Hello, everybody!
I would like to know the formulas of each type of polyhendral geometry on Dynamo!
If you know some, share it! (and let me know which package you used and which code did you use)
I want to master all type of polyhendral geometry on Dynamo!
What’s the Secret?
Thanks for Attention.
A bit of an answer (not all) to your question
Oh no! They are so complex! hahaha
I wanted something simpler.
I work with bamboo, this photo below is the Icosahedron I have.
I wanted to explore other shapes, experiment with Dynamo and then the work with bamboo.
At least you now know who to ask 
Anyone?
If the edges are adequate you could use the below definition for the Platonic Solids
h = (1+Math.Sqrt(5))/2-1;
phd01 = Dictionary.ByKeysValues(["Tetrahedron","Hexahedron","Octahedron","Dodecahedron","Icosahedron"],
[[1,1,1,1,-1,-1,-1,1,-1,-1,-1,1],[1,1,1,1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,-1,-1,1,-1,-1,-1],
[0,0,1,0,0,-1,0,1,0,0,-1,0,1,0,0,-1,0,0],[0,h,1/h,0,h,-1/h,0,-h,1/h,0,-h,-1/h,h,1/h,0,h,-1/h,0,-h,1/h,0,
-h,-1/h,0,1/h,0,h,1/h,0,-h,-1/h,0,h,-1/h,0,-h,1,1,1,1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,-1,-1,1,-1,-1,-1],
[0,1,1/h,0,1,-1/h,0,-1,1/h,0,-1,-1/h,1,1/h,0,1,-1/h,0,-1,1/h,0,-1,-1/h,0,1/h,0,1,1/h,0,-1,-1/h,0,1,-1/h,0,-1]]);
xyz01 = List.Transpose(List.Chop(phd01.ValueAtKey(p),3));
pnt01 = Point.ByCoordinates(xyz01[0],xyz01[1],xyz01[2]);
pnt02 = List.Combinations(pnt01,2,false);
dst01 = Math.Round(List.FirstItem(pnt02<1>).DistanceTo(List.LastItem(pnt02<1>)),3);
pnt03 = List.SortByKey(pnt02,dst01);
pnt04 = List.GroupByKey(pnt03["sortedList"],pnt03["sortedKeys"])["groups"];
edg01 = Line.ByBestFitThroughPoints(List.FirstItem(pnt04));
Note: Depending on yourDynamo version you might need to alter “sortedList” , “sortedKeys” , “groups” in the last two lines to match the spelling output ports of the nodes List.SortByKey and List.GroupByKey
An improvement on the above - solids
h = (1+Math.Sqrt(5))/2-1;
phd01 = Dictionary.ByKeysValues(["Tetrahedron","Hexahedron","Octahedron","Dodecahedron","Icosahedron"],
[[1,1,1,1,-1,-1,-1,1,-1,-1,-1,1],[1,1,1,1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,-1,-1,1,-1,-1,-1],
[0,0,1,0,0,-1,0,1,0,0,-1,0,1,0,0,-1,0,0],[0,h,1/h,0,h,-1/h,0,-h,1/h,0,-h,-1/h,h,1/h,0,h,-1/h,0,-h,1/h,0,
-h,-1/h,0,1/h,0,h,1/h,0,-h,-1/h,0,h,-1/h,0,-h,1,1,1,1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,-1,-1,1,-1,-1,-1],
[0,1,1/h,0,1,-1/h,0,-1,1/h,0,-1,-1/h,1,1/h,0,1,-1/h,0,-1,1/h,0,-1,-1/h,0,1/h,0,1,1/h,0,-1,-1/h,0,1,-1/h,0,-1]]);
xyz01 = List.Transpose(List.Chop(phd01.ValueAtKey(p),3));
pnt01 = Point.ByCoordinates(xyz01[0],xyz01[1],xyz01[2]);
phd02 = Dictionary.ByKeysValues(["Tetrahedron","Hexahedron","Octahedron","Dodecahedron","Icosahedron"],[[3,4],[4,6],[3,8],[5,16],[3,20]]);
pnt02 = List.Combinations(pnt01,phd02.ValueAtKey(p)[0],false);
bln01 = List.AllTrue(pnt02.DoesIntersect(Circle.ByBestFitThroughPoints(pnt02))<1>);
pnt03 = List.FilterByBoolMask(pnt02,bln01)["in"];
rad01 = Math.Round(Circle.ByBestFitThroughPoints(pnt03).Radius,6);
pnt04 = List.GroupByKey(pnt03,rad01);
pnt05 = List.FirstItem(List.SortByKey(pnt04["groups"],pnt04["unique keys"])["sortedList"]);
pln01 = Plane.ByBestFitThroughPoints(pnt05);
dir01 = Vector.ByTwoPoints(pln01.Origin,pnt05);
ang01 = Math.Round(dir01.AngleAboutAxis(pln01.XAxis,pln01.Normal),3);
srf01 = List.SortByKey(pnt05<1>,ang01<1>)["sortedList"];
sld01 = PolySurface.ByJoinedSurfaces(Surface.ByPerimeterPoints(srf01)).ExtractSolids();