Polytope of Type {2,10,8}

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

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

Permutation Representation (Magma) :

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

to this polytope