Polytope of Type {2,10,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,10}*1920
if this polytope has a name.
Group : SmallGroup(1920,240990)
Rank : 4
Schlafli Type : {2,10,10}
Number of vertices, edges, etc : 2, 48, 240, 48
Order of s₀s₁s₂s₃ : 6
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 : {2,10,10}*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 := ( 4,29)( 5,21)( 6,17)( 9,24)(10,50)(11,30)(12,45)(13,27)(14,49)(15,37)
(16,39)(18,34)(20,23)(25,44)(26,28)(31,38)(32,47)(33,35)(42,43)(46,48);;
s2 := ( 4,12)( 5,13)( 9,39)(10,25)(11,27)(14,28)(15,29)(16,30)(20,37)(21,24)
(22,49)(23,35)(26,42)(31,43)(32,44)(33,45)(36,48)(38,40)(41,47)(46,50);;
s3 := ( 3,22)( 4,25)( 5,47)( 6, 9)( 7,41)( 8,40)(10,12)(11,42)(13,28)(14,35)
(15,38)(16,48)(17,24)(18,23)(19,36)(20,34)(21,32)(26,27)(29,44)(30,43)(31,37)
(33,49)(39,46)(45,50);;
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*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s3*s2*s1*s3*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope