Polytope of Type {24,4} with group SmallGroup(384,18046)

Overview

Group: SmallGroup(384,18046)
Rank: 3
Schläfli Type: {24,4}
Vertices, edges, …: 48, 96, 8
Order of s₀s₁s₂: 6
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

{12,4}*192c

4-fold

{6,4}*96

8-fold

16-fold

32-fold

{3,2}*12

48-fold

{2,2}*8

Covers minimal covers in bold

2-fold

3-fold

5-fold

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

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

4 facets

4 of {24}*48

24 vertex figures

24 of {4}*8

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.