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Polytope of Type {12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6}*192b
if this polytope has a name.
Group : SmallGroup(192,1481)
Rank : 3
Schlafli Type : {12,6}
Number of vertices, edges, etc : 16, 48, 8
Order of s0s1s2 : 8
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {12,6,2} of size 384
   {12,6,4} of size 768
   {12,6,6} of size 1152
   {12,6,10} of size 1920
Vertex Figure Of :
   {2,12,6} of size 384
   {4,12,6} of size 768
   {3,12,6} of size 960
   {6,12,6} of size 1152
   {10,12,6} of size 1920
   {6,12,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,3}*96, {6,6}*96
   4-fold quotients : {3,6}*48, {6,3}*48
   8-fold quotients : {3,3}*24
   24-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,12}*384b, {12,6}*384, {12,12}*384c
   3-fold covers : {12,6}*576c, {12,6}*576d
   4-fold covers : {12,6}*768c, {12,6}*768d, {12,6}*768e, {24,6}*768, {12,24}*768a, {12,24}*768b, {12,12}*768a
   5-fold covers : {12,30}*960a, {60,6}*960b
   6-fold covers : {12,12}*1152d, {12,12}*1152e, {12,12}*1152f, {12,6}*1152a, {12,6}*1152e, {12,12}*1152q
   7-fold covers : {12,42}*1344a, {84,6}*1344b
   9-fold covers : {12,18}*1728a, {36,6}*1728c, {12,6}*1728c, {12,6}*1728d, {12,6}*1728g
   10-fold covers : {12,60}*1920a, {60,12}*1920a, {12,60}*1920b, {60,6}*1920, {12,30}*1920, {60,12}*1920d
Permutation Representation (GAP) :
s0 := ( 3, 5)( 4, 6)( 7, 8)( 9,17)(10,18)(11,21)(12,22)(13,19)(14,20)(15,24)
(16,23)(25,26)(27,30)(28,29)(33,42)(34,41)(35,46)(36,45)(37,44)(38,43)(39,47)
(40,48)(51,53)(52,54)(55,56)(57,65)(58,66)(59,69)(60,70)(61,67)(62,68)(63,72)
(64,71)(73,74)(75,78)(76,77)(81,90)(82,89)(83,94)(84,93)(85,92)(86,91)(87,95)
(88,96);;
s1 := ( 1,33)( 2,34)( 3,36)( 4,35)( 5,39)( 6,40)( 7,37)( 8,38)( 9,25)(10,26)
(11,28)(12,27)(13,31)(14,32)(15,29)(16,30)(17,41)(18,42)(19,44)(20,43)(21,47)
(22,48)(23,45)(24,46)(49,81)(50,82)(51,84)(52,83)(53,87)(54,88)(55,85)(56,86)
(57,73)(58,74)(59,76)(60,75)(61,79)(62,80)(63,77)(64,78)(65,89)(66,90)(67,92)
(68,91)(69,95)(70,96)(71,93)(72,94);;
s2 := ( 1,79)( 2,80)( 3,76)( 4,75)( 5,77)( 6,78)( 7,73)( 8,74)( 9,95)(10,96)
(11,92)(12,91)(13,93)(14,94)(15,89)(16,90)(17,87)(18,88)(19,84)(20,83)(21,85)
(22,86)(23,81)(24,82)(25,55)(26,56)(27,52)(28,51)(29,53)(30,54)(31,49)(32,50)
(33,71)(34,72)(35,68)(36,67)(37,69)(38,70)(39,65)(40,66)(41,63)(42,64)(43,60)
(44,59)(45,61)(46,62)(47,57)(48,58);;
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*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(96)!( 3, 5)( 4, 6)( 7, 8)( 9,17)(10,18)(11,21)(12,22)(13,19)(14,20)
(15,24)(16,23)(25,26)(27,30)(28,29)(33,42)(34,41)(35,46)(36,45)(37,44)(38,43)
(39,47)(40,48)(51,53)(52,54)(55,56)(57,65)(58,66)(59,69)(60,70)(61,67)(62,68)
(63,72)(64,71)(73,74)(75,78)(76,77)(81,90)(82,89)(83,94)(84,93)(85,92)(86,91)
(87,95)(88,96);
s1 := Sym(96)!( 1,33)( 2,34)( 3,36)( 4,35)( 5,39)( 6,40)( 7,37)( 8,38)( 9,25)
(10,26)(11,28)(12,27)(13,31)(14,32)(15,29)(16,30)(17,41)(18,42)(19,44)(20,43)
(21,47)(22,48)(23,45)(24,46)(49,81)(50,82)(51,84)(52,83)(53,87)(54,88)(55,85)
(56,86)(57,73)(58,74)(59,76)(60,75)(61,79)(62,80)(63,77)(64,78)(65,89)(66,90)
(67,92)(68,91)(69,95)(70,96)(71,93)(72,94);
s2 := Sym(96)!( 1,79)( 2,80)( 3,76)( 4,75)( 5,77)( 6,78)( 7,73)( 8,74)( 9,95)
(10,96)(11,92)(12,91)(13,93)(14,94)(15,89)(16,90)(17,87)(18,88)(19,84)(20,83)
(21,85)(22,86)(23,81)(24,82)(25,55)(26,56)(27,52)(28,51)(29,53)(30,54)(31,49)
(32,50)(33,71)(34,72)(35,68)(36,67)(37,69)(38,70)(39,65)(40,66)(41,63)(42,64)
(43,60)(44,59)(45,61)(46,62)(47,57)(48,58);
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*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
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