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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,8,2,2}*640
if this polytope has a name.
Group : SmallGroup(640,21152)
Rank : 5
Schlafli Type : {10,8,2,2}
Number of vertices, edges, etc : 10, 40, 8, 2, 2
Order of s0s1s2s3s4 : 40
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,8,2,2,2} of size 1280
   {10,8,2,2,3} of size 1920
Vertex Figure Of :
   {2,10,8,2,2} of size 1280
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,4,2,2}*320
   4-fold quotients : {10,2,2,2}*160
   5-fold quotients : {2,8,2,2}*128
   8-fold quotients : {5,2,2,2}*80
   10-fold quotients : {2,4,2,2}*64
   20-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,8,4,2}*1280a, {20,8,2,2}*1280a, {10,8,2,4}*1280, {10,16,2,2}*1280
   3-fold covers : {30,8,2,2}*1920, {10,8,2,6}*1920, {10,8,6,2}*1920, {10,24,2,2}*1920
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 := (41,42);;
s4 := (43,44);;
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, 
s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
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(44)!( 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(44)!( 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(44)!( 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(44)!(41,42);
s4 := Sym(44)!(43,44);
poly := sub<Sym(44)|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, s3*s4*s3*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, 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 >; 
 

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