Polytope of Type {24,4} with group SmallGroup(1920,240816)

Overview

Group: SmallGroup(1920,240816)
Rank: 3
Schläfli Type: {24,4}
Vertices, edges, …: 240, 480, 40
Order of s₀s₁s₂: 10
Order of s₀s₁s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{12,4}*960b

4-fold

8-fold

16-fold

{6,4}*120

240-fold

{2,2}*8

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

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

20 facets

20 of {24}*48

120 vertex figures

120 of {4}*8

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

20 facets

20 of {24}*48

120 vertex figures

120 of {4}*8

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

16 facets

12 of {24}*48
4 of {8}*16

80 vertex figures

80 of {4}*8

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.