Polytope of Type {4,8,3} with group SmallGroup(384,17958)

Overview

Group: SmallGroup(384,17958)
Rank: 4
Schläfli Type: {4,8,3}
Vertices, edges, …: 4, 32, 24, 6
Order of s₀s₁s₂s₃: 12
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

4-fold

{2,4,3}*96

8-fold

16-fold

{2,2,3}*24

Covers minimal covers in bold

2-fold

3-fold

5-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := (49,73)(50,74)(51,75)(52,76)(53,77)(54,78)(55,79)(56,80)(57,81)(58,82)(59,83)(60,84)(61,85)(62,86)(63,87)(64,88)(65,89)(66,90)(67,91)(68,92)(69,93)(70,94)(71,95)(72,96);;
s1 := ( 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)(25,77)(26,78)(27,80)(28,79)(29,74)(30,73)(31,75)(32,76)(33,85)(34,86)(35,88)(36,87)(37,82)(38,81)(39,83)(40,84)(41,93)(42,94)(43,96)(44,95)(45,90)(46,89)(47,91)(48,92);;
s2 := ( 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);;
s3 := ( 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,s3]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s2*s1*s2*s3*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)!(49,73)(50,74)(51,75)(52,76)(53,77)(54,78)(55,79)(56,80)(57,81)(58,82)(59,83)(60,84)(61,85)(62,86)(63,87)(64,88)(65,89)(66,90)(67,91)(68,92)(69,93)(70,94)(71,95)(72,96);
s1 := 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)(25,77)(26,78)(27,80)(28,79)(29,74)(30,73)(31,75)(32,76)(33,85)(34,86)(35,88)(36,87)(37,82)(38,81)(39,83)(40,84)(41,93)(42,94)(43,96)(44,95)(45,90)(46,89)(47,91)(48,92);
s2 := 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);
s3 := 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,s3>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References