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

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

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

Permutation Representation (Magma) :

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

to this polytope