Polytope of Type {5,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,8}*480
if this polytope has a name.
Group : SmallGroup(480,948)
Rank : 3
Schlafli Type : {5,8}
Number of vertices, edges, etc : 30, 120, 48
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {5,8,2} of size 960
   {5,8,4} of size 1920
Vertex Figure Of :
   {2,5,8} of size 960
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,4}*240
   4-fold quotients : {5,4}*120
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,8}*960c
   3-fold covers : {15,8}*1440
   4-fold covers : {10,8}*1920b, {20,8}*1920c, {20,8}*1920d
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {5,8}

Twisty Puzzle