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Polytope of Type {2,40,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,40,2}*320
if this polytope has a name.
Group : SmallGroup(320,1412)
Rank : 4
Schlafli Type : {2,40,2}
Number of vertices, edges, etc : 2, 40, 40, 2
Order of s0s1s2s3 : 40
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,40,2,2} of size 640
   {2,40,2,3} of size 960
   {2,40,2,4} of size 1280
   {2,40,2,5} of size 1600
   {2,40,2,6} of size 1920
Vertex Figure Of :
   {2,2,40,2} of size 640
   {3,2,40,2} of size 960
   {4,2,40,2} of size 1280
   {5,2,40,2} of size 1600
   {6,2,40,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,20,2}*160
   4-fold quotients : {2,10,2}*80
   5-fold quotients : {2,8,2}*64
   8-fold quotients : {2,5,2}*40
   10-fold quotients : {2,4,2}*32
   20-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,40,4}*640a, {4,40,2}*640a, {2,80,2}*640
   3-fold covers : {2,40,6}*960, {6,40,2}*960, {2,120,2}*960
   4-fold covers : {2,40,4}*1280a, {4,40,2}*1280a, {2,40,8}*1280b, {2,40,8}*1280c, {8,40,2}*1280b, {8,40,2}*1280c, {4,40,4}*1280d, {2,80,4}*1280a, {4,80,2}*1280a, {2,80,4}*1280b, {4,80,2}*1280b, {2,160,2}*1280
   5-fold covers : {2,200,2}*1600, {2,40,10}*1600a, {2,40,10}*1600b, {10,40,2}*1600a, {10,40,2}*1600b
   6-fold covers : {2,120,4}*1920a, {4,120,2}*1920a, {4,40,6}*1920a, {6,40,4}*1920a, {2,40,12}*1920a, {12,40,2}*1920a, {2,240,2}*1920, {2,80,6}*1920, {6,80,2}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8,11)( 9,13)(10,12)(14,15)(16,21)(17,23)(18,22)(19,25)
(20,24)(27,32)(28,31)(29,34)(30,33)(35,36)(37,40)(38,39)(41,42);;
s2 := ( 3, 9)( 4, 6)( 5,17)( 7,19)( 8,12)(10,14)(11,27)(13,29)(15,20)(16,22)
(18,24)(21,35)(23,37)(25,30)(26,31)(28,33)(32,41)(34,38)(36,39)(40,42);;
s3 := (43,44);;
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, 
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*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*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, 5)( 6, 7)( 8,11)( 9,13)(10,12)(14,15)(16,21)(17,23)(18,22)
(19,25)(20,24)(27,32)(28,31)(29,34)(30,33)(35,36)(37,40)(38,39)(41,42);
s2 := Sym(44)!( 3, 9)( 4, 6)( 5,17)( 7,19)( 8,12)(10,14)(11,27)(13,29)(15,20)
(16,22)(18,24)(21,35)(23,37)(25,30)(26,31)(28,33)(32,41)(34,38)(36,39)(40,42);
s3 := Sym(44)!(43,44);
poly := sub<Sym(44)|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, 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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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