Polytope of Type {6,10}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,10}*960b
if this polytope has a name.
Group : SmallGroup(960,10891)
Rank : 3
Schlafli Type : {6,10}
Number of vertices, edges, etc : 48, 240, 80
Order of s₀s₁s₂ : 10
Order of s₀s₁s₂s₁ : 20
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,10,2} of size 1920
Vertex Figure Of :
   {2,6,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,10}*480c
   4-fold quotients : {3,10}*240, {6,5}*240b, {6,10}*240c, {6,10}*240d, {6,10}*240e, {6,10}*240f
   8-fold quotients : {3,5}*120, {3,10}*120a, {3,10}*120b, {6,5}*120b, {6,5}*120c
   16-fold quotients : {3,5}*60
   120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,20}*1920d, {12,10}*1920c
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s0*s1> of order 2.
      60 facets:
         40 of {3}*6
         20 of {6}*12
      24 vertex figures:
         24 of {10}*20
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 2.
      40 facets:
         40 of {6}*12
      24 vertex figures:
         24 of {10}*20
   P/N, where N=<s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      40 facets:
         40 of {6}*12
      36 vertex figures:
         24 of {5}*10
         12 of {10}*20
   P/N, where N=<s0*s1*s0*s1> of order 3.
      32 facets:
         8 of {2}*4
         24 of {6}*12
      16 vertex figures:
         16 of {10}*20

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {6,10}

Twisty Puzzle