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Polytope of Type {6,12}

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