Polytope of Type {4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12}*192b
if this polytope has a name.
Group : SmallGroup(192,1470)
Rank : 3
Schlafli Type : {4,12}
Number of vertices, edges, etc : 8, 48, 24
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,12,2} of size 384
   {4,12,3} of size 768
   {4,12,3} of size 768
   {4,12,4} of size 768
   {4,12,4} of size 768
   {4,12,4} of size 768
   {4,12,6} of size 1152
   {4,12,6} of size 1152
   {4,12,6} of size 1152
   {4,12,6} of size 1728
   {4,12,10} of size 1920
Vertex Figure Of :
   {2,4,12} of size 384
   {4,4,12} of size 768
   {6,4,12} of size 1152
   {10,4,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,12}*96b, {4,12}*96c, {4,6}*96
   4-fold quotients : {2,12}*48, {4,3}*48, {4,6}*48b, {4,6}*48c
   8-fold quotients : {4,3}*24, {2,6}*24
   12-fold quotients : {2,4}*16
   16-fold quotients : {2,3}*12
   24-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12}*384d, {8,12}*384e, {8,12}*384f, {4,24}*384c, {4,24}*384d
   3-fold covers : {4,36}*576b, {12,12}*576f, {12,12}*576g
   4-fold covers : {8,24}*768i, {8,24}*768j, {8,24}*768k, {8,24}*768l, {4,12}*768b, {8,12}*768q, {8,12}*768r, {8,12}*768s, {4,24}*768i, {4,12}*768d, {8,12}*768t, {4,24}*768j, {8,12}*768u, {4,12}*768e, {4,24}*768k, {8,12}*768w, {4,12}*768f, {4,24}*768l, {4,48}*768c, {4,48}*768d
   5-fold covers : {20,12}*960b, {4,60}*960b
   6-fold covers : {4,36}*1152d, {8,36}*1152e, {8,36}*1152f, {4,72}*1152c, {4,72}*1152d, {24,12}*1152i, {24,12}*1152j, {24,12}*1152k, {24,12}*1152l, {12,24}*1152o, {12,24}*1152p, {12,24}*1152q, {12,24}*1152r, {12,12}*1152n, {12,12}*1152o
   7-fold covers : {28,12}*1344b, {4,84}*1344b
   9-fold covers : {4,108}*1728b, {36,12}*1728c, {12,36}*1728e, {12,36}*1728f, {12,12}*1728k, {12,12}*1728l, {12,12}*1728w, {12,12}*1728ab
   10-fold covers : {40,12}*1920e, {40,12}*1920f, {20,24}*1920c, {20,24}*1920d, {20,12}*1920c, {4,60}*1920d, {8,60}*1920e, {8,60}*1920f, {4,120}*1920c, {4,120}*1920d
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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