Polytope of Type {4,12,6} with group SmallGroup(768,1088763)

Overview

Group: SmallGroup(768,1088763)
Rank: 4
Schläfli Type: {4,12,6}
Vertices, edges, …: 4, 32, 48, 8
Order of s₀s₁s₂s₃: 4
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

8-fold

12-fold

{4,4,2}*64

16-fold

{2,3,3}*48

24-fold

48-fold

{2,2,2}*16

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := (49,61)(50,62)(51,63)(52,64)(53,65)(54,66)(55,67)(56,68)(57,69)(58,70)(59,71)(60,72)(73,85)(74,86)(75,87)(76,88)(77,89)(78,90)(79,91)(80,92)(81,93)(82,94)(83,95)(84,96);;
s1 := ( 1,49)( 2,50)( 3,52)( 4,51)( 5,57)( 6,58)( 7,60)( 8,59)( 9,53)(10,54)(11,56)(12,55)(13,61)(14,62)(15,64)(16,63)(17,69)(18,70)(19,72)(20,71)(21,65)(22,66)(23,68)(24,67)(25,73)(26,74)(27,76)(28,75)(29,81)(30,82)(31,84)(32,83)(33,77)(34,78)(35,80)(36,79)(37,85)(38,86)(39,88)(40,87)(41,93)(42,94)(43,96)(44,95)(45,89)(46,90)(47,92)(48,91);;
s2 := ( 1, 9)( 2,11)( 3,10)( 4,12)( 6, 7)(13,21)(14,23)(15,22)(16,24)(18,19)(25,33)(26,35)(27,34)(28,36)(30,31)(37,45)(38,47)(39,46)(40,48)(42,43)(49,81)(50,83)(51,82)(52,84)(53,77)(54,79)(55,78)(56,80)(57,73)(58,75)(59,74)(60,76)(61,93)(62,95)(63,94)(64,96)(65,89)(66,91)(67,90)(68,92)(69,85)(70,87)(71,86)(72,88);;
s3 := ( 1, 2)( 5,10)( 6, 9)( 7,11)( 8,12)(13,14)(17,22)(18,21)(19,23)(20,24)(25,26)(29,34)(30,33)(31,35)(32,36)(37,38)(41,46)(42,45)(43,47)(44,48)(49,50)(53,58)(54,57)(55,59)(56,60)(61,62)(65,70)(66,69)(67,71)(68,72)(73,74)(77,82)(78,81)(79,83)(80,84)(85,86)(89,94)(90,93)(91,95)(92,96);;
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*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(96)!(49,61)(50,62)(51,63)(52,64)(53,65)(54,66)(55,67)(56,68)(57,69)(58,70)(59,71)(60,72)(73,85)(74,86)(75,87)(76,88)(77,89)(78,90)(79,91)(80,92)(81,93)(82,94)(83,95)(84,96);
s1 := Sym(96)!( 1,49)( 2,50)( 3,52)( 4,51)( 5,57)( 6,58)( 7,60)( 8,59)( 9,53)(10,54)(11,56)(12,55)(13,61)(14,62)(15,64)(16,63)(17,69)(18,70)(19,72)(20,71)(21,65)(22,66)(23,68)(24,67)(25,73)(26,74)(27,76)(28,75)(29,81)(30,82)(31,84)(32,83)(33,77)(34,78)(35,80)(36,79)(37,85)(38,86)(39,88)(40,87)(41,93)(42,94)(43,96)(44,95)(45,89)(46,90)(47,92)(48,91);
s2 := Sym(96)!( 1, 9)( 2,11)( 3,10)( 4,12)( 6, 7)(13,21)(14,23)(15,22)(16,24)(18,19)(25,33)(26,35)(27,34)(28,36)(30,31)(37,45)(38,47)(39,46)(40,48)(42,43)(49,81)(50,83)(51,82)(52,84)(53,77)(54,79)(55,78)(56,80)(57,73)(58,75)(59,74)(60,76)(61,93)(62,95)(63,94)(64,96)(65,89)(66,91)(67,90)(68,92)(69,85)(70,87)(71,86)(72,88);
s3 := Sym(96)!( 1, 2)( 5,10)( 6, 9)( 7,11)( 8,12)(13,14)(17,22)(18,21)(19,23)(20,24)(25,26)(29,34)(30,33)(31,35)(32,36)(37,38)(41,46)(42,45)(43,47)(44,48)(49,50)(53,58)(54,57)(55,59)(56,60)(61,62)(65,70)(66,69)(67,71)(68,72)(73,74)(77,82)(78,81)(79,83)(80,84)(85,86)(89,94)(90,93)(91,95)(92,96);
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*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

References