Polytope of Type {2,48}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,48}*192
if this polytope has a name.
Group : SmallGroup(192,461)
Rank : 3
Schlafli Type : {2,48}
Number of vertices, edges, etc : 2, 48, 48
Order of s0s1s2 : 48
Order of s0s1s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,48,2} of size 384
   {2,48,4} of size 768
   {2,48,4} of size 768
   {2,48,4} of size 768
   {2,48,4} of size 768
   {2,48,6} of size 1152
   {2,48,6} of size 1152
   {2,48,6} of size 1152
   {2,48,10} of size 1920
Vertex Figure Of :
   {2,2,48} of size 384
   {3,2,48} of size 576
   {4,2,48} of size 768
   {5,2,48} of size 960
   {6,2,48} of size 1152
   {7,2,48} of size 1344
   {9,2,48} of size 1728
   {10,2,48} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,24}*96
   3-fold quotients : {2,16}*64
   4-fold quotients : {2,12}*48
   6-fold quotients : {2,8}*32
   8-fold quotients : {2,6}*24
   12-fold quotients : {2,4}*16
   16-fold quotients : {2,3}*12
   24-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,48}*384a, {2,96}*384
   3-fold covers : {2,144}*576, {6,48}*576a, {6,48}*576b
   4-fold covers : {4,48}*768a, {8,48}*768c, {8,48}*768d, {4,96}*768a, {4,96}*768b, {2,192}*768, {4,48}*768c
   5-fold covers : {10,48}*960, {2,240}*960
   6-fold covers : {4,144}*1152a, {12,48}*1152a, {12,48}*1152b, {2,288}*1152, {6,96}*1152b, {6,96}*1152c
   7-fold covers : {14,48}*1344, {2,336}*1344
   9-fold covers : {2,432}*1728, {6,144}*1728a, {6,144}*1728b, {18,48}*1728a, {6,48}*1728a, {6,48}*1728b, {6,48}*1728f, {6,48}*1728h
   10-fold covers : {4,240}*1920a, {20,48}*1920a, {2,480}*1920, {10,96}*1920
Permutation Representation (GAP) : 
s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8,11)( 9,13)(10,12)(14,17)(15,19)(16,18)(20,23)(21,25)
(22,24)(26,29)(27,31)(28,30)(32,35)(33,37)(34,36)(38,41)(39,43)(40,42)(45,48)
(46,47)(49,50);;
s2 := ( 3, 9)( 4, 6)( 5,15)( 7,10)( 8,12)(11,21)(13,16)(14,18)(17,27)(19,22)
(20,24)(23,33)(25,28)(26,30)(29,39)(31,34)(32,36)(35,45)(37,40)(38,42)(41,49)
(43,46)(44,47)(48,50);;
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*s1*s0*s1, s0*s2*s0*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*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*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*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(50)!(1,2);
s1 := Sym(50)!( 4, 5)( 6, 7)( 8,11)( 9,13)(10,12)(14,17)(15,19)(16,18)(20,23)
(21,25)(22,24)(26,29)(27,31)(28,30)(32,35)(33,37)(34,36)(38,41)(39,43)(40,42)
(45,48)(46,47)(49,50);
s2 := Sym(50)!( 3, 9)( 4, 6)( 5,15)( 7,10)( 8,12)(11,21)(13,16)(14,18)(17,27)
(19,22)(20,24)(23,33)(25,28)(26,30)(29,39)(31,34)(32,36)(35,45)(37,40)(38,42)
(41,49)(43,46)(44,47)(48,50);
poly := sub<Sym(50)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s1*s0*s1, s0*s2*s0*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*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*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*s1*s2 >;

to this polytope