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

Overview

Group: SmallGroup(384,17958)
Rank: 4
Schläfli Type: {3,8,4}
Vertices, edges, …: 6, 24, 32, 4
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

{3,4,2}*96

8-fold

16-fold

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

References