Questions?
See the FAQ
or other info.

Polytope of Type {10,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,6,2}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240973)
Rank : 4
Schlafli Type : {10,6,2}
Number of vertices, edges, etc : 80, 240, 48, 2
Order of s0s1s2s3 : 8
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 : {5,6,2}*960, {10,6,2}*960a, {10,6,2}*960b
   4-fold quotients : {5,6,2}*480a, {10,6,2}*480a, {10,6,2}*480b
   8-fold quotients : {5,6,2}*240a
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3,25)( 4,26)( 5,24)( 6,23)( 7,16)( 8,15)( 9,17)(10,18)(19,37)(20,38)
(21,35)(22,36)(27,33)(28,34)(29,31)(30,32)(39,40)(41,42);;
s1 := ( 1, 2)( 7, 8)( 9,10)(11,19)(12,20)(13,21)(14,22)(15,27)(16,28)(17,29)
(18,30)(23,35)(24,36)(25,37)(26,38)(31,42)(32,41)(33,40)(34,39);;
s2 := ( 5, 6)( 7,20)( 8,19)( 9,21)(10,22)(11,13)(12,14)(15,37)(16,38)(17,35)
(18,36)(23,24)(27,32)(28,31)(29,34)(30,33)(39,40);;
s3 := (43,44);;
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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(44)!( 3,25)( 4,26)( 5,24)( 6,23)( 7,16)( 8,15)( 9,17)(10,18)(19,37)
(20,38)(21,35)(22,36)(27,33)(28,34)(29,31)(30,32)(39,40)(41,42);
s1 := Sym(44)!( 1, 2)( 7, 8)( 9,10)(11,19)(12,20)(13,21)(14,22)(15,27)(16,28)
(17,29)(18,30)(23,35)(24,36)(25,37)(26,38)(31,42)(32,41)(33,40)(34,39);
s2 := Sym(44)!( 5, 6)( 7,20)( 8,19)( 9,21)(10,22)(11,13)(12,14)(15,37)(16,38)
(17,35)(18,36)(23,24)(27,32)(28,31)(29,34)(30,33)(39,40);
s3 := Sym(44)!(43,44);
poly := sub<Sym(44)|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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1 >; 
 

to this polytope