Polytope of Type {4,12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,4}*384e
if this polytope has a name.
Group : SmallGroup(384,17873)
Rank : 4
Schlafli Type : {4,12,4}
Number of vertices, edges, etc : 4, 24, 24, 4
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,12,4,2} of size 768
Vertex Figure Of :
   {2,4,12,4} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,12,2}*192c, {4,6,4}*192c
   4-fold quotients : {4,6,2}*96c
   8-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12,8}*768d, {4,12,4}*768f
   3-fold covers : {4,36,4}*1152e, {4,12,12}*1152f, {4,12,12}*1152g
   5-fold covers : {4,12,20}*1920c, {4,60,4}*1920e
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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