Polytope of Type {2,12,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,10}*1920e
if this polytope has a name.
Group : SmallGroup(1920,240988)
Rank : 4
Schlafli Type : {2,12,10}
Number of vertices, edges, etc : 2, 48, 240, 40
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 : {2,12,5}*960, {2,6,10}*960c
   4-fold quotients : {2,3,10}*480, {2,6,5}*480b, {2,6,10}*480c, {2,6,10}*480d, {2,6,10}*480e, {2,6,10}*480f
   8-fold quotients : {2,3,5}*240, {2,3,10}*240a, {2,3,10}*240b, {2,6,5}*240b, {2,6,5}*240c
   16-fold quotients : {2,3,5}*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 := ( 3,10)( 4, 6)( 5,35)( 7,26)( 8,27)( 9,23)(11,18)(12,19)(13,34)(14,31)
(15,33)(16,36)(17,45)(20,29)(21,28)(22,48)(24,41)(25,42)(30,37)(32,46)(38,40)
(39,49)(43,44)(47,50);;
s3 := ( 3,34)( 4,48)( 5,15)( 6,14)( 7,33)( 8,46)( 9,42)(10,40)(11,49)(12,38)
(13,31)(16,32)(17,37)(18,35)(19,36)(20,45)(21,30)(22,27)(23,25)(24,43)(26,50)
(28,39)(29,47)(41,44)(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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)!( 3,10)( 4, 6)( 5,35)( 7,26)( 8,27)( 9,23)(11,18)(12,19)(13,34)
(14,31)(15,33)(16,36)(17,45)(20,29)(21,28)(22,48)(24,41)(25,42)(30,37)(32,46)
(38,40)(39,49)(43,44)(47,50);
s3 := Sym(52)!( 3,34)( 4,48)( 5,15)( 6,14)( 7,33)( 8,46)( 9,42)(10,40)(11,49)
(12,38)(13,31)(16,32)(17,37)(18,35)(19,36)(20,45)(21,30)(22,27)(23,25)(24,43)
(26,50)(28,39)(29,47)(41,44)(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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope