Polytope of Type {40,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,2}*160
if this polytope has a name.
Group : SmallGroup(160,124)
Rank : 3
Schlafli Type : {40,2}
Number of vertices, edges, etc : 40, 40, 2
Order of s₀s₁s₂ : 40
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {40,2,2} of size 320
   {40,2,3} of size 480
   {40,2,4} of size 640
   {40,2,5} of size 800
   {40,2,6} of size 960
   {40,2,7} of size 1120
   {40,2,8} of size 1280
   {40,2,9} of size 1440
   {40,2,10} of size 1600
   {40,2,11} of size 1760
   {40,2,12} of size 1920
Vertex Figure Of :
   {2,40,2} of size 320
   {4,40,2} of size 640
   {4,40,2} of size 640
   {6,40,2} of size 960
   {4,40,2} of size 1280
   {8,40,2} of size 1280
   {8,40,2} of size 1280
   {8,40,2} of size 1280
   {8,40,2} of size 1280
   {4,40,2} of size 1280
   {10,40,2} of size 1600
   {10,40,2} of size 1600
   {10,40,2} of size 1600
   {12,40,2} of size 1920
   {12,40,2} of size 1920
   {6,40,2} of size 1920
   {6,40,2} of size 1920
   {6,40,2} of size 1920
   {6,40,2} of size 1920
   {6,40,2} of size 1920
   {10,40,2} of size 1920
   {10,40,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {20,2}*80
   4-fold quotients : {10,2}*40
   5-fold quotients : {8,2}*32
   8-fold quotients : {5,2}*20
   10-fold quotients : {4,2}*16
   20-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {40,4}*320a, {80,2}*320
   3-fold covers : {40,6}*480, {120,2}*480
   4-fold covers : {40,4}*640a, {40,8}*640a, {40,8}*640b, {80,4}*640a, {80,4}*640b, {160,2}*640
   5-fold covers : {200,2}*800, {40,10}*800a, {40,10}*800b
   6-fold covers : {80,6}*960, {40,12}*960a, {120,4}*960a, {240,2}*960
   7-fold covers : {40,14}*1120, {280,2}*1120
   8-fold covers : {40,8}*1280a, {40,4}*1280a, {40,8}*1280d, {80,4}*1280a, {80,4}*1280b, {40,16}*1280a, {40,16}*1280b, {80,8}*1280c, {80,8}*1280d, {40,16}*1280d, {80,8}*1280e, {80,8}*1280f, {40,16}*1280f, {160,4}*1280a, {160,4}*1280b, {320,2}*1280
   9-fold covers : {40,18}*1440, {360,2}*1440, {120,6}*1440a, {120,6}*1440b, {120,6}*1440c, {40,6}*1440
   10-fold covers : {200,4}*1600a, {400,2}*1600, {80,10}*1600a, {80,10}*1600b, {40,20}*1600c, {40,20}*1600d
   11-fold covers : {40,22}*1760, {440,2}*1760
   12-fold covers : {120,4}*1920a, {40,12}*1920a, {120,8}*1920b, {120,8}*1920c, {40,24}*1920a, {40,24}*1920c, {240,4}*1920a, {80,12}*1920a, {240,4}*1920b, {80,12}*1920b, {480,2}*1920, {160,6}*1920, {40,6}*1920d, {120,6}*1920a, {120,4}*1920c
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);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2, 
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(42)!( 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(42)!( 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(42)!(41,42);
poly := sub<Sym(42)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2, 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 >;

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