Polytope of Type {4,12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,4}*384c
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 : {2,12,4}*192c, {4,6,4}*192b
   4-fold quotients : {2,6,4}*96c
   8-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,12,4}*768d, {4,12,4}*768e
   3-fold covers : {4,36,4}*1152c, {12,12,4}*1152e, {12,12,4}*1152g
   5-fold covers : {20,12,4}*1920c, {4,60,4}*1920c
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)( 2,51)( 3,50)( 4,52)( 5,57)( 6,59)( 7,58)( 8,60)( 9,53)(10,55)
(11,54)(12,56)(13,61)(14,63)(15,62)(16,64)(17,69)(18,71)(19,70)(20,72)(21,65)
(22,67)(23,66)(24,68)(25,73)(26,75)(27,74)(28,76)(29,81)(30,83)(31,82)(32,84)
(33,77)(34,79)(35,78)(36,80)(37,85)(38,87)(39,86)(40,88)(41,93)(42,95)(43,94)
(44,96)(45,89)(46,91)(47,90)(48,92);;
s2 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12)(13,17)(14,18)(15,20)(16,19)(23,24)
(25,29)(26,30)(27,32)(28,31)(35,36)(37,41)(38,42)(39,44)(40,43)(47,48)(49,77)
(50,78)(51,80)(52,79)(53,73)(54,74)(55,76)(56,75)(57,81)(58,82)(59,84)(60,83)
(61,89)(62,90)(63,92)(64,91)(65,85)(66,86)(67,88)(68,87)(69,93)(70,94)(71,96)
(72,95);;
s3 := ( 1,28)( 2,27)( 3,26)( 4,25)( 5,32)( 6,31)( 7,30)( 8,29)( 9,36)(10,35)
(11,34)(12,33)(13,40)(14,39)(15,38)(16,37)(17,44)(18,43)(19,42)(20,41)(21,48)
(22,47)(23,46)(24,45)(49,76)(50,75)(51,74)(52,73)(53,80)(54,79)(55,78)(56,77)
(57,84)(58,83)(59,82)(60,81)(61,88)(62,87)(63,86)(64,85)(65,92)(66,91)(67,90)
(68,89)(69,96)(70,95)(71,94)(72,93);;
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, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s1 ];;
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)( 2,51)( 3,50)( 4,52)( 5,57)( 6,59)( 7,58)( 8,60)( 9,53)
(10,55)(11,54)(12,56)(13,61)(14,63)(15,62)(16,64)(17,69)(18,71)(19,70)(20,72)
(21,65)(22,67)(23,66)(24,68)(25,73)(26,75)(27,74)(28,76)(29,81)(30,83)(31,82)
(32,84)(33,77)(34,79)(35,78)(36,80)(37,85)(38,87)(39,86)(40,88)(41,93)(42,95)
(43,94)(44,96)(45,89)(46,91)(47,90)(48,92);
s2 := Sym(96)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12)(13,17)(14,18)(15,20)(16,19)
(23,24)(25,29)(26,30)(27,32)(28,31)(35,36)(37,41)(38,42)(39,44)(40,43)(47,48)
(49,77)(50,78)(51,80)(52,79)(53,73)(54,74)(55,76)(56,75)(57,81)(58,82)(59,84)
(60,83)(61,89)(62,90)(63,92)(64,91)(65,85)(66,86)(67,88)(68,87)(69,93)(70,94)
(71,96)(72,95);
s3 := Sym(96)!( 1,28)( 2,27)( 3,26)( 4,25)( 5,32)( 6,31)( 7,30)( 8,29)( 9,36)
(10,35)(11,34)(12,33)(13,40)(14,39)(15,38)(16,37)(17,44)(18,43)(19,42)(20,41)
(21,48)(22,47)(23,46)(24,45)(49,76)(50,75)(51,74)(52,73)(53,80)(54,79)(55,78)
(56,77)(57,84)(58,83)(59,82)(60,81)(61,88)(62,87)(63,86)(64,85)(65,92)(66,91)
(67,90)(68,89)(69,96)(70,95)(71,94)(72,93);
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, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s1 >;

References : None.
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