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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}*192b
if this polytope has a name.
Group : SmallGroup(192,1470)
Rank : 3
Schlafli Type : {12,4}
Number of vertices, edges, etc : 24, 48, 8
Order of s0s1s2 : 12
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {12,4,2} of size 384
   {12,4,4} of size 768
   {12,4,6} of size 1152
   {12,4,10} of size 1920
Vertex Figure Of :
   {2,12,4} of size 384
   {3,12,4} of size 768
   {3,12,4} of size 768
   {4,12,4} of size 768
   {4,12,4} of size 768
   {4,12,4} of size 768
   {6,12,4} of size 1152
   {6,12,4} of size 1152
   {6,12,4} of size 1152
   {6,12,4} of size 1728
   {10,12,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,4}*96b, {12,4}*96c, {6,4}*96
   4-fold quotients : {12,2}*48, {3,4}*48, {6,4}*48b, {6,4}*48c
   8-fold quotients : {3,4}*24, {6,2}*24
   12-fold quotients : {4,2}*16
   16-fold quotients : {3,2}*12
   24-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,4}*384d, {12,8}*384e, {12,8}*384f, {24,4}*384c, {24,4}*384d
   3-fold covers : {36,4}*576b, {12,12}*576d, {12,12}*576e
   4-fold covers : {24,8}*768i, {24,8}*768j, {24,8}*768k, {24,8}*768l, {12,4}*768b, {12,8}*768q, {12,8}*768r, {12,8}*768s, {24,4}*768i, {12,4}*768d, {12,8}*768t, {24,4}*768j, {12,8}*768u, {12,4}*768e, {24,4}*768k, {12,8}*768w, {12,4}*768f, {24,4}*768l, {48,4}*768c, {48,4}*768d
   5-fold covers : {12,20}*960b, {60,4}*960b
   6-fold covers : {36,4}*1152d, {36,8}*1152e, {36,8}*1152f, {72,4}*1152c, {72,4}*1152d, {12,24}*1152i, {12,24}*1152j, {12,24}*1152k, {12,24}*1152l, {24,12}*1152o, {24,12}*1152p, {24,12}*1152q, {24,12}*1152r, {12,12}*1152k, {12,12}*1152m
   7-fold covers : {12,28}*1344b, {84,4}*1344b
   9-fold covers : {108,4}*1728b, {12,36}*1728c, {36,12}*1728e, {36,12}*1728f, {12,12}*1728i, {12,12}*1728j, {12,12}*1728v, {12,12}*1728aa
   10-fold covers : {12,40}*1920e, {12,40}*1920f, {24,20}*1920c, {24,20}*1920d, {12,20}*1920c, {60,4}*1920d, {60,8}*1920e, {60,8}*1920f, {120,4}*1920c, {120,4}*1920d
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)
(25,37)(26,39)(27,38)(28,40)(29,45)(30,47)(31,46)(32,48)(33,41)(34,43)(35,42)
(36,44)(50,51)(53,57)(54,59)(55,58)(56,60)(62,63)(65,69)(66,71)(67,70)(68,72)
(73,85)(74,87)(75,86)(76,88)(77,93)(78,95)(79,94)(80,96)(81,89)(82,91)(83,90)
(84,92);;
s1 := ( 1,29)( 2,30)( 3,32)( 4,31)( 5,25)( 6,26)( 7,28)( 8,27)( 9,33)(10,34)
(11,36)(12,35)(13,41)(14,42)(15,44)(16,43)(17,37)(18,38)(19,40)(20,39)(21,45)
(22,46)(23,48)(24,47)(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);;
s2 := ( 1,52)( 2,51)( 3,50)( 4,49)( 5,56)( 6,55)( 7,54)( 8,53)( 9,60)(10,59)
(11,58)(12,57)(13,64)(14,63)(15,62)(16,61)(17,68)(18,67)(19,66)(20,65)(21,72)
(22,71)(23,70)(24,69)(25,76)(26,75)(27,74)(28,73)(29,80)(30,79)(31,78)(32,77)
(33,84)(34,83)(35,82)(36,81)(37,88)(38,87)(39,86)(40,85)(41,92)(42,91)(43,90)
(44,89)(45,96)(46,95)(47,94)(48,93);;
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*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*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(96)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)
(20,24)(25,37)(26,39)(27,38)(28,40)(29,45)(30,47)(31,46)(32,48)(33,41)(34,43)
(35,42)(36,44)(50,51)(53,57)(54,59)(55,58)(56,60)(62,63)(65,69)(66,71)(67,70)
(68,72)(73,85)(74,87)(75,86)(76,88)(77,93)(78,95)(79,94)(80,96)(81,89)(82,91)
(83,90)(84,92);
s1 := Sym(96)!( 1,29)( 2,30)( 3,32)( 4,31)( 5,25)( 6,26)( 7,28)( 8,27)( 9,33)
(10,34)(11,36)(12,35)(13,41)(14,42)(15,44)(16,43)(17,37)(18,38)(19,40)(20,39)
(21,45)(22,46)(23,48)(24,47)(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);
s2 := Sym(96)!( 1,52)( 2,51)( 3,50)( 4,49)( 5,56)( 6,55)( 7,54)( 8,53)( 9,60)
(10,59)(11,58)(12,57)(13,64)(14,63)(15,62)(16,61)(17,68)(18,67)(19,66)(20,65)
(21,72)(22,71)(23,70)(24,69)(25,76)(26,75)(27,74)(28,73)(29,80)(30,79)(31,78)
(32,77)(33,84)(34,83)(35,82)(36,81)(37,88)(38,87)(39,86)(40,85)(41,92)(42,91)
(43,90)(44,89)(45,96)(46,95)(47,94)(48,93);
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*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*s0*s1 >; 
 
References : None.
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