Polytope of Type {22,4,4} with group SmallGroup(704,1038)

Overview

Group: SmallGroup(704,1038)
Rank: 4
Schläfli Type: {22,4,4}
Vertices, edges, …: 22, 44, 8, 4
Order of s₀s₁s₂s₃: 44
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: {{22,4|2},{4,4|2}}. if this polytope has another name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

{11,2,2}*88

11-fold

{2,4,4}*64

22-fold

44-fold

{2,2,2}*16

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := ( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(13,22)(14,21)(15,20)(16,19)(17,18)(24,33)(25,32)(26,31)(27,30)(28,29)(35,44)(36,43)(37,42)(38,41)(39,40)(46,55)(47,54)(48,53)(49,52)(50,51)(57,66)(58,65)(59,64)(60,63)(61,62)(68,77)(69,76)(70,75)(71,74)(72,73)(79,88)(80,87)(81,86)(82,85)(83,84);;
s1 := ( 1, 2)( 3,11)( 4,10)( 5, 9)( 6, 8)(12,13)(14,22)(15,21)(16,20)(17,19)(23,24)(25,33)(26,32)(27,31)(28,30)(34,35)(36,44)(37,43)(38,42)(39,41)(45,57)(46,56)(47,66)(48,65)(49,64)(50,63)(51,62)(52,61)(53,60)(54,59)(55,58)(67,79)(68,78)(69,88)(70,87)(71,86)(72,85)(73,84)(74,83)(75,82)(76,81)(77,80);;
s2 := ( 1,45)( 2,46)( 3,47)( 4,48)( 5,49)( 6,50)( 7,51)( 8,52)( 9,53)(10,54)(11,55)(12,56)(13,57)(14,58)(15,59)(16,60)(17,61)(18,62)(19,63)(20,64)(21,65)(22,66)(23,67)(24,68)(25,69)(26,70)(27,71)(28,72)(29,73)(30,74)(31,75)(32,76)(33,77)(34,78)(35,79)(36,80)(37,81)(38,82)(39,83)(40,84)(41,85)(42,86)(43,87)(44,88);;
s3 := (45,67)(46,68)(47,69)(48,70)(49,71)(50,72)(51,73)(52,74)(53,75)(54,76)(55,77)(56,78)(57,79)(58,80)(59,81)(60,82)(61,83)(62,84)(63,85)(64,86)(65,87)(66,88);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(88)!( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(13,22)(14,21)(15,20)(16,19)(17,18)(24,33)(25,32)(26,31)(27,30)(28,29)(35,44)(36,43)(37,42)(38,41)(39,40)(46,55)(47,54)(48,53)(49,52)(50,51)(57,66)(58,65)(59,64)(60,63)(61,62)(68,77)(69,76)(70,75)(71,74)(72,73)(79,88)(80,87)(81,86)(82,85)(83,84);
s1 := Sym(88)!( 1, 2)( 3,11)( 4,10)( 5, 9)( 6, 8)(12,13)(14,22)(15,21)(16,20)(17,19)(23,24)(25,33)(26,32)(27,31)(28,30)(34,35)(36,44)(37,43)(38,42)(39,41)(45,57)(46,56)(47,66)(48,65)(49,64)(50,63)(51,62)(52,61)(53,60)(54,59)(55,58)(67,79)(68,78)(69,88)(70,87)(71,86)(72,85)(73,84)(74,83)(75,82)(76,81)(77,80);
s2 := Sym(88)!( 1,45)( 2,46)( 3,47)( 4,48)( 5,49)( 6,50)( 7,51)( 8,52)( 9,53)(10,54)(11,55)(12,56)(13,57)(14,58)(15,59)(16,60)(17,61)(18,62)(19,63)(20,64)(21,65)(22,66)(23,67)(24,68)(25,69)(26,70)(27,71)(28,72)(29,73)(30,74)(31,75)(32,76)(33,77)(34,78)(35,79)(36,80)(37,81)(38,82)(39,83)(40,84)(41,85)(42,86)(43,87)(44,88);
s3 := Sym(88)!(45,67)(46,68)(47,69)(48,70)(49,71)(50,72)(51,73)(52,74)(53,75)(54,76)(55,77)(56,78)(57,79)(58,80)(59,81)(60,82)(61,83)(62,84)(63,85)(64,86)(65,87)(66,88);
poly := sub<Sym(88)|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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References