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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,10,8}*1920
if this polytope has a name.
Group : SmallGroup(1920,235343)
Rank : 5
Schlafli Type : {6,2,10,8}
Number of vertices, edges, etc : 6, 6, 10, 40, 8
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 : {3,2,10,8}*960, {6,2,10,4}*960
   3-fold quotients : {2,2,10,8}*640
   4-fold quotients : {3,2,10,4}*480, {6,2,10,2}*480
   5-fold quotients : {6,2,2,8}*384
   6-fold quotients : {2,2,10,4}*320
   8-fold quotients : {3,2,10,2}*240, {6,2,5,2}*240
   10-fold quotients : {3,2,2,8}*192, {6,2,2,4}*192
   12-fold quotients : {2,2,10,2}*160
   15-fold quotients : {2,2,2,8}*128
   16-fold quotients : {3,2,5,2}*120
   20-fold quotients : {3,2,2,4}*96, {6,2,2,2}*96
   24-fold quotients : {2,2,5,2}*80
   30-fold quotients : {2,2,2,4}*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 := ( 8,11)( 9,10)(13,16)(14,15)(18,21)(19,20)(23,26)(24,25)(28,31)(29,30)
(33,36)(34,35)(38,41)(39,40)(43,46)(44,45);;
s3 := ( 7, 8)( 9,11)(12,13)(14,16)(17,23)(18,22)(19,26)(20,25)(21,24)(27,43)
(28,42)(29,46)(30,45)(31,44)(32,38)(33,37)(34,41)(35,40)(36,39);;
s4 := ( 7,27)( 8,28)( 9,29)(10,30)(11,31)(12,32)(13,33)(14,34)(15,35)(16,36)
(17,42)(18,43)(19,44)(20,45)(21,46)(22,37)(23,38)(24,39)(25,40)(26,41);;
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, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)!( 8,11)( 9,10)(13,16)(14,15)(18,21)(19,20)(23,26)(24,25)(28,31)
(29,30)(33,36)(34,35)(38,41)(39,40)(43,46)(44,45);
s3 := Sym(46)!( 7, 8)( 9,11)(12,13)(14,16)(17,23)(18,22)(19,26)(20,25)(21,24)
(27,43)(28,42)(29,46)(30,45)(31,44)(32,38)(33,37)(34,41)(35,40)(36,39);
s4 := Sym(46)!( 7,27)( 8,28)( 9,29)(10,30)(11,31)(12,32)(13,33)(14,34)(15,35)
(16,36)(17,42)(18,43)(19,44)(20,45)(21,46)(22,37)(23,38)(24,39)(25,40)(26,41);
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, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope