Polytope of Type {2,8,10}

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

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

Permutation Representation (Magma) :

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

to this polytope