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The cubic D10

Posted 9 months ago
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I'm not yet sure when it happened, but the standard d10 die has a lot of right angles now. I've been a gamer a long time, and not all of my d10 are like this, but it seems pretty standard now.

np={{1,0,1/2 Sqrt[-2+Sqrt[5]]},{1,1/2 (3-Sqrt[5]),1/2 Sqrt[5 (-2+Sqrt[5])]},{1/2 (-1+Sqrt[5]),1/2 (-1+Sqrt[5]),3/2 Sqrt[-2+Sqrt[5]]},{1/2 (3-Sqrt[5]),1,1/2 Sqrt[5 (-2+Sqrt[5])]},{0,1,1/2 Sqrt[-2+Sqrt[5]]},{0,1,-(1/2) Sqrt[-2+Sqrt[5]]},{0,1/2 (-1+Sqrt[5]),-(1/2) Sqrt[5 (-2+Sqrt[5])]},{1/2 (3-Sqrt[5]),1/2 (3-Sqrt[5]),-(3/2) Sqrt[-2+Sqrt[5]]},{1/2 (-1+Sqrt[5]),0,-(1/2) Sqrt[5 (-2+Sqrt[5])]},{1,0,-(1/2) Sqrt[-2+Sqrt[5]]},{1,1,-(1/2) Sqrt[-2+Sqrt[5]]},{0,0,1/2 Sqrt[-2+Sqrt[5]]}};
Graphics3D[{Table[Style[Text[n,np[[n]]],20],{n,1,12}],Opacity[.7],Table[Polygon[np[[Append[Mod[{a,a+1,a+2},10,1],11+If[OddQ[a],1,0]]]]],{a,1,10}], Opacity[.3], Blue, Polygon[{{0,0,-1/2},{1,0,-1/2},{1,1,-1/2},{0,1,-1/2},{0,0,-1/2}}],Polygon[{{0,0,1/2},{1,0,1/2},{1,1,1/2},{0,1,1/2},{0,0,1/2}}]}, SphericalRegion-> True, Boxed->False]  

enter image description here

From five directions the cross-section is a perfect square.

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