Polytope of Type {6,40} with group SmallGroup(1920,240864)

Overview

Group: SmallGroup(1920,240864)
Rank: 3
Schläfli Type: {6,40}
Vertices, edges, …: 24, 480, 160
Order of s₀s₁s₂: 4
Order of s₀s₁s₂s₁: 8
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{6,20}*960a

4-fold

{6,10}*480b

8-fold

16-fold

{6,5}*120a

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

None.

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References