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Polytope of Type {48,2}

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

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