Polytope of Type {6,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,16}*192
Also Known As : {6,16|2}. if this polytope has another name.
Group : SmallGroup(192,469)
Rank : 3
Schlafli Type : {6,16}
Number of vertices, edges, etc : 6, 48, 16
Order of s₀s₁s₂ : 48
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,16,2} of size 384
   {6,16,4} of size 768
   {6,16,4} of size 768
   {6,16,6} of size 1152
   {6,16,10} of size 1920
Vertex Figure Of :
   {2,6,16} of size 384
   {3,6,16} of size 576
   {4,6,16} of size 768
   {3,6,16} of size 768
   {4,6,16} of size 768
   {6,6,16} of size 1152
   {6,6,16} of size 1152
   {6,6,16} of size 1152
   {9,6,16} of size 1728
   {3,6,16} of size 1728
   {10,6,16} of size 1920
   {5,6,16} of size 1920
   {5,6,16} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,8}*96
   3-fold quotients : {2,16}*64
   4-fold quotients : {6,4}*48a
   6-fold quotients : {2,8}*32
   8-fold quotients : {6,2}*24
   12-fold quotients : {2,4}*16
   16-fold quotients : {3,2}*12
   24-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,16}*384a, {6,32}*384
   3-fold covers : {18,16}*576, {6,48}*576a, {6,48}*576c
   4-fold covers : {12,16}*768a, {24,16}*768c, {24,16}*768d, {12,32}*768a, {12,32}*768b, {6,64}*768, {6,16}*768b
   5-fold covers : {6,80}*960, {30,16}*960
   6-fold covers : {36,16}*1152a, {12,48}*1152b, {12,48}*1152c, {18,32}*1152, {6,96}*1152a, {6,96}*1152c
   7-fold covers : {6,112}*1344, {42,16}*1344
   9-fold covers : {54,16}*1728, {6,144}*1728a, {18,48}*1728a, {6,48}*1728b, {18,48}*1728b, {6,48}*1728c, {6,48}*1728f, {6,16}*1728b
   10-fold covers : {60,16}*1920a, {12,80}*1920a, {30,32}*1920, {6,160}*1920
Permutation Representation (GAP) :

s0 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)
(32,33)(35,36)(38,39)(41,42)(44,45)(47,48);;
s1 := ( 1, 2)( 4, 5)( 7,11)( 8,10)( 9,12)(13,20)(14,19)(15,21)(16,23)(17,22)
(18,24)(25,44)(26,43)(27,45)(28,47)(29,46)(30,48)(31,38)(32,37)(33,39)(34,41)
(35,40)(36,42);;
s2 := ( 1,25)( 2,26)( 3,27)( 4,28)( 5,29)( 6,30)( 7,34)( 8,35)( 9,36)(10,31)
(11,32)(12,33)(13,43)(14,44)(15,45)(16,46)(17,47)(18,48)(19,37)(20,38)(21,39)
(22,40)(23,41)(24,42);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*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(48)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)
(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48);
s1 := Sym(48)!( 1, 2)( 4, 5)( 7,11)( 8,10)( 9,12)(13,20)(14,19)(15,21)(16,23)
(17,22)(18,24)(25,44)(26,43)(27,45)(28,47)(29,46)(30,48)(31,38)(32,37)(33,39)
(34,41)(35,40)(36,42);
s2 := Sym(48)!( 1,25)( 2,26)( 3,27)( 4,28)( 5,29)( 6,30)( 7,34)( 8,35)( 9,36)
(10,31)(11,32)(12,33)(13,43)(14,44)(15,45)(16,46)(17,47)(18,48)(19,37)(20,38)
(21,39)(22,40)(23,41)(24,42);
poly := sub<Sym(48)|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, 
s1*s2*s1*s2*s1*s2*s1*s2*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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