Polytope of Type {4,6} with group SmallGroup(384,18046)

Overview

Group: SmallGroup(384,18046)
Rank: 3
Schläfli Type: {4,6}
Vertices, edges, …: 32, 96, 48
Order of s₀s₁s₂: 24
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

{4,6}*192b

4-fold

{4,6}*96

8-fold

16-fold

24-fold

{4,2}*16

32-fold

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

28 facets

20 of {4}*8
8 of {2}*4

16 vertex figures

16 of {6}*12

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

24 facets

24 of {4}*8

20 vertex figures

8 of {3}*6
12 of {6}*12

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

16 facets

16 of {4}*8

16 vertex figures

8 of {2}*4
8 of {6}*12

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.