Polytope of Type {10,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,6}*960a
if this polytope has a name.
Group : SmallGroup(960,10869)
Rank : 3
Schlafli Type : {10,6}
Number of vertices, edges, etc : 80, 240, 48
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {10,6,2} of size 1920
Vertex Figure Of :
   {2,10,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,6}*480, {10,6}*480a, {10,6}*480b
   4-fold quotients : {5,6}*240a, {10,6}*240a, {10,6}*240b
   8-fold quotients : {5,6}*120a
   120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,12}*1920b, {20,6}*1920c
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s2*s1*s2> of order 3.
      16 facets:
         16 of {10}*20
      32 vertex figures:
         8 of {2}*4
         24 of {6}*12

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {10,6}

Twisty Puzzle