Polytope of Type {15,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,6}*960
if this polytope has a name.
Group : SmallGroup(960,5762)
Rank : 3
Schlafli Type : {15,6}
Number of vertices, edges, etc : 80, 240, 32
Order of s₀s₁s₂ : 40
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {15,6,2} of size 1920
Vertex Figure Of :
   {2,15,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   4-fold quotients : {15,6}*240
   5-fold quotients : {3,6}*192
   20-fold quotients : {3,6}*48
   40-fold quotients : {3,3}*24
   48-fold quotients : {5,2}*20
Covers (Minimal Covers in Boldface) :
   2-fold covers : {15,12}*1920, {30,6}*1920a
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1> of order 2.
      16 facets:
         16 of {15}*30
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s1*s0*s2*s1*s2*s1*s0*s2*s1*s2> of order 4.
      8 facets:
         8 of {15}*30
      20 vertex figures:
         20 of {6}*12
   P/N, where N=<s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2> of order 4.
      8 facets:
         8 of {15}*30
      20 vertex figures:
         20 of {6}*12

Permutation Representation (GAP) :

s0 := ( 3, 4)( 5,12)( 6,11)( 7, 9)( 8,10)(13,14)(17,65)(18,66)(19,68)(20,67)(21,76)(22,75)(23,73)(24,74)(25,71)(26,72)(27,70)(28,69)(29,78)(30,77)(31,79)(32,80)(33,49)(34,50)(35,52)(36,51)(37,60)(38,59)(39,57)(40,58)(41,55)(42,56)(43,54)(44,53)(45,62)(46,61)(47,63)(48,64);;
s1 := ( 1,17)( 2,19)( 3,18)( 4,20)( 5,24)( 6,22)( 7,23)( 8,21)( 9,32)(10,30)(11,31)(12,29)(13,28)(14,26)(15,27)(16,25)(33,65)(34,67)(35,66)(36,68)(37,72)(38,70)(39,71)(40,69)(41,80)(42,78)(43,79)(44,77)(45,76)(46,74)(47,75)(48,73)(50,51)(53,56)(57,64)(58,62)(59,63)(60,61);;
s2 := ( 1,15)( 2,16)( 3,14)( 4,13)( 5, 6)(11,12)(17,31)(18,32)(19,30)(20,29)(21,22)(27,28)(33,47)(34,48)(35,46)(36,45)(37,38)(43,44)(49,63)(50,64)(51,62)(52,61)(53,54)(59,60)(65,79)(66,80)(67,78)(68,77)(69,70)(75,76);;
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*s2*s1*s0*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(80)!( 3, 4)( 5,12)( 6,11)( 7, 9)( 8,10)(13,14)(17,65)(18,66)(19,68)(20,67)(21,76)(22,75)(23,73)(24,74)(25,71)(26,72)(27,70)(28,69)(29,78)(30,77)(31,79)(32,80)(33,49)(34,50)(35,52)(36,51)(37,60)(38,59)(39,57)(40,58)(41,55)(42,56)(43,54)(44,53)(45,62)(46,61)(47,63)(48,64);
s1 := Sym(80)!( 1,17)( 2,19)( 3,18)( 4,20)( 5,24)( 6,22)( 7,23)( 8,21)( 9,32)(10,30)(11,31)(12,29)(13,28)(14,26)(15,27)(16,25)(33,65)(34,67)(35,66)(36,68)(37,72)(38,70)(39,71)(40,69)(41,80)(42,78)(43,79)(44,77)(45,76)(46,74)(47,75)(48,73)(50,51)(53,56)(57,64)(58,62)(59,63)(60,61);
s2 := Sym(80)!( 1,15)( 2,16)( 3,14)( 4,13)( 5, 6)(11,12)(17,31)(18,32)(19,30)(20,29)(21,22)(27,28)(33,47)(34,48)(35,46)(36,45)(37,38)(43,44)(49,63)(50,64)(51,62)(52,61)(53,54)(59,60)(65,79)(66,80)(67,78)(68,77)(69,70)(75,76);
poly := sub<Sym(80)|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*s2*s1*s0*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2 >;

References : None.
to this polytope

Polytope of Type {15,6}

Twisty Puzzle