Polytope of Type {8,10,2}

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

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

to this polytope