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Polytope of Type {2,12,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,10}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240976)
Rank : 4
Schlafli Type : {2,12,10}
Number of vertices, edges, etc : 2, 48, 240, 40
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 : {2,6,10}*960b
   4-fold quotients : {2,6,5}*480a, {2,6,10}*480a, {2,6,10}*480b
   8-fold quotients : {2,6,5}*240a
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 3, 5)( 4,40)( 6,15)( 7,14)( 8,32)( 9,37)(10,50)(11,30)(12,29)(13,27)
(16,17)(18,48)(19,33)(20,21)(22,38)(23,45)(24,34)(25,43)(26,44)(28,31)(35,47)
(36,46)(39,49)(41,42);;
s2 := ( 4,36)( 5,23)( 6,41)( 8,42)( 9,38)(10,12)(11,31)(13,25)(14,47)(16,24)
(17,26)(18,35)(20,49)(21,40)(27,29)(28,33)(30,44)(32,48)(37,46)(43,45);;
s3 := ( 4,29)( 6,14)( 7,15)( 8,16)( 9,11)(12,40)(13,35)(17,32)(18,28)(20,26)
(21,44)(22,39)(23,46)(25,42)(27,47)(30,37)(31,48)(36,45)(38,49)(41,43);;
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, 
s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s3*s2*s1*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(50)!(1,2);
s1 := Sym(50)!( 3, 5)( 4,40)( 6,15)( 7,14)( 8,32)( 9,37)(10,50)(11,30)(12,29)
(13,27)(16,17)(18,48)(19,33)(20,21)(22,38)(23,45)(24,34)(25,43)(26,44)(28,31)
(35,47)(36,46)(39,49)(41,42);
s2 := Sym(50)!( 4,36)( 5,23)( 6,41)( 8,42)( 9,38)(10,12)(11,31)(13,25)(14,47)
(16,24)(17,26)(18,35)(20,49)(21,40)(27,29)(28,33)(30,44)(32,48)(37,46)(43,45);
s3 := Sym(50)!( 4,29)( 6,14)( 7,15)( 8,16)( 9,11)(12,40)(13,35)(17,32)(18,28)
(20,26)(21,44)(22,39)(23,46)(25,42)(27,47)(30,37)(31,48)(36,45)(38,49)(41,43);
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, s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s3*s2*s1*s3 >;

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