Polytope of Type {24,10} with group SmallGroup(1920,240882)

Overview

Group: SmallGroup(1920,240882)
Rank: 3
Schläfli Type: {24,10}
Vertices, edges, …: 96, 480, 40
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

Quotients maximal quotients in bold

2-fold

{12,10}*960c

4-fold

8-fold

16-fold

32-fold

{3,5}*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*s0*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^2> of order 2

20 facets

20 of {24}*48

48 vertex figures

48 of {10}*20

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

References

None.

to this polytope.