Polytope of Type {10,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,8}*160
Also Known As : {10,8|2}. if this polytope has another name.
Group : SmallGroup(160,131)
Rank : 3
Schlafli Type : {10,8}
Number of vertices, edges, etc : 10, 40, 8
Order of s₀s₁s₂ : 40
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,8,2} of size 320
   {10,8,4} of size 640
   {10,8,4} of size 640
   {10,8,6} of size 960
   {10,8,3} of size 960
   {10,8,4} of size 1280
   {10,8,8} of size 1280
   {10,8,8} of size 1280
   {10,8,8} of size 1280
   {10,8,8} of size 1280
   {10,8,4} of size 1280
   {10,8,10} of size 1600
   {10,8,12} of size 1920
   {10,8,12} of size 1920
   {10,8,3} of size 1920
   {10,8,6} of size 1920
   {10,8,6} of size 1920
Vertex Figure Of :
   {2,10,8} of size 320
   {4,10,8} of size 640
   {5,10,8} of size 800
   {3,10,8} of size 960
   {5,10,8} of size 960
   {6,10,8} of size 960
   {8,10,8} of size 1280
   {10,10,8} of size 1600
   {10,10,8} of size 1600
   {10,10,8} of size 1600
   {12,10,8} of size 1920
   {4,10,8} of size 1920
   {6,10,8} of size 1920
   {3,10,8} of size 1920
   {5,10,8} of size 1920
   {6,10,8} of size 1920
   {6,10,8} of size 1920
   {10,10,8} of size 1920
   {10,10,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,4}*80
   4-fold quotients : {10,2}*40
   5-fold quotients : {2,8}*32
   8-fold quotients : {5,2}*20
   10-fold quotients : {2,4}*16
   20-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,8}*320a, {10,16}*320
   3-fold covers : {10,24}*480, {30,8}*480
   4-fold covers : {40,8}*640b, {20,8}*640a, {40,8}*640d, {20,16}*640a, {20,16}*640b, {10,32}*640
   5-fold covers : {50,8}*800, {10,40}*800a, {10,40}*800c
   6-fold covers : {10,48}*960, {20,24}*960a, {60,8}*960a, {30,16}*960
   7-fold covers : {10,56}*1120, {70,8}*1120
   8-fold covers : {40,8}*1280a, {20,8}*1280a, {40,8}*1280c, {20,16}*1280a, {20,16}*1280b, {80,8}*1280a, {80,8}*1280b, {40,16}*1280c, {80,8}*1280d, {40,16}*1280d, {40,16}*1280e, {80,8}*1280f, {40,16}*1280f, {20,32}*1280a, {20,32}*1280b, {10,64}*1280
   9-fold covers : {10,72}*1440, {90,8}*1440, {30,24}*1440a, {30,24}*1440b, {30,24}*1440c, {30,8}*1440
   10-fold covers : {100,8}*1600a, {50,16}*1600, {10,80}*1600a, {20,40}*1600b, {20,40}*1600c, {10,80}*1600c
   11-fold covers : {10,88}*1760, {110,8}*1760
   12-fold covers : {60,8}*1920a, {20,24}*1920a, {120,8}*1920a, {120,8}*1920c, {40,24}*1920a, {40,24}*1920b, {60,16}*1920a, {20,48}*1920a, {60,16}*1920b, {20,48}*1920b, {30,32}*1920, {10,96}*1920, {20,24}*1920c, {30,24}*1920a, {30,8}*1920g
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);;
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, 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(40)!( 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(40)!( 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(40)!( 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);
poly := sub<Sym(40)|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, 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 >;

References : None.
to this polytope