Polytope of Type {6,15}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,15}*1440a
if this polytope has a name.
Group : SmallGroup(1440,4612)
Rank : 3
Schlafli Type : {6,15}
Number of vertices, edges, etc : 48, 360, 120
Order of s0s1s2 : 24
Order of s0s1s2s1 : 8
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 : {6,15}*720a
   3-fold quotients : {6,5}*480
   6-fold quotients : {6,5}*240a
   12-fold quotients : {6,5}*120a
   120-fold quotients : {2,3}*12
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*s2*s1*s0*s2*s1*s2> of order 3.
      48 facets:
         36 of {6}*12
         12 of {2}*4
      16 vertex figures:
         16 of {15}*30

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