Polytope of Type {10,16}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,16}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240469)
Rank : 3
Schlafli Type : {10,16}
Number of vertices, edges, etc : 60, 480, 96
Order of s₀s₁s₂ : 48
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,8}*960a
   4-fold quotients : {10,4}*480a
   8-fold quotients : {10,4}*240a
   16-fold quotients : {5,4}*120
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1> of order 3.
      32 facets:
         32 of {10}*20
      20 vertex figures:
         20 of {16}*32
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1*s0> of order 5.
      32 facets:
         16 of {10}*20
         16 of {2}*4
      12 vertex figures:
         12 of {16}*32

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {10,16}

Twisty Puzzle