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Polytope of Type {2,4,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,20}*320
if this polytope has a name.
Group : SmallGroup(320,1159)
Rank : 4
Schlafli Type : {2,4,20}
Number of vertices, edges, etc : 2, 4, 40, 20
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,20,2} of size 640
   {2,4,20,4} of size 1280
   {2,4,20,6} of size 1920
Vertex Figure Of :
   {2,2,4,20} of size 640
   {3,2,4,20} of size 960
   {4,2,4,20} of size 1280
   {5,2,4,20} of size 1600
   {6,2,4,20} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,20}*160, {2,4,10}*160
   4-fold quotients : {2,2,10}*80
   5-fold quotients : {2,4,4}*64
   8-fold quotients : {2,2,5}*40
   10-fold quotients : {2,2,4}*32, {2,4,2}*32
   20-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,20}*640, {2,4,40}*640a, {2,4,20}*640, {2,4,40}*640b, {2,8,20}*640a, {2,8,20}*640b
   3-fold covers : {6,4,20}*960, {2,12,20}*960, {2,4,60}*960a
   4-fold covers : {2,8,20}*1280a, {2,4,40}*1280a, {2,8,40}*1280a, {2,8,40}*1280b, {2,8,40}*1280c, {2,8,40}*1280d, {8,4,20}*1280a, {4,4,40}*1280a, {8,4,20}*1280b, {4,4,40}*1280b, {4,8,20}*1280a, {4,4,20}*1280a, {4,4,20}*1280b, {4,8,20}*1280b, {4,8,20}*1280c, {4,8,20}*1280d, {2,16,20}*1280a, {2,4,80}*1280a, {2,16,20}*1280b, {2,4,80}*1280b, {2,4,20}*1280a, {2,4,40}*1280b, {2,8,20}*1280b
   5-fold covers : {2,4,100}*1600, {10,4,20}*1600, {2,20,20}*1600a, {2,20,20}*1600b
   6-fold covers : {4,4,60}*1920, {4,12,20}*1920a, {12,4,20}*1920, {2,8,60}*1920a, {2,4,120}*1920a, {6,8,20}*1920a, {6,4,40}*1920a, {2,12,40}*1920a, {2,24,20}*1920a, {2,8,60}*1920b, {2,4,120}*1920b, {6,8,20}*1920b, {6,4,40}*1920b, {2,12,40}*1920b, {2,24,20}*1920b, {2,4,60}*1920a, {6,4,20}*1920a, {2,12,20}*1920a
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,43)( 4,44)( 5,45)( 6,46)( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)
(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,68)
(24,69)(25,70)(26,71)(27,72)(28,63)(29,64)(30,65)(31,66)(32,67)(33,78)(34,79)
(35,80)(36,81)(37,82)(38,73)(39,74)(40,75)(41,76)(42,77);;
s2 := ( 3,23)( 4,27)( 5,26)( 6,25)( 7,24)( 8,28)( 9,32)(10,31)(11,30)(12,29)
(13,33)(14,37)(15,36)(16,35)(17,34)(18,38)(19,42)(20,41)(21,40)(22,39)(43,63)
(44,67)(45,66)(46,65)(47,64)(48,68)(49,72)(50,71)(51,70)(52,69)(53,73)(54,77)
(55,76)(56,75)(57,74)(58,78)(59,82)(60,81)(61,80)(62,79);;
s3 := ( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,19)(20,22)(23,34)(24,33)
(25,37)(26,36)(27,35)(28,39)(29,38)(30,42)(31,41)(32,40)(43,44)(45,47)(48,49)
(50,52)(53,54)(55,57)(58,59)(60,62)(63,74)(64,73)(65,77)(66,76)(67,75)(68,79)
(69,78)(70,82)(71,81)(72,80);;
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*s1*s2*s1*s2*s1*s2, 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*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(82)!(1,2);
s1 := Sym(82)!( 3,43)( 4,44)( 5,45)( 6,46)( 7,47)( 8,48)( 9,49)(10,50)(11,51)
(12,52)(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)
(23,68)(24,69)(25,70)(26,71)(27,72)(28,63)(29,64)(30,65)(31,66)(32,67)(33,78)
(34,79)(35,80)(36,81)(37,82)(38,73)(39,74)(40,75)(41,76)(42,77);
s2 := Sym(82)!( 3,23)( 4,27)( 5,26)( 6,25)( 7,24)( 8,28)( 9,32)(10,31)(11,30)
(12,29)(13,33)(14,37)(15,36)(16,35)(17,34)(18,38)(19,42)(20,41)(21,40)(22,39)
(43,63)(44,67)(45,66)(46,65)(47,64)(48,68)(49,72)(50,71)(51,70)(52,69)(53,73)
(54,77)(55,76)(56,75)(57,74)(58,78)(59,82)(60,81)(61,80)(62,79);
s3 := Sym(82)!( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,19)(20,22)(23,34)
(24,33)(25,37)(26,36)(27,35)(28,39)(29,38)(30,42)(31,41)(32,40)(43,44)(45,47)
(48,49)(50,52)(53,54)(55,57)(58,59)(60,62)(63,74)(64,73)(65,77)(66,76)(67,75)
(68,79)(69,78)(70,82)(71,81)(72,80);
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*s1*s2*s1*s2*s1*s2, 
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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