Polytope of Type {3,8}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope