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Polytope of Type {5,12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,12,4}*1920
if this polytope has a name.
Group : SmallGroup(1920,240872)
Rank : 4
Schlafli Type : {5,12,4}
Number of vertices, edges, etc : 20, 120, 96, 4
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 2
Special Properties :
   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 : {5,6,4}*960b, {5,12,2}*960
   4-fold quotients : {5,6,4}*480b, {5,6,2}*480b
   8-fold quotients : {5,3,2}*240, {5,6,2}*240b, {5,6,2}*240c
   16-fold quotients : {5,3,2}*120
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,31)( 2,32)( 3,29)( 4,30)( 5,39)( 6,40)( 7,37)( 8,38)( 9,36)(10,35)
(11,34)(12,33)(13,50)(14,49)(15,46)(16,45)(17,43)(18,44)(19,51)(20,52)(21,41)
(22,42)(23,48)(24,47)(25,55)(26,56)(27,54)(28,53);;
s1 := ( 1,31)( 2,32)( 3,29)( 4,30)( 5,35)( 6,36)( 7,34)( 8,33)( 9,49)(10,50)
(11,52)(12,51)(13,55)(14,56)(15,46)(16,45)(17,43)(18,44)(19,53)(20,54)(21,38)
(22,37)(23,39)(24,40)(25,48)(26,47)(27,42)(28,41);;
s2 := ( 3, 4)( 5,11)( 6,12)( 9,10)(13,18)(14,17)(15,22)(16,21)(19,23)(20,24)
(27,28)(29,30)(33,40)(34,39)(35,36)(41,45)(42,46)(43,49)(44,50)(47,52)(48,51)
(53,54);;
s3 := ( 1, 3)( 2, 4)(29,31)(30,32);;
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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1, 
s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(56)!( 1,31)( 2,32)( 3,29)( 4,30)( 5,39)( 6,40)( 7,37)( 8,38)( 9,36)
(10,35)(11,34)(12,33)(13,50)(14,49)(15,46)(16,45)(17,43)(18,44)(19,51)(20,52)
(21,41)(22,42)(23,48)(24,47)(25,55)(26,56)(27,54)(28,53);
s1 := Sym(56)!( 1,31)( 2,32)( 3,29)( 4,30)( 5,35)( 6,36)( 7,34)( 8,33)( 9,49)
(10,50)(11,52)(12,51)(13,55)(14,56)(15,46)(16,45)(17,43)(18,44)(19,53)(20,54)
(21,38)(22,37)(23,39)(24,40)(25,48)(26,47)(27,42)(28,41);
s2 := Sym(56)!( 3, 4)( 5,11)( 6,12)( 9,10)(13,18)(14,17)(15,22)(16,21)(19,23)
(20,24)(27,28)(29,30)(33,40)(34,39)(35,36)(41,45)(42,46)(43,49)(44,50)(47,52)
(48,51)(53,54);
s3 := Sym(56)!( 1, 3)( 2, 4)(29,31)(30,32);
poly := sub<Sym(56)|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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1, 
s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1 >; 
 
References : None.
to this polytope