Polytope of Type {40,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,2,2}*320
if this polytope has a name.
Group : SmallGroup(320,1412)
Rank : 4
Schlafli Type : {40,2,2}
Number of vertices, edges, etc : 40, 40, 2, 2
Order of s₀s₁s₂s₃ : 40
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {40,2,2,2} of size 640
   {40,2,2,3} of size 960
   {40,2,2,4} of size 1280
   {40,2,2,5} of size 1600
   {40,2,2,6} of size 1920
Vertex Figure Of :
   {2,40,2,2} of size 640
   {4,40,2,2} of size 1280
   {4,40,2,2} of size 1280
   {6,40,2,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {20,2,2}*160
   4-fold quotients : {10,2,2}*80
   5-fold quotients : {8,2,2}*64
   8-fold quotients : {5,2,2}*40
   10-fold quotients : {4,2,2}*32
   20-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {40,4,2}*640a, {40,2,4}*640, {80,2,2}*640
   3-fold covers : {40,2,6}*960, {40,6,2}*960, {120,2,2}*960
   4-fold covers : {40,4,2}*1280a, {40,8,2}*1280b, {40,8,2}*1280c, {40,2,8}*1280, {40,4,4}*1280a, {80,4,2}*1280a, {80,4,2}*1280b, {80,2,4}*1280, {160,2,2}*1280
   5-fold covers : {200,2,2}*1600, {40,2,10}*1600, {40,10,2}*1600a, {40,10,2}*1600b
   6-fold covers : {120,4,2}*1920a, {40,4,6}*1920a, {40,12,2}*1920a, {120,2,4}*1920, {40,6,4}*1920a, {40,2,12}*1920, {240,2,2}*1920, {80,2,6}*1920, {80,6,2}*1920
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,21)(16,20)(17,23)
(18,22)(25,30)(26,29)(27,32)(28,31)(33,34)(35,38)(36,37)(39,40);;
s1 := ( 1, 7)( 2, 4)( 3,15)( 5,17)( 6,10)( 8,12)( 9,25)(11,27)(13,18)(14,20)
(16,22)(19,33)(21,35)(23,28)(24,29)(26,31)(30,39)(32,36)(34,37)(38,40);;
s2 := (41,42);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,21)(16,20)
(17,23)(18,22)(25,30)(26,29)(27,32)(28,31)(33,34)(35,38)(36,37)(39,40);
s1 := Sym(44)!( 1, 7)( 2, 4)( 3,15)( 5,17)( 6,10)( 8,12)( 9,25)(11,27)(13,18)
(14,20)(16,22)(19,33)(21,35)(23,28)(24,29)(26,31)(30,39)(32,36)(34,37)(38,40);
s2 := Sym(44)!(41,42);
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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope