Polytope of Type {16,6}

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

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

References : None.
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