Polytope of Type {10,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,8,2}*320
if this polytope has a name.
Group : SmallGroup(320,1426)
Rank : 4
Schlafli Type : {10,8,2}
Number of vertices, edges, etc : 10, 40, 8, 2
Order of s₀s₁s₂s₃ : 40
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,8,2,2} of size 640
   {10,8,2,3} of size 960
   {10,8,2,4} of size 1280
   {10,8,2,5} of size 1600
   {10,8,2,6} of size 1920
Vertex Figure Of :
   {2,10,8,2} of size 640
   {4,10,8,2} of size 1280
   {5,10,8,2} of size 1600
   {6,10,8,2} of size 1920
   {3,10,8,2} of size 1920
   {5,10,8,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,4,2}*160
   4-fold quotients : {10,2,2}*80
   5-fold quotients : {2,8,2}*64
   8-fold quotients : {5,2,2}*40
   10-fold quotients : {2,4,2}*32
   20-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,8,2}*640a, {10,8,4}*640a, {10,16,2}*640
   3-fold covers : {10,24,2}*960, {10,8,6}*960, {30,8,2}*960
   4-fold covers : {10,8,4}*1280a, {20,8,2}*1280a, {10,8,8}*1280b, {10,8,8}*1280c, {40,8,2}*1280a, {40,8,2}*1280c, {20,8,4}*1280d, {10,16,4}*1280a, {20,16,2}*1280a, {10,16,4}*1280b, {20,16,2}*1280b, {10,32,2}*1280
   5-fold covers : {50,8,2}*1600, {10,40,2}*1600a, {10,8,10}*1600, {10,40,2}*1600c
   6-fold covers : {30,8,4}*1920a, {60,8,2}*1920a, {10,8,12}*1920a, {20,8,6}*1920a, {10,24,4}*1920a, {20,24,2}*1920a, {30,16,2}*1920, {10,16,6}*1920, {10,48,2}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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