Polytope of Type {6,12} with group SmallGroup(384,17958)

Overview

Group: SmallGroup(384,17958)
Rank: 3
Schläfli Type: {6,12}
Vertices, edges, …: 16, 96, 32
Order of s₀s₁s₂: 8
Order of s₀s₁s₂s₁: 12
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-fold

8-fold

16-fold

{3,3}*24

24-fold

{2,4}*16

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)^3> of order 2

24 facets

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

8 vertex figures

8 of {12}*24

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

16 facets

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

8 vertex figures

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

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.