Polytope of Type {4,12,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,3}*384
if this polytope has a name.
Group : SmallGroup(384,17958)
Rank : 4
Schlafli Type : {4,12,3}
Number of vertices, edges, etc : 4, 32, 24, 4
Order of s₀s₁s₂s₃ : 8
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,12,3,2} of size 768
Vertex Figure Of :
   {2,4,12,3} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,6,3}*192, {2,12,3}*192
   4-fold quotients : {2,6,3}*96
   8-fold quotients : {2,3,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,12,3}*768, {4,12,6}*768b
   3-fold covers : {12,12,3}*1152, {4,12,3}*1152b
   5-fold covers : {20,12,3}*1920, {4,12,15}*1920
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 := ( 1,49)( 2,50)( 3,54)( 4,53)( 5,52)( 6,51)( 7,56)( 8,55)( 9,65)(10,66)
(11,70)(12,69)(13,68)(14,67)(15,72)(16,71)(17,57)(18,58)(19,62)(20,61)(21,60)
(22,59)(23,64)(24,63)(25,73)(26,74)(27,78)(28,77)(29,76)(30,75)(31,80)(32,79)
(33,89)(34,90)(35,94)(36,93)(37,92)(38,91)(39,96)(40,95)(41,81)(42,82)(43,86)
(44,85)(45,84)(46,83)(47,88)(48,87);;
s2 := ( 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);;
s3 := ( 1, 8)( 2, 7)( 3, 4)( 9,24)(10,23)(11,20)(12,19)(13,21)(14,22)(15,18)
(16,17)(25,32)(26,31)(27,28)(33,48)(34,47)(35,44)(36,43)(37,45)(38,46)(39,42)
(40,41)(49,55)(50,56)(53,54)(57,71)(58,72)(59,67)(60,68)(61,70)(62,69)(63,65)
(64,66)(73,79)(74,80)(77,78)(81,95)(82,96)(83,91)(84,92)(85,94)(86,93)(87,89)
(88,90);;
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, 
s3*s1*s2*s1*s2*s1*s2*s3*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)!( 1,49)( 2,50)( 3,54)( 4,53)( 5,52)( 6,51)( 7,56)( 8,55)( 9,65)
(10,66)(11,70)(12,69)(13,68)(14,67)(15,72)(16,71)(17,57)(18,58)(19,62)(20,61)
(21,60)(22,59)(23,64)(24,63)(25,73)(26,74)(27,78)(28,77)(29,76)(30,75)(31,80)
(32,79)(33,89)(34,90)(35,94)(36,93)(37,92)(38,91)(39,96)(40,95)(41,81)(42,82)
(43,86)(44,85)(45,84)(46,83)(47,88)(48,87);
s2 := 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);
s3 := Sym(96)!( 1, 8)( 2, 7)( 3, 4)( 9,24)(10,23)(11,20)(12,19)(13,21)(14,22)
(15,18)(16,17)(25,32)(26,31)(27,28)(33,48)(34,47)(35,44)(36,43)(37,45)(38,46)
(39,42)(40,41)(49,55)(50,56)(53,54)(57,71)(58,72)(59,67)(60,68)(61,70)(62,69)
(63,65)(64,66)(73,79)(74,80)(77,78)(81,95)(82,96)(83,91)(84,92)(85,94)(86,93)
(87,89)(88,90);
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, s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope