Polytope of Type {6,40}

Play with this polytope as a twisty puzzle

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

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {6,40}

Twisty Puzzle