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Polytope of Type {2,10,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,12}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240976)
Rank : 4
Schlafli Type : {2,10,12}
Number of vertices, edges, etc : 2, 40, 240, 48
Order of s0s1s2s3 : 8
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 : {2,10,6}*960b
   4-fold quotients : {2,5,6}*480a, {2,10,6}*480a, {2,10,6}*480b
   8-fold quotients : {2,5,6}*240a
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 6)( 5,30)( 7,15)( 9,17)(10,44)(11,26)(12,37)(13,33)(14,36)(16,35)
(20,31)(21,23)(22,39)(24,25)(27,43)(28,42)(29,41)(32,38)(45,47)(48,49);;
s2 := ( 4,29)( 5,10)( 6,14)( 8,28)( 9,11)(12,46)(13,42)(16,18)(17,32)(20,26)
(21,30)(23,40)(24,33)(25,35)(27,47)(31,48)(36,45)(37,44)(38,49)(41,43);;
s3 := ( 3, 8)( 4,23)( 5,17)( 6,21)( 7,26)( 9,30)(10,31)(11,15)(12,36)(13,47)
(14,37)(16,48)(18,50)(19,46)(20,44)(22,27)(24,29)(25,41)(28,32)(33,45)(34,40)
(35,49)(38,42)(39,43);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s3*s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(50)!(1,2);
s1 := Sym(50)!( 4, 6)( 5,30)( 7,15)( 9,17)(10,44)(11,26)(12,37)(13,33)(14,36)
(16,35)(20,31)(21,23)(22,39)(24,25)(27,43)(28,42)(29,41)(32,38)(45,47)(48,49);
s2 := Sym(50)!( 4,29)( 5,10)( 6,14)( 8,28)( 9,11)(12,46)(13,42)(16,18)(17,32)
(20,26)(21,30)(23,40)(24,33)(25,35)(27,47)(31,48)(36,45)(37,44)(38,49)(41,43);
s3 := Sym(50)!( 3, 8)( 4,23)( 5,17)( 6,21)( 7,26)( 9,30)(10,31)(11,15)(12,36)
(13,47)(14,37)(16,48)(18,50)(19,46)(20,44)(22,27)(24,29)(25,41)(28,32)(33,45)
(34,40)(35,49)(38,42)(39,43);
poly := sub<Sym(50)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s3*s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2 >; 
 

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