Polytope of Type {10,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,6,2}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240990)
Rank : 4
Schlafli Type : {10,6,2}
Number of vertices, edges, etc : 80, 240, 48, 2
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 : {10,6,2}*960c
   4-fold quotients : {5,6,2}*480b, {10,3,2}*480, {10,6,2}*480c, {10,6,2}*480d, {10,6,2}*480e, {10,6,2}*480f
   8-fold quotients : {5,3,2}*240, {5,6,2}*240b, {5,6,2}*240c, {10,3,2}*240a, {10,3,2}*240b
   16-fold quotients : {5,3,2}*120
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope