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Polytope of Type {48}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48}*96
Also Known As : 48-gon, {48}. if this polytope has another name.
Group : SmallGroup(96,6)
Rank : 2
Schlafli Type : {48}
Number of vertices, edges, etc : 48, 48
Order of s0s1 : 48
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {48,2} of size 192
   {48,4} of size 384
   {48,4} of size 384
   {48,4} of size 384
   {48,4} of size 384
   {48,6} of size 576
   {48,6} of size 576
   {48,6} of size 576
   {48,4} of size 768
   {48,4} of size 768
   {48,8} of size 768
   {48,8} of size 768
   {48,8} of size 768
   {48,8} of size 768
   {48,8} of size 768
   {48,8} of size 768
   {48,4} of size 768
   {48,4} of size 768
   {48,6} of size 768
   {48,6} of size 768
   {48,10} of size 960
   {48,12} of size 1152
   {48,12} of size 1152
   {48,12} of size 1152
   {48,4} of size 1152
   {48,12} of size 1152
   {48,12} of size 1152
   {48,12} of size 1152
   {48,4} of size 1152
   {48,14} of size 1344
   {48,18} of size 1728
   {48,6} of size 1728
   {48,6} of size 1728
   {48,18} of size 1728
   {48,6} of size 1728
   {48,6} of size 1728
   {48,6} of size 1728
   {48,6} of size 1728
   {48,6} of size 1728
   {48,6} of size 1728
   {48,20} of size 1920
   {48,20} of size 1920
   {48,6} of size 1920
   {48,6} of size 1920
   {48,10} of size 1920
   {48,10} of size 1920
   {48,10} of size 1920
   {48,10} of size 1920
   {48,6} of size 1920
   {48,6} of size 1920
Vertex Figure Of :
   {2,48} of size 192
   {4,48} of size 384
   {4,48} of size 384
   {4,48} of size 384
   {4,48} of size 384
   {6,48} of size 576
   {6,48} of size 576
   {6,48} of size 576
   {4,48} of size 768
   {4,48} of size 768
   {8,48} of size 768
   {8,48} of size 768
   {8,48} of size 768
   {8,48} of size 768
   {8,48} of size 768
   {8,48} of size 768
   {4,48} of size 768
   {4,48} of size 768
   {6,48} of size 768
   {6,48} of size 768
   {10,48} of size 960
   {12,48} of size 1152
   {12,48} of size 1152
   {12,48} of size 1152
   {4,48} of size 1152
   {12,48} of size 1152
   {12,48} of size 1152
   {12,48} of size 1152
   {4,48} of size 1152
   {14,48} of size 1344
   {18,48} of size 1728
   {6,48} of size 1728
   {6,48} of size 1728
   {18,48} of size 1728
   {6,48} of size 1728
   {6,48} of size 1728
   {6,48} of size 1728
   {6,48} of size 1728
   {6,48} of size 1728
   {6,48} of size 1728
   {20,48} of size 1920
   {20,48} of size 1920
   {6,48} of size 1920
   {6,48} of size 1920
   {10,48} of size 1920
   {10,48} of size 1920
   {10,48} of size 1920
   {10,48} of size 1920
   {6,48} of size 1920
   {6,48} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {24}*48
   3-fold quotients : {16}*32
   4-fold quotients : {12}*24
   6-fold quotients : {8}*16
   8-fold quotients : {6}*12
   12-fold quotients : {4}*8
   16-fold quotients : {3}*6
   24-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {96}*192
   3-fold covers : {144}*288
   4-fold covers : {192}*384
   5-fold covers : {240}*480
   6-fold covers : {288}*576
   7-fold covers : {336}*672
   8-fold covers : {384}*768
   9-fold covers : {432}*864
   10-fold covers : {480}*960
   11-fold covers : {528}*1056
   12-fold covers : {576}*1152
   13-fold covers : {624}*1248
   14-fold covers : {672}*1344
   15-fold covers : {720}*1440
   17-fold covers : {816}*1632
   18-fold covers : {864}*1728
   19-fold covers : {912}*1824
   20-fold covers : {960}*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);;
poly := Group([s0,s1]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*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*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(48)!( 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(48)!( 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);
poly := sub<Sym(48)|s0,s1>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*s0*s1 >; 
 
References : None.
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