Polytope of Type {10,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,12}*960a
if this polytope has a name.
Group : SmallGroup(960,10870)
Rank : 3
Schlafli Type : {10,12}
Number of vertices, edges, etc : 40, 240, 48
Order of s0s1s2 : 8
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,12,2} of size 1920
Vertex Figure Of :
   {2,10,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,6}*480b
   4-fold quotients : {5,6}*240a, {10,6}*240a, {10,6}*240b
   8-fold quotients : {5,6}*120a
   120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,12}*1920b, {20,12}*1920i, {20,12}*1920j
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) : 
s0 := ( 2, 4)( 3,28)( 5,13)( 7,15)( 8,42)( 9,24)(10,35)(11,31)(12,34)(14,33)(18,29)(19,21)(20,37)(22,23)(25,41)(26,40)(27,39)(30,36)(43,45)(46,47);;
s1 := ( 2,27)( 3, 8)( 4,12)( 6,26)( 7, 9)(10,44)(11,40)(14,16)(15,30)(18,24)(19,28)(21,38)(22,31)(23,33)(25,45)(29,46)(34,43)(35,42)(36,47)(39,41);;
s2 := ( 1, 6)( 2,21)( 3,15)( 4,19)( 5,24)( 7,28)( 8,29)( 9,13)(10,34)(11,45)(12,35)(14,46)(16,48)(17,44)(18,42)(20,25)(22,27)(23,39)(26,30)(31,43)(32,38)(33,47)(36,40)(37,41);;
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*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(48)!( 2, 4)( 3,28)( 5,13)( 7,15)( 8,42)( 9,24)(10,35)(11,31)(12,34)(14,33)(18,29)(19,21)(20,37)(22,23)(25,41)(26,40)(27,39)(30,36)(43,45)(46,47);
s1 := Sym(48)!( 2,27)( 3, 8)( 4,12)( 6,26)( 7, 9)(10,44)(11,40)(14,16)(15,30)(18,24)(19,28)(21,38)(22,31)(23,33)(25,45)(29,46)(34,43)(35,42)(36,47)(39,41);
s2 := Sym(48)!( 1, 6)( 2,21)( 3,15)( 4,19)( 5,24)( 7,28)( 8,29)( 9,13)(10,34)(11,45)(12,35)(14,46)(16,48)(17,44)(18,42)(20,25)(22,27)(23,39)(26,30)(31,43)(32,38)(33,47)(36,40)(37,41);
poly := sub<Sym(48)|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*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1 >;
References : None.
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