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Polytope of Type {2,16,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,16,10}*640
if this polytope has a name.
Group : SmallGroup(640,15829)
Rank : 4
Schlafli Type : {2,16,10}
Number of vertices, edges, etc : 2, 16, 80, 10
Order of s0s1s2s3 : 80
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,16,10,2} of size 1280
Vertex Figure Of :
   {2,2,16,10} of size 1280
   {3,2,16,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,8,10}*320
   4-fold quotients : {2,4,10}*160
   5-fold quotients : {2,16,2}*128
   8-fold quotients : {2,2,10}*80
   10-fold quotients : {2,8,2}*64
   16-fold quotients : {2,2,5}*40
   20-fold quotients : {2,4,2}*32
   40-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,16,10}*1280a, {2,16,20}*1280a, {2,32,10}*1280
   3-fold covers : {2,16,30}*1920, {6,16,10}*1920, {2,48,10}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (13,18)(14,19)(15,20)(16,21)(17,22)(23,33)(24,34)(25,35)(26,36)(27,37)
(28,38)(29,39)(30,40)(31,41)(32,42)(43,63)(44,64)(45,65)(46,66)(47,67)(48,68)
(49,69)(50,70)(51,71)(52,72)(53,78)(54,79)(55,80)(56,81)(57,82)(58,73)(59,74)
(60,75)(61,76)(62,77);;
s2 := ( 3,43)( 4,47)( 5,46)( 6,45)( 7,44)( 8,48)( 9,52)(10,51)(11,50)(12,49)
(13,58)(14,62)(15,61)(16,60)(17,59)(18,53)(19,57)(20,56)(21,55)(22,54)(23,73)
(24,77)(25,76)(26,75)(27,74)(28,78)(29,82)(30,81)(31,80)(32,79)(33,63)(34,67)
(35,66)(36,65)(37,64)(38,68)(39,72)(40,71)(41,70)(42,69);;
s3 := ( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,19)(20,22)(23,24)(25,27)
(28,29)(30,32)(33,34)(35,37)(38,39)(40,42)(43,44)(45,47)(48,49)(50,52)(53,54)
(55,57)(58,59)(60,62)(63,64)(65,67)(68,69)(70,72)(73,74)(75,77)(78,79)
(80,82);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(82)!(1,2);
s1 := Sym(82)!(13,18)(14,19)(15,20)(16,21)(17,22)(23,33)(24,34)(25,35)(26,36)
(27,37)(28,38)(29,39)(30,40)(31,41)(32,42)(43,63)(44,64)(45,65)(46,66)(47,67)
(48,68)(49,69)(50,70)(51,71)(52,72)(53,78)(54,79)(55,80)(56,81)(57,82)(58,73)
(59,74)(60,75)(61,76)(62,77);
s2 := Sym(82)!( 3,43)( 4,47)( 5,46)( 6,45)( 7,44)( 8,48)( 9,52)(10,51)(11,50)
(12,49)(13,58)(14,62)(15,61)(16,60)(17,59)(18,53)(19,57)(20,56)(21,55)(22,54)
(23,73)(24,77)(25,76)(26,75)(27,74)(28,78)(29,82)(30,81)(31,80)(32,79)(33,63)
(34,67)(35,66)(36,65)(37,64)(38,68)(39,72)(40,71)(41,70)(42,69);
s3 := Sym(82)!( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,19)(20,22)(23,24)
(25,27)(28,29)(30,32)(33,34)(35,37)(38,39)(40,42)(43,44)(45,47)(48,49)(50,52)
(53,54)(55,57)(58,59)(60,62)(63,64)(65,67)(68,69)(70,72)(73,74)(75,77)(78,79)
(80,82);
poly := sub<Sym(82)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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