# Generate random pentagons with grasshopper

I am looking to generate pentagons with randomly rounded edges in order to create patterns and then cut them out of paper.

I have some data:

• the 5 points of the patagon must vary in a circumscribed circle in order to respect a certain geometry
• the pentagons have a radius leave which must be able to be adjusted (not random)
• the rounded pentagons must all be inscribed in a rectangle whose dimensions should be able to be set (not random);
• the number of petagons to be generated must be able to be defined (for example 100 forms).

Patron.3dm (47.4 KB)

Hi Olivier gassies,

When you say 5 points of the pentagon must vary in a circumscribed circle, do you mean that the pentagon has to be circumscribed but not regular?
Is the leave radius constant for all pentagons being generated or different for each of the 100 and is it the same for each vertex or possibly different for each vertex?
If the pentagon must be inscribed, does that mean the diameter of the circle vary?

Hello Christopher,

The pentagon must indeed be circumscribed and not regular. The rounding is identical for each series. The diameter of the pentagon may vary.

The idea is to experiment with a random series of shapes written in a constrained paper format.

I wonder if the voronoi diagram is not a track too.

thank you

Hi Olivier gassies,

No idea if this is what you are looking for as the randomise is a bit random, if you want to retain the pentagon shape, maybe split the circle that circumscribed into 5 and then evaluate on each part to get a more pentagon shape.
pentagon.gh (11.7 KB)

you will have to add more rules to the grasshopper script to generate something that fills more of the space.

If you are looking for pentagons that cover a surface, this discipline is called tiling or tessellations; there have been some interesting discoveries in the last few years, and I even based some work two year ago off of one of these, please see the link for the backgroundhttps://www.quantamagazine.org/pentagon-tiling-proof-solves-century-old-math-problem-20170711/ theory.

Hi Markz,

All depends on @oliviergassies needs/wants as they specified for a circumscribable pentagons of different sizes.

Helle everybody,