Polytope of Type {10,24} with group SmallGroup(1920,240816)

Overview

Group: SmallGroup(1920,240816)
Rank: 3
Schläfli Type: {10,24}
Vertices, edges, …: 40, 480, 96
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

{10,12}*960b

4-fold

8-fold

16-fold

{5,6}*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

Click an entry to reveal its facets and vertex figures.

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

48 facets

48 of {10}*20

20 vertex figures

20 of {24}*48

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.