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Polytope of Type {48,2,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,2,10}*1920
if this polytope has a name.
Group : SmallGroup(1920,203905)
Rank : 4
Schlafli Type : {48,2,10}
Number of vertices, edges, etc : 48, 48, 10, 10
Order of s0s1s2s3 : 240
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {48,2,5}*960, {24,2,10}*960
   3-fold quotients : {16,2,10}*640
   4-fold quotients : {24,2,5}*480, {12,2,10}*480
   5-fold quotients : {48,2,2}*384
   6-fold quotients : {16,2,5}*320, {8,2,10}*320
   8-fold quotients : {12,2,5}*240, {6,2,10}*240
   10-fold quotients : {24,2,2}*192
   12-fold quotients : {8,2,5}*160, {4,2,10}*160
   15-fold quotients : {16,2,2}*128
   16-fold quotients : {3,2,10}*120, {6,2,5}*120
   20-fold quotients : {12,2,2}*96
   24-fold quotients : {4,2,5}*80, {2,2,10}*80
   30-fold quotients : {8,2,2}*64
   32-fold quotients : {3,2,5}*60
   40-fold quotients : {6,2,2}*48
   48-fold quotients : {2,2,5}*40
   60-fold quotients : {4,2,2}*32
   80-fold quotients : {3,2,2}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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 := (51,52)(53,54)(55,56)(57,58);;
s3 := (49,53)(50,51)(52,57)(54,55)(56,58);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(58)!( 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(58)!( 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(58)!(51,52)(53,54)(55,56)(57,58);
s3 := Sym(58)!(49,53)(50,51)(52,57)(54,55)(56,58);
poly := sub<Sym(58)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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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