Polytope of Type {8,10,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,10,2}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240973)
Rank : 4
Schlafli Type : {8,10,2}
Number of vertices, edges, etc : 48, 240, 60, 2
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 : {8,5,2}*960, {4,10,2}*960c
   4-fold quotients : {4,5,2}*480, {4,10,2}*480a, {4,10,2}*480b
   8-fold quotients : {4,5,2}*240
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope