Polytope of Type {10,24}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,24}*1920f
if this polytope has a name.
Group : SmallGroup(1920,240882)
Rank : 3
Schlafli Type : {10,24}
Number of vertices, edges, etc : 40, 480, 96
Order of s₀s₁s₂ : 40
Order of s₀s₁s₂s₁ : 20
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,12}*960c
   4-fold quotients : {10,12}*480c, {10,12}*480d, {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 : {2,4}*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*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2> of order 2.
      48 facets:
         48 of {10}*20
      20 vertex figures:
         20 of {24}*48

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {10,24}

Twisty Puzzle