Dodecahedral 2024

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num=11;​​tet=num{{-1,-1,1},{-1,1,-1},{1,-1,-1},{1,1,1}};​​pick=Select[Tuples[Range[-num-1,num+1],{3}],OddQ[Total[#]]&&Total[#]!=-num&&Min[ResourceFunction["Areal"][tet,#]]>=0&];​​tet={{11,11,11},{-10,-10,11},{-10,11,-10},{11,-10,-10}};​​interest=Select[pick,Max[Denominator[ResourceFunction["Areal"][tet,#]]]<7&];​​edge=Complement[Select[Subsets[Range[Length[interest]],{2}],EuclideanDistance@@interest[[#]]==7Sqrt[2]&],{{16,19},{14,19},{12,18},{12,14},{8,10},{10,14},{9,16},{15,16},{2,7},{7,9},{3,9},{3,10},{2,6},{2,5},{11,12},{6,11},{3,8},{6,8},{5,7},{5,13},{15,19},{13,15},{13,18},{11,18}}];​​Graphics3D[{Opacity[.5],Sphere[#,1/Sqrt[2]]&/@pick,​​Green,Opacity[1],Sphere[#,1/Sqrt[2]]&/@interest,​​Tube[interest[[#]],.5]&/@edge​​},Boxed->False]
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Length[pick]
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2024