Polytope of Type {8,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6}*1440a
if this polytope has a name.
Group : SmallGroup(1440,4612)
Rank : 3
Schlafli Type : {8,6}
Number of vertices, edges, etc : 120, 360, 90
Order of s0s1s2 : 30
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-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 : {4,6}*720
   3-fold quotients : {8,6}*480b
   6-fold quotients : {4,6}*240c
   12-fold quotients : {4,6}*120
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*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 3.
      30 facets:
         30 of {8}*16
      44 vertex figures:
         38 of {6}*12
         6 of {2}*4
   P/N, where N=<s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2> of order 5.
      18 facets:
         18 of {8}*16
      24 vertex figures:
         24 of {6}*12

Permutation Representation (GAP) : 
s0 := ( 1,13)( 2,14)( 3,16)( 4,15)( 5, 7)( 6, 8)( 9,26)(10,27)(11,25)(12,28)(17,32)(18,31)(19,30)(20,29)(21,24)(22,23)(33,34)(35,36)(38,40);;
s1 := ( 5,10)( 6, 9)( 7,11)( 8,12)(13,18)(14,17)(15,20)(16,19)(21,39)(22,37)(23,40)(24,38)(25,36)(26,35)(27,34)(28,33)(29,30)(31,32)(42,43);;
s2 := ( 3, 4)( 5, 8)( 6, 7)( 9,31)(10,32)(11,29)(12,30)(15,16)(17,27)(18,26)(19,28)(20,25)(21,34)(22,35)(23,36)(24,33)(38,40)(41,42);;
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*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, 
s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(43)!( 1,13)( 2,14)( 3,16)( 4,15)( 5, 7)( 6, 8)( 9,26)(10,27)(11,25)(12,28)(17,32)(18,31)(19,30)(20,29)(21,24)(22,23)(33,34)(35,36)(38,40);
s1 := Sym(43)!( 5,10)( 6, 9)( 7,11)( 8,12)(13,18)(14,17)(15,20)(16,19)(21,39)(22,37)(23,40)(24,38)(25,36)(26,35)(27,34)(28,33)(29,30)(31,32)(42,43);
s2 := Sym(43)!( 3, 4)( 5, 8)( 6, 7)( 9,31)(10,32)(11,29)(12,30)(15,16)(17,27)(18,26)(19,28)(20,25)(21,34)(22,35)(23,36)(24,33)(38,40)(41,42);
poly := sub<Sym(43)|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*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, 
s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1 >;
References : None.
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