Polytope of Type {20,3}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,3}*1440a
if this polytope has a name.
Group : SmallGroup(1440,4642)
Rank : 3
Schlafli Type : {20,3}
Number of vertices, edges, etc : 240, 360, 36
Order of s₀s₁s₂ : 60
Order of s₀s₁s₂s₁ : 20
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,3}*720b
   3-fold quotients : {20,3}*480
   4-fold quotients : {10,3}*360
   6-fold quotients : {10,3}*240
   12-fold quotients : {5,3}*120, {10,3}*120a, {10,3}*120b
   24-fold quotients : {5,3}*60
   120-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1> of order 3.
      12 facets:
         12 of {20}*40
      80 vertex figures:
         80 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0> of order 5.
      12 facets:
         6 of {20}*40
         6 of {4}*8
      48 vertex figures:
         48 of {3}*6

Permutation Representation (GAP) :

s0 := ( 1, 4)( 2,34)( 3,45)( 5,43)( 6,27)( 7,25)( 8,30)( 9,36)(10,38)(11,40)(12,37)(13,29)(14,42)(15,31)(16,23)(17,44)(18,24)(19,26)(20,21)(22,46)(28,32)(33,48)(35,39)(41,47);;
s1 := ( 2,23)( 3,39)( 4,33)( 5,17)( 6, 7)( 8,20)( 9,22)(10,34)(11,29)(12,16)(13,24)(14,26)(15,41)(18,32)(19,48)(25,44)(27,38)(36,40)(42,46)(43,47)(50,51);;
s2 := ( 1,27)( 2,20)( 3,19)( 4, 6)( 5,30)( 7,32)( 8,43)( 9,12)(13,39)(15,22)(16,41)(18,33)(21,34)(23,47)(24,48)(25,28)(26,45)(29,35)(31,46)(36,37)(49,50);;
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, s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(51)!( 1, 4)( 2,34)( 3,45)( 5,43)( 6,27)( 7,25)( 8,30)( 9,36)(10,38)(11,40)(12,37)(13,29)(14,42)(15,31)(16,23)(17,44)(18,24)(19,26)(20,21)(22,46)(28,32)(33,48)(35,39)(41,47);
s1 := Sym(51)!( 2,23)( 3,39)( 4,33)( 5,17)( 6, 7)( 8,20)( 9,22)(10,34)(11,29)(12,16)(13,24)(14,26)(15,41)(18,32)(19,48)(25,44)(27,38)(36,40)(42,46)(43,47)(50,51);
s2 := Sym(51)!( 1,27)( 2,20)( 3,19)( 4, 6)( 5,30)( 7,32)( 8,43)( 9,12)(13,39)(15,22)(16,41)(18,33)(21,34)(23,47)(24,48)(25,28)(26,45)(29,35)(31,46)(36,37)(49,50);
poly := sub<Sym(51)|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, s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1 >;

References : None.
to this polytope

Polytope of Type {20,3}

Twisty Puzzle