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

Overview

Group: SmallGroup(1440,4642)
Rank: 3
Schläfli Type: {3,20}
Vertices, edges, …: 36, 360, 240
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

{3,10}*720b

3-fold

{3,20}*480

4-fold

{3,10}*360

6-fold

{3,10}*240

12-fold

24-fold

{3,5}*60

120-fold

{3,2}*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=<s1*s0*(s2*s1)^6*s0*s2*s1*s2> of order 3

80 facets

80 of {3}*6

12 vertex figures

12 of {20}*40

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

48 facets

48 of {3}*6

12 vertex figures

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

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.