Polytope of Type {8,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,3}*96
if this polytope has a name.
Group : SmallGroup(96,193)
Rank : 3
Schlafli Type : {8,3}
Number of vertices, edges, etc : 16, 24, 6
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {8,3,2} of size 192
   {8,3,4} of size 384
   {8,3,6} of size 576
   {8,3,3} of size 768
   {8,3,4} of size 768
   {8,3,4} of size 768
   {8,3,6} of size 1728
Vertex Figure Of :
   {2,8,3} of size 192
   {4,8,3} of size 384
   {6,8,3} of size 576
   {4,8,3} of size 768
   {4,8,3} of size 768
   {8,8,3} of size 768
   {4,8,3} of size 768
   {4,8,3} of size 768
   {10,8,3} of size 960
   {12,8,3} of size 1152
   {14,8,3} of size 1344
   {18,8,3} of size 1728
   {20,8,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,3}*48
   4-fold quotients : {4,3}*24
   8-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,6}*192b
   3-fold covers : {8,9}*288, {24,3}*288
   4-fold covers : {8,3}*384, {8,12}*384e, {8,6}*384f, {8,12}*384h
   5-fold covers : {8,15}*480
   6-fold covers : {8,18}*576b, {24,6}*576b, {24,6}*576e
   7-fold covers : {8,21}*672
   8-fold covers : {16,3}*768a, {8,6}*768d, {8,6}*768e, {8,6}*768f, {8,24}*768i, {8,24}*768j, {8,6}*768j, {8,24}*768n, {8,12}*768p, {8,24}*768p, {8,12}*768s
   9-fold covers : {8,27}*864, {24,9}*864, {24,3}*864
   10-fold covers : {40,6}*960e, {8,30}*960b
   11-fold covers : {8,33}*1056
   12-fold covers : {8,9}*1152, {8,36}*1152e, {8,18}*1152f, {8,36}*1152h, {24,3}*1152a, {24,12}*1152k, {24,12}*1152l, {24,12}*1152m, {24,6}*1152d, {24,6}*1152l, {24,12}*1152v, {24,3}*1152b
   13-fold covers : {8,39}*1248
   14-fold covers : {56,6}*1344c, {8,42}*1344b
   15-fold covers : {8,45}*1440, {24,15}*1440
   17-fold covers : {8,51}*1632
   18-fold covers : {8,54}*1728b, {72,6}*1728c, {24,18}*1728b, {24,6}*1728b, {24,18}*1728e, {24,6}*1728e, {24,6}*1728f
   19-fold covers : {8,57}*1824
   20-fold covers : {8,15}*1920a, {40,12}*1920f, {40,6}*1920b, {40,12}*1920h, {8,60}*1920e, {8,30}*1920f, {8,60}*1920h
Permutation Representation (GAP) :

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

References : None.
to this polytope