Polytope of Type {40,4} with group SmallGroup(1920,240864)

Overview

Group: SmallGroup(1920,240864)
Rank: 3
Schläfli Type: {40,4}
Vertices, edges, …: 240, 480, 24
Order of s₀s₁s₂: 6
Order of s₀s₁s₂s₁: 12
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{20,4}*960d

4-fold

{10,4}*480c

8-fold

16-fold

{5,4}*120

240-fold

{2,2}*8

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References