Polytope of Type {4,8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,8,6}*768d
if this polytope has a name.
Group : SmallGroup(768,1089286)
Rank : 4
Schlafli Type : {4,8,6}
Number of vertices, edges, etc : 4, 32, 48, 12
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,4,6}*384d, {2,8,6}*384c
   4-fold quotients : {4,4,3}*192b, {2,4,6}*192
   8-fold quotients : {4,2,6}*96, {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
   16-fold quotients : {4,2,3}*48, {2,4,3}*48, {2,2,6}*48
   24-fold quotients : {4,2,2}*32
   32-fold quotients : {2,2,3}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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 := ( 1,56)( 2,55)( 3,54)( 4,53)( 5,51)( 6,52)( 7,49)( 8,50)( 9,64)(10,63)
(11,62)(12,61)(13,59)(14,60)(15,57)(16,58)(17,72)(18,71)(19,70)(20,69)(21,67)
(22,68)(23,65)(24,66)(25,80)(26,79)(27,78)(28,77)(29,75)(30,76)(31,73)(32,74)
(33,88)(34,87)(35,86)(36,85)(37,83)(38,84)(39,81)(40,82)(41,96)(42,95)(43,94)
(44,93)(45,91)(46,92)(47,89)(48,90);;
s2 := ( 3, 4)( 5, 7)( 6, 8)( 9,17)(10,18)(11,20)(12,19)(13,23)(14,24)(15,21)
(16,22)(27,28)(29,31)(30,32)(33,41)(34,42)(35,44)(36,43)(37,47)(38,48)(39,45)
(40,46)(51,52)(53,55)(54,56)(57,65)(58,66)(59,68)(60,67)(61,71)(62,72)(63,69)
(64,70)(75,76)(77,79)(78,80)(81,89)(82,90)(83,92)(84,91)(85,95)(86,96)(87,93)
(88,94);;
s3 := ( 1,17)( 2,18)( 3,22)( 4,21)( 5,20)( 6,19)( 7,24)( 8,23)(11,14)(12,13)
(15,16)(25,41)(26,42)(27,46)(28,45)(29,44)(30,43)(31,48)(32,47)(35,38)(36,37)
(39,40)(49,66)(50,65)(51,69)(52,70)(53,67)(54,68)(55,71)(56,72)(57,58)(59,61)
(60,62)(73,90)(74,89)(75,93)(76,94)(77,91)(78,92)(79,95)(80,96)(81,82)(83,85)
(84,86);;
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*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)!( 1,56)( 2,55)( 3,54)( 4,53)( 5,51)( 6,52)( 7,49)( 8,50)( 9,64)
(10,63)(11,62)(12,61)(13,59)(14,60)(15,57)(16,58)(17,72)(18,71)(19,70)(20,69)
(21,67)(22,68)(23,65)(24,66)(25,80)(26,79)(27,78)(28,77)(29,75)(30,76)(31,73)
(32,74)(33,88)(34,87)(35,86)(36,85)(37,83)(38,84)(39,81)(40,82)(41,96)(42,95)
(43,94)(44,93)(45,91)(46,92)(47,89)(48,90);
s2 := Sym(96)!( 3, 4)( 5, 7)( 6, 8)( 9,17)(10,18)(11,20)(12,19)(13,23)(14,24)
(15,21)(16,22)(27,28)(29,31)(30,32)(33,41)(34,42)(35,44)(36,43)(37,47)(38,48)
(39,45)(40,46)(51,52)(53,55)(54,56)(57,65)(58,66)(59,68)(60,67)(61,71)(62,72)
(63,69)(64,70)(75,76)(77,79)(78,80)(81,89)(82,90)(83,92)(84,91)(85,95)(86,96)
(87,93)(88,94);
s3 := Sym(96)!( 1,17)( 2,18)( 3,22)( 4,21)( 5,20)( 6,19)( 7,24)( 8,23)(11,14)
(12,13)(15,16)(25,41)(26,42)(27,46)(28,45)(29,44)(30,43)(31,48)(32,47)(35,38)
(36,37)(39,40)(49,66)(50,65)(51,69)(52,70)(53,67)(54,68)(55,71)(56,72)(57,58)
(59,61)(60,62)(73,90)(74,89)(75,93)(76,94)(77,91)(78,92)(79,95)(80,96)(81,82)
(83,85)(84,86);
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s1*s2 >;

References : None.
to this polytope