Polytope of Type {10,8,2,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,8,2,6}*1920
if this polytope has a name.
Group : SmallGroup(1920,235343)
Rank : 5
Schlafli Type : {10,8,2,6}
Number of vertices, edges, etc : 10, 40, 8, 6, 6
Order of s₀s₁s₂s₃s₄ : 120
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {10,8,2,3}*960, {10,4,2,6}*960
   3-fold quotients : {10,8,2,2}*640
   4-fold quotients : {10,4,2,3}*480, {10,2,2,6}*480
   5-fold quotients : {2,8,2,6}*384
   6-fold quotients : {10,4,2,2}*320
   8-fold quotients : {5,2,2,6}*240, {10,2,2,3}*240
   10-fold quotients : {2,8,2,3}*192, {2,4,2,6}*192
   12-fold quotients : {10,2,2,2}*160
   15-fold quotients : {2,8,2,2}*128
   16-fold quotients : {5,2,2,3}*120
   20-fold quotients : {2,4,2,3}*96, {2,2,2,6}*96
   24-fold quotients : {5,2,2,2}*80
   30-fold quotients : {2,4,2,2}*64
   40-fold quotients : {2,2,2,3}*48
   60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)
(27,30)(28,29)(32,35)(33,34)(37,40)(38,39);;
s1 := ( 1, 2)( 3, 5)( 6, 7)( 8,10)(11,17)(12,16)(13,20)(14,19)(15,18)(21,37)
(22,36)(23,40)(24,39)(25,38)(26,32)(27,31)(28,35)(29,34)(30,33);;
s2 := ( 1,21)( 2,22)( 3,23)( 4,24)( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)(10,30)
(11,36)(12,37)(13,38)(14,39)(15,40)(16,31)(17,32)(18,33)(19,34)(20,35);;
s3 := (43,44)(45,46);;
s4 := (41,45)(42,43)(44,46);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(46)!( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)
(23,24)(27,30)(28,29)(32,35)(33,34)(37,40)(38,39);
s1 := Sym(46)!( 1, 2)( 3, 5)( 6, 7)( 8,10)(11,17)(12,16)(13,20)(14,19)(15,18)
(21,37)(22,36)(23,40)(24,39)(25,38)(26,32)(27,31)(28,35)(29,34)(30,33);
s2 := Sym(46)!( 1,21)( 2,22)( 3,23)( 4,24)( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)
(10,30)(11,36)(12,37)(13,38)(14,39)(15,40)(16,31)(17,32)(18,33)(19,34)(20,35);
s3 := Sym(46)!(43,44)(45,46);
s4 := Sym(46)!(41,45)(42,43)(44,46);
poly := sub<Sym(46)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*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 >;

to this polytope