Polytope of Type {8,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*192a
Also Known As : {8,12|2}. if this polytope has another name.
Group : SmallGroup(192,332)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 8, 48, 12
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,12,2} of size 384
   {8,12,4} of size 768
   {8,12,3} of size 768
   {8,12,4} of size 768
   {8,12,4} of size 768
   {8,12,6} of size 1152
   {8,12,6} of size 1152
   {8,12,6} of size 1152
   {8,12,3} of size 1152
   {8,12,6} of size 1728
   {8,12,6} of size 1728
   {8,12,6} of size 1728
   {8,12,10} of size 1920
Vertex Figure Of :
   {2,8,12} of size 384
   {4,8,12} of size 768
   {4,8,12} of size 768
   {6,8,12} of size 1152
   {3,8,12} of size 1152
   {10,8,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,12}*96a, {8,6}*96
   3-fold quotients : {8,4}*64a
   4-fold quotients : {2,12}*48, {4,6}*48a
   6-fold quotients : {4,4}*32, {8,2}*32
   8-fold quotients : {2,6}*24
   12-fold quotients : {2,4}*16, {4,2}*16
   16-fold quotients : {2,3}*12
   24-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,24}*384b, {8,12}*384a, {8,24}*384d, {16,12}*384a, {16,12}*384b
   3-fold covers : {8,36}*576a, {24,12}*576b, {24,12}*576c
   4-fold covers : {8,24}*768a, {8,12}*768a, {8,24}*768c, {16,12}*768a, {16,12}*768b, {8,48}*768a, {8,48}*768b, {16,24}*768c, {8,48}*768d, {16,24}*768d, {16,24}*768e, {8,48}*768f, {16,24}*768f, {32,12}*768a, {32,12}*768b, {8,12}*768u
   5-fold covers : {40,12}*960a, {8,60}*960a
   6-fold covers : {8,36}*1152a, {24,12}*1152b, {24,12}*1152c, {8,72}*1152a, {8,72}*1152c, {24,24}*1152b, {24,24}*1152f, {24,24}*1152g, {24,24}*1152h, {16,36}*1152a, {48,12}*1152b, {48,12}*1152c, {16,36}*1152b, {48,12}*1152e, {48,12}*1152f
   7-fold covers : {56,12}*1344a, {8,84}*1344a
   9-fold covers : {8,108}*1728a, {24,36}*1728b, {24,12}*1728b, {72,12}*1728a, {24,36}*1728c, {24,12}*1728d, {24,12}*1728o, {8,12}*1728e, {8,12}*1728g, {24,12}*1728v
   10-fold covers : {8,60}*1920a, {40,12}*1920a, {8,120}*1920a, {8,120}*1920c, {40,24}*1920a, {40,24}*1920c, {16,60}*1920a, {80,12}*1920a, {16,60}*1920b, {80,12}*1920b
Permutation Representation (GAP) :

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