Polytope of Type {40,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,6}*1920h
if this polytope has a name.
Group : SmallGroup(1920,240882)
Rank : 3
Schlafli Type : {40,6}
Number of vertices, edges, etc : 160, 480, 24
Order of s₀s₁s₂ : 40
Order of s₀s₁s₂s₁ : 20
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {20,6}*960c
   4-fold quotients : {20,6}*480a, {20,6}*480b, {10,6}*480c
   8-fold quotients : {5,6}*240b, {10,3}*240, {10,6}*240c, {10,6}*240d, {10,6}*240e, {10,6}*240f
   16-fold quotients : {5,3}*120, {5,6}*120b, {5,6}*120c, {10,3}*120a, {10,3}*120b
   32-fold quotients : {5,3}*60
   120-fold quotients : {4,2}*16
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 2.
      12 facets:
         12 of {40}*80
      80 vertex figures:
         80 of {6}*12

Permutation Representation (GAP) :

s0 := ( 1,61)( 2,53)( 3,70)( 4,71)( 5,72)( 6,50)( 7,58)( 8,60)( 9,49)(10,81)(11,82)(12,83)(13,87)(14,55)(15,56)(16,57)(17,51)(18,68)(19,52)(20,92)(21,54)(22,94)(23,69)(24,77)(25,65)(26,66)(27,67)(28,59)(29,63)(30,85)(31,62)(32,64)(33,86)(34,79)(35,80)(36,76)(37,90)(38,74)(39,75)(40,78)(41,93)(42,88)(43,73)(44,91)(45,96)(46,84)(47,89)(48,95);;
s1 := ( 1,51)( 2,55)( 3,52)( 4,59)( 5,58)( 6,62)( 7,56)( 8,66)( 9,65)(10,60)(11,53)(12,68)(13,70)(14,63)(15,74)(16,73)(17,67)(18,57)(19,76)(20,49)(21,79)(22,71)(23,82)(24,81)(25,75)(26,64)(27,84)(28,50)(29,86)(30,89)(31,77)(32,91)(33,83)(34,72)(35,92)(36,54)(37,93)(38,80)(39,94)(40,95)(41,85)(42,96)(43,87)(44,61)(45,90)(46,69)(47,78)(48,88);;
s2 := ( 1,13)( 2, 9)( 3,33)( 4,23)( 5,24)( 6,37)( 8,19)(10,22)(11,44)(12,35)(14,47)(15,42)(16,40)(20,34)(25,45)(26,41)(27,30)(31,43)(36,48)(38,46)(49,53)(50,90)(52,60)(55,89)(56,88)(57,78)(61,87)(62,73)(65,96)(66,93)(67,85)(69,71)(70,86)(72,77)(74,84)(76,95)(79,92)(80,83)(81,94)(82,91);;
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*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(96)!( 1,61)( 2,53)( 3,70)( 4,71)( 5,72)( 6,50)( 7,58)( 8,60)( 9,49)(10,81)(11,82)(12,83)(13,87)(14,55)(15,56)(16,57)(17,51)(18,68)(19,52)(20,92)(21,54)(22,94)(23,69)(24,77)(25,65)(26,66)(27,67)(28,59)(29,63)(30,85)(31,62)(32,64)(33,86)(34,79)(35,80)(36,76)(37,90)(38,74)(39,75)(40,78)(41,93)(42,88)(43,73)(44,91)(45,96)(46,84)(47,89)(48,95);
s1 := Sym(96)!( 1,51)( 2,55)( 3,52)( 4,59)( 5,58)( 6,62)( 7,56)( 8,66)( 9,65)(10,60)(11,53)(12,68)(13,70)(14,63)(15,74)(16,73)(17,67)(18,57)(19,76)(20,49)(21,79)(22,71)(23,82)(24,81)(25,75)(26,64)(27,84)(28,50)(29,86)(30,89)(31,77)(32,91)(33,83)(34,72)(35,92)(36,54)(37,93)(38,80)(39,94)(40,95)(41,85)(42,96)(43,87)(44,61)(45,90)(46,69)(47,78)(48,88);
s2 := Sym(96)!( 1,13)( 2, 9)( 3,33)( 4,23)( 5,24)( 6,37)( 8,19)(10,22)(11,44)(12,35)(14,47)(15,42)(16,40)(20,34)(25,45)(26,41)(27,30)(31,43)(36,48)(38,46)(49,53)(50,90)(52,60)(55,89)(56,88)(57,78)(61,87)(62,73)(65,96)(66,93)(67,85)(69,71)(70,86)(72,77)(74,84)(76,95)(79,92)(80,83)(81,94)(82,91);
poly := sub<Sym(96)|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*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References : None.
to this polytope

Polytope of Type {40,6}

Twisty Puzzle