Polytope of Type {20,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,6,2}*1920e
if this polytope has a name.
Group : SmallGroup(1920,240988)
Rank : 4
Schlafli Type : {20,6,2}
Number of vertices, edges, etc : 80, 240, 24, 2
Order of s₀s₁s₂s₃ : 20
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 : {20,3,2}*960, {10,6,2}*960c
   4-fold quotients : {5,6,2}*480b, {10,3,2}*480, {10,6,2}*480c, {10,6,2}*480d, {10,6,2}*480e, {10,6,2}*480f
   8-fold quotients : {5,3,2}*240, {5,6,2}*240b, {5,6,2}*240c, {10,3,2}*240a, {10,3,2}*240b
   16-fold quotients : {5,3,2}*120
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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