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Polytope of Type {12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4}*384a
if this polytope has a name.
Group : SmallGroup(384,1706)
Rank : 3
Schlafli Type : {12,4}
Number of vertices, edges, etc : 48, 96, 16
Order of s0s1s2 : 24
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {12,4,2} of size 768
Vertex Figure Of :
   {2,12,4} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,4}*192a
   3-fold quotients : {4,4}*128
   4-fold quotients : {12,4}*96a
   6-fold quotients : {4,4}*64
   8-fold quotients : {12,2}*48, {6,4}*48a
   12-fold quotients : {4,4}*32
   16-fold quotients : {6,2}*24
   24-fold quotients : {2,4}*16, {4,2}*16
   32-fold quotients : {3,2}*12
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,8}*768a, {24,4}*768a, {12,4}*768a, {12,8}*768c, {24,4}*768c
   3-fold covers : {36,4}*1152a, {12,12}*1152a, {12,12}*1152c
   5-fold covers : {60,4}*1920a, {12,20}*1920a
Permutation Representation (GAP) :
s0 := ( 1,49)( 2,51)( 3,50)( 4,52)( 5,54)( 6,53)( 7,55)( 8,57)( 9,56)(10,58)
(11,60)(12,59)(13,70)(14,72)(15,71)(16,67)(17,69)(18,68)(19,64)(20,66)(21,65)
(22,61)(23,63)(24,62)(25,73)(26,75)(27,74)(28,76)(29,78)(30,77)(31,79)(32,81)
(33,80)(34,82)(35,84)(36,83)(37,94)(38,96)(39,95)(40,91)(41,93)(42,92)(43,88)
(44,90)(45,89)(46,85)(47,87)(48,86);;
s1 := ( 1, 2)( 4, 5)( 7,11)( 8,10)( 9,12)(13,14)(16,17)(19,23)(20,22)(21,24)
(25,38)(26,37)(27,39)(28,41)(29,40)(30,42)(31,47)(32,46)(33,48)(34,44)(35,43)
(36,45)(49,50)(52,53)(55,59)(56,58)(57,60)(61,62)(64,65)(67,71)(68,70)(69,72)
(73,86)(74,85)(75,87)(76,89)(77,88)(78,90)(79,95)(80,94)(81,96)(82,92)(83,91)
(84,93);;
s2 := ( 1,25)( 2,26)( 3,27)( 4,28)( 5,29)( 6,30)( 7,31)( 8,32)( 9,33)(10,34)
(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)
(22,46)(23,47)(24,48)(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);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(96)!( 1,49)( 2,51)( 3,50)( 4,52)( 5,54)( 6,53)( 7,55)( 8,57)( 9,56)
(10,58)(11,60)(12,59)(13,70)(14,72)(15,71)(16,67)(17,69)(18,68)(19,64)(20,66)
(21,65)(22,61)(23,63)(24,62)(25,73)(26,75)(27,74)(28,76)(29,78)(30,77)(31,79)
(32,81)(33,80)(34,82)(35,84)(36,83)(37,94)(38,96)(39,95)(40,91)(41,93)(42,92)
(43,88)(44,90)(45,89)(46,85)(47,87)(48,86);
s1 := Sym(96)!( 1, 2)( 4, 5)( 7,11)( 8,10)( 9,12)(13,14)(16,17)(19,23)(20,22)
(21,24)(25,38)(26,37)(27,39)(28,41)(29,40)(30,42)(31,47)(32,46)(33,48)(34,44)
(35,43)(36,45)(49,50)(52,53)(55,59)(56,58)(57,60)(61,62)(64,65)(67,71)(68,70)
(69,72)(73,86)(74,85)(75,87)(76,89)(77,88)(78,90)(79,95)(80,94)(81,96)(82,92)
(83,91)(84,93);
s2 := Sym(96)!( 1,25)( 2,26)( 3,27)( 4,28)( 5,29)( 6,30)( 7,31)( 8,32)( 9,33)
(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)
(21,45)(22,46)(23,47)(24,48)(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);
poly := sub<Sym(96)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope