Polytope of Type {40,6} with group SmallGroup(1920,240882)

Overview

Group: SmallGroup(1920,240882)
Rank: 3
Schläfli Type: {40,6}
Vertices, edges, …: 160, 480, 24
Order of s₀s₁s₂: 40
Order of s₀s₁s₂s₁: 20
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie

Quotients maximal quotients in bold

2-fold

{20,6}*960c

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=<(s0*s1)^2*s0*s2*(s1*s0)^2*s2*s1*s0*s1*s2> of order 2

12 facets

12 of {40}*80

80 vertex figures

80 of {6}*12

Representations

Permutation Representation (GAP)

s0 := ( 1,61)( 2,53)( 3,70)( 4,71)( 5,72)( 6,50)( 7,58)( 8,60)( 9,49)(10,81)(11,82)(12,83)(13,87)(14,55)(15,56)(16,57)(17,51)(18,68)(19,52)(20,92)(21,54)(22,94)(23,69)(24,77)(25,65)(26,66)(27,67)(28,59)(29,63)(30,85)(31,62)(32,64)(33,86)(34,79)(35,80)(36,76)(37,90)(38,74)(39,75)(40,78)(41,93)(42,88)(43,73)(44,91)(45,96)(46,84)(47,89)(48,95);;
s1 := ( 1,51)( 2,55)( 3,52)( 4,59)( 5,58)( 6,62)( 7,56)( 8,66)( 9,65)(10,60)(11,53)(12,68)(13,70)(14,63)(15,74)(16,73)(17,67)(18,57)(19,76)(20,49)(21,79)(22,71)(23,82)(24,81)(25,75)(26,64)(27,84)(28,50)(29,86)(30,89)(31,77)(32,91)(33,83)(34,72)(35,92)(36,54)(37,93)(38,80)(39,94)(40,95)(41,85)(42,96)(43,87)(44,61)(45,90)(46,69)(47,78)(48,88);;
s2 := ( 1,13)( 2, 9)( 3,33)( 4,23)( 5,24)( 6,37)( 8,19)(10,22)(11,44)(12,35)(14,47)(15,42)(16,40)(20,34)(25,45)(26,41)(27,30)(31,43)(36,48)(38,46)(49,53)(50,90)(52,60)(55,89)(56,88)(57,78)(61,87)(62,73)(65,96)(66,93)(67,85)(69,71)(70,86)(72,77)(74,84)(76,95)(79,92)(80,83)(81,94)(82,91);;
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*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(96)!( 1,61)( 2,53)( 3,70)( 4,71)( 5,72)( 6,50)( 7,58)( 8,60)( 9,49)(10,81)(11,82)(12,83)(13,87)(14,55)(15,56)(16,57)(17,51)(18,68)(19,52)(20,92)(21,54)(22,94)(23,69)(24,77)(25,65)(26,66)(27,67)(28,59)(29,63)(30,85)(31,62)(32,64)(33,86)(34,79)(35,80)(36,76)(37,90)(38,74)(39,75)(40,78)(41,93)(42,88)(43,73)(44,91)(45,96)(46,84)(47,89)(48,95);
s1 := Sym(96)!( 1,51)( 2,55)( 3,52)( 4,59)( 5,58)( 6,62)( 7,56)( 8,66)( 9,65)(10,60)(11,53)(12,68)(13,70)(14,63)(15,74)(16,73)(17,67)(18,57)(19,76)(20,49)(21,79)(22,71)(23,82)(24,81)(25,75)(26,64)(27,84)(28,50)(29,86)(30,89)(31,77)(32,91)(33,83)(34,72)(35,92)(36,54)(37,93)(38,80)(39,94)(40,95)(41,85)(42,96)(43,87)(44,61)(45,90)(46,69)(47,78)(48,88);
s2 := Sym(96)!( 1,13)( 2, 9)( 3,33)( 4,23)( 5,24)( 6,37)( 8,19)(10,22)(11,44)(12,35)(14,47)(15,42)(16,40)(20,34)(25,45)(26,41)(27,30)(31,43)(36,48)(38,46)(49,53)(50,90)(52,60)(55,89)(56,88)(57,78)(61,87)(62,73)(65,96)(66,93)(67,85)(69,71)(70,86)(72,77)(74,84)(76,95)(79,92)(80,83)(81,94)(82,91);
poly := sub<Sym(96)|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*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References

None.

to this polytope.