold

{2,2}*8

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)^3> of order 2

24 facets

24 of {20}*40

120 vertex figures

80 of {3}*6
40 of {6}*12

P/N, where N=<(s1*s0)^2*s1*(s2*s1*s0)^2*s1> of order 3

16 facets

16 of {20}*40

64 vertex figures

48 of {6}*12
16 of {2}*4

Representations

Permutation Representation (GAP)

s0 := ( 3, 4)( 7,10)( 8, 9)(11,12)(13,15)(14,16)(17,22)(18,21)(23,24)(25,28)(26,27)(29,30)(33,34)(35,37)(36,38)(41,44)(42,43)(45,49)(46,50)(47,48)(53,55)(54,56);;
s1 := ( 1,29)( 2,30)( 3,31)( 4,32)( 5,35)( 6,36)( 7,34)( 8,33)( 9,49)(10,50)(11,52)(12,51)(13,55)(14,56)(15,46)(16,45)(17,43)(18,44)(19,53)(20,54)(21,38)(22,37)(23,39)(24,40)(25,48)(26,47)(27,42)(28,41);;
s2 := ( 1,31)( 2,32)( 3,29)( 4,30)( 5,51)( 6,52)( 7,53)( 8,54)( 9,56)(10,55)(11,47)(12,48)(13,44)(14,43)(15,41)(16,42)(17,50)(18,49)(19,40)(20,39)(21,45)(22,46)(23,34)(24,33)(25,36)(26,35)(27,37)(28,38);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1, 
s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

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

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1, 
s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1 >;

References

None.

to this polytope.