Polytope of Type {20,3} with group SmallGroup(1440,4642)

Overview

Group: SmallGroup(1440,4642)
Rank: 3
Schläfli Type: {20,3}
Vertices, edges, …: 240, 360, 36
Order of s₀s₁s₂: 60
Order of s₀s₁s₂s₁: 20
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{10,3}*720b

3-fold

{20,3}*480

4-fold

{10,3}*360

6-fold

{10,3}*240

12-fold

24-fold

{5,3}*60

120-fold

{2,3}*12

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*s0*(s2*(s1*s0)^2)^2*s1> of order 3

12 facets

12 of {20}*40

80 vertex figures

80 of {3}*6

P/N, where N=<(s0*s1)^2*s0*s2*(s1*s0)^3*s1*s2*(s1*s0)^2> of order 5

12 facets

6 of {20}*40
6 of {4}*8

48 vertex figures

48 of {3}*6

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.