Polytope of Type {3,12,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,12,3}*480
if this polytope has a name.
Group : SmallGroup(480,948)
Rank : 4
Schlafli Type : {3,12,3}
Number of vertices, edges, etc : 5, 40, 40, 5
Order of s₀s₁s₂s₃ : 10
Order of s₀s₁s₂s₃s₂s₁ : 12
Special Properties :
   Universal
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,12,3,2} of size 960
Vertex Figure Of :
   {2,3,12,3} of size 960
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,6,3}*240
   4-fold quotients : {3,3,3}*120
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,12,6}*960, {6,12,3}*960
   3-fold covers : {3,12,3}*1440a, {3,12,3}*1440b
   4-fold covers : {3,12,12}*1920, {12,12,3}*1920, {6,12,6}*1920b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope