Polytope of Type {8,10}

Play with this polytope as a twisty puzzle

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

Permutation Representation (GAP) : 
s0 := ( 1, 3)( 2, 4)( 5,25)( 6,26)( 7,17)( 8,18)( 9,22)(10,21)(11,13)(12,14)(15,29)(16,30)(19,36)(20,35)(23,34)(24,33)(27,39)(28,40)(31,32)(41,44)(42,43)(45,47)(46,48)(49,70)(50,69)(51,62)(52,61)(53,65)(54,66)(55,58)(56,57)(59,74)(60,73)(63,79)(64,80)(67,77)(68,78)(71,84)(72,83)(81,82)(85,87)(86,88);;
s1 := ( 3, 4)( 7,32)( 8,31)( 9,36)(10,35)(13,39)(14,40)(15,34)(16,33)(17,37)(18,38)(19,29)(20,30)(21,23)(22,24)(25,43)(26,44)(27,28)(41,42)(47,48)(51,76)(52,75)(53,80)(54,79)(57,83)(58,84)(59,78)(60,77)(61,81)(62,82)(63,73)(64,74)(65,67)(66,68)(69,87)(70,88)(71,72)(85,86);;
s2 := ( 1,45)( 2,46)( 3,47)( 4,48)( 5,57)( 6,58)( 7,53)( 8,54)( 9,52)(10,51)(11,69)(12,70)(13,50)(14,49)(15,73)(16,74)(17,65)(18,66)(19,88)(20,87)(21,62)(22,61)(23,71)(24,72)(25,56)(26,55)(27,68)(28,67)(29,60)(30,59)(31,81)(32,82)(33,83)(34,84)(35,85)(36,86)(37,76)(38,75)(39,78)(40,77)(41,80)(42,79)(43,63)(44,64);;
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*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1, 
s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(88)!( 1, 3)( 2, 4)( 5,25)( 6,26)( 7,17)( 8,18)( 9,22)(10,21)(11,13)(12,14)(15,29)(16,30)(19,36)(20,35)(23,34)(24,33)(27,39)(28,40)(31,32)(41,44)(42,43)(45,47)(46,48)(49,70)(50,69)(51,62)(52,61)(53,65)(54,66)(55,58)(56,57)(59,74)(60,73)(63,79)(64,80)(67,77)(68,78)(71,84)(72,83)(81,82)(85,87)(86,88);
s1 := Sym(88)!( 3, 4)( 7,32)( 8,31)( 9,36)(10,35)(13,39)(14,40)(15,34)(16,33)(17,37)(18,38)(19,29)(20,30)(21,23)(22,24)(25,43)(26,44)(27,28)(41,42)(47,48)(51,76)(52,75)(53,80)(54,79)(57,83)(58,84)(59,78)(60,77)(61,81)(62,82)(63,73)(64,74)(65,67)(66,68)(69,87)(70,88)(71,72)(85,86);
s2 := Sym(88)!( 1,45)( 2,46)( 3,47)( 4,48)( 5,57)( 6,58)( 7,53)( 8,54)( 9,52)(10,51)(11,69)(12,70)(13,50)(14,49)(15,73)(16,74)(17,65)(18,66)(19,88)(20,87)(21,62)(22,61)(23,71)(24,72)(25,56)(26,55)(27,68)(28,67)(29,60)(30,59)(31,81)(32,82)(33,83)(34,84)(35,85)(36,86)(37,76)(38,75)(39,78)(40,77)(41,80)(42,79)(43,63)(44,64);
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1, 
s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2 >;
References : None.
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