Polytope of Type {2,10,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,6}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240990)
Rank : 4
Schlafli Type : {2,10,6}
Number of vertices, edges, etc : 2, 80, 240, 48
Order of s₀s₁s₂s₃ : 10
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 : {2,10,6}*960c
   4-fold quotients : {2,5,6}*480b, {2,10,3}*480, {2,10,6}*480c, {2,10,6}*480d, {2,10,6}*480e, {2,10,6}*480f
   8-fold quotients : {2,5,3}*240, {2,5,6}*240b, {2,5,6}*240c, {2,10,3}*240a, {2,10,3}*240b
   16-fold quotients : {2,5,3}*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)( 4,44)( 5,32)( 6,24)( 7,41)( 8,40)( 9,17)(10,45)(11,43)(12,50)
(13,26)(14,33)(15,31)(16,46)(18,20)(19,36)(21,47)(23,34)(25,29)(27,28)(30,42)
(35,49)(37,38)(39,48);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s3*s2*s3*s2*s3*s2*s1*s2*s1*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, 
s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s1 ];;
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)( 4,44)( 5,32)( 6,24)( 7,41)( 8,40)( 9,17)(10,45)(11,43)
(12,50)(13,26)(14,33)(15,31)(16,46)(18,20)(19,36)(21,47)(23,34)(25,29)(27,28)
(30,42)(35,49)(37,38)(39,48);
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s3*s2*s3*s2*s3*s2*s1*s2*s1*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, 
s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s1 >;

to this polytope