Polytope of Type {2,10,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,20}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240988)
Rank : 4
Schlafli Type : {2,10,20}
Number of vertices, edges, etc : 2, 24, 240, 48
Order of s₀s₁s₂s₃ : 12
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 : {2,5,20}*960, {2,10,10}*960
   4-fold quotients : {2,5,10}*480, {2,10,5}*480, {2,10,10}*480a, {2,10,10}*480b, {2,10,10}*480c, {2,10,10}*480d
   8-fold quotients : {2,5,5}*240, {2,5,10}*240a, {2,5,10}*240b, {2,10,5}*240a, {2,10,5}*240b
   16-fold quotients : {2,5,5}*120
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4,47)( 5,43)( 6,19)( 7,21)( 9,32)(10,50)(11,38)(12,49)(13,25)(14,36)
(15,24)(16,42)(17,41)(22,28)(23,31)(26,40)(27,39)(29,48)(30,33)(37,44);;
s2 := ( 4, 5)( 6,19)( 7,21)( 9,30)(10,37)(11,31)(12,17)(13,28)(14,41)(15,27)
(16,29)(22,40)(23,35)(24,46)(25,33)(26,32)(34,44)(36,43)(42,45)(47,49)
(51,52);;
s3 := ( 3,34)( 4,29)( 5,24)( 6,36)( 7,30)( 8,46)( 9,16)(10,26)(11,12)(13,23)
(14,19)(15,43)(17,44)(18,35)(20,45)(21,33)(22,39)(25,31)(27,28)(32,42)(37,41)
(38,49)(40,50)(47,48);;
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*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(52)!(1,2);
s1 := Sym(52)!( 4,47)( 5,43)( 6,19)( 7,21)( 9,32)(10,50)(11,38)(12,49)(13,25)
(14,36)(15,24)(16,42)(17,41)(22,28)(23,31)(26,40)(27,39)(29,48)(30,33)(37,44);
s2 := Sym(52)!( 4, 5)( 6,19)( 7,21)( 9,30)(10,37)(11,31)(12,17)(13,28)(14,41)
(15,27)(16,29)(22,40)(23,35)(24,46)(25,33)(26,32)(34,44)(36,43)(42,45)(47,49)
(51,52);
s3 := Sym(52)!( 3,34)( 4,29)( 5,24)( 6,36)( 7,30)( 8,46)( 9,16)(10,26)(11,12)
(13,23)(14,19)(15,43)(17,44)(18,35)(20,45)(21,33)(22,39)(25,31)(27,28)(32,42)
(37,41)(38,49)(40,50)(47,48);
poly := sub<Sym(52)|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*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s1*s2*s1*s2 >;

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