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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,8,2}*640
if this polytope has a name.
Group : SmallGroup(640,21152)
Rank : 5
Schlafli Type : {2,10,8,2}
Number of vertices, edges, etc : 2, 10, 40, 8, 2
Order of s0s1s2s3s4 : 40
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,10,8,2,2} of size 1280
   {2,10,8,2,3} of size 1920
Vertex Figure Of :
   {2,2,10,8,2} of size 1280
   {3,2,10,8,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,10,4,2}*320
   4-fold quotients : {2,10,2,2}*160
   5-fold quotients : {2,2,8,2}*128
   8-fold quotients : {2,5,2,2}*80
   10-fold quotients : {2,2,4,2}*64
   20-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,10,8,4}*1280a, {2,20,8,2}*1280a, {4,10,8,2}*1280, {2,10,16,2}*1280
   3-fold covers : {2,30,8,2}*1920, {2,10,8,6}*1920, {6,10,8,2}*1920, {2,10,24,2}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)(25,26)
(29,32)(30,31)(34,37)(35,36)(39,42)(40,41);;
s2 := ( 3, 4)( 5, 7)( 8, 9)(10,12)(13,19)(14,18)(15,22)(16,21)(17,20)(23,39)
(24,38)(25,42)(26,41)(27,40)(28,34)(29,33)(30,37)(31,36)(32,35);;
s3 := ( 3,23)( 4,24)( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)(10,30)(11,31)(12,32)
(13,38)(14,39)(15,40)(16,41)(17,42)(18,33)(19,34)(20,35)(21,36)(22,37);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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)!(1,2);
s1 := Sym(44)!( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)
(25,26)(29,32)(30,31)(34,37)(35,36)(39,42)(40,41);
s2 := Sym(44)!( 3, 4)( 5, 7)( 8, 9)(10,12)(13,19)(14,18)(15,22)(16,21)(17,20)
(23,39)(24,38)(25,42)(26,41)(27,40)(28,34)(29,33)(30,37)(31,36)(32,35);
s3 := Sym(44)!( 3,23)( 4,24)( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)(10,30)(11,31)
(12,32)(13,38)(14,39)(15,40)(16,41)(17,42)(18,33)(19,34)(20,35)(21,36)(22,37);
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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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