Monday, April 13, 2015

Regular Polyhedrons

It's not surprising that most of regular polyhedrons can't be created easily in Revit. Just few of 3d software have a feature which can create regular polyhedrons instantly.(eg. 3ds-max)

It is well known that there are only 5 regular polyhedrons.

And it's quite easy to make them with paper works.
But it's not that simple to create them as 3D computational model. You have to deal with a bit complicated angles to create one.



Once I've tried a similar a few years ago as follow with AC. But it can't cover all 5 types at once.
So I tried to develop an advanced method with Dynamo.

semi-regular polyhedron Soccer-ball

1st Approach

I just tried with folding method which is just like paper work.
Folding(rotation) angles can be found depend on number of vertexes of side polygons as below.




This method can create most of regular polyhedrons easily except Icosahedron  which has 20 faces.


2nd Approach




The other way is cutting a sphere by planes which are aligned at each faces of a polyhedron.




In this concept, the locations and angles of planes which cut a sphere can be found from the formulas at folding method.
Ridiculous!!!!!

And I developed a custom node which can create dual-polyhedrons from given polyhedron.


You can create a polyhedron which has a lot of faces by using this node repeatedly.


One more additional dyf creates a polyhedron with all triangle faces from given regular or semi-regular polyhedron.

Now, you can easily create any regular or semi-regular polyhedrons in Revit.
You can download above dyf as usual.

Enjoy. :)

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