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

Overview

Group: SmallGroup(1920,240872)
Rank: 3
Schläfli Type: {6,20}
Vertices, edges, …: 48, 480, 160
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

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

{3,5}*60

120-fold

{2,4}*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=<(s0*s1)^3> of order 2

120 facets

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

24 vertex figures

24 of {20}*40

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

64 facets

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

16 vertex figures

16 of {20}*40

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.