Polytope of Type {10,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,8}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240798)
Rank : 3
Schlafli Type : {10,8}
Number of vertices, edges, etc : 120, 480, 96
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {10,8}*960c, {10,8}*960d, {10,4}*960
   4-fold quotients : {5,8}*480, {10,4}*480a, {10,4}*480b, {10,4}*480c
   8-fold quotients : {5,4}*240, {10,4}*240a, {10,4}*240b
   16-fold quotients : {5,4}*120
   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*s1*s0*s1*s0*s1*s0*s1> of order 2.
      72 facets:
         48 of {5}*10
         24 of {10}*20
      60 vertex figures:
         60 of {8}*16
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 3.
      32 facets:
         32 of {10}*20
      40 vertex figures:
         40 of {8}*16
   P/N, where N=<s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 5.
      32 facets:
         16 of {10}*20
         16 of {2}*4
      24 vertex figures:
         24 of {8}*16

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {10,8}

Twisty Puzzle