Polytope of Type {12,8}

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

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