Finding the center point of a Rhombicuboctahedron

[[Ja...]]

Hello All, Wondering if anyone has a solid method for finding a center point of a Rhombicuboctahedron. I need to use all planes to find the center point as my XYZ Datum. I have tried various methods and all we unsuccessful. Thanks everyone.

Rhombicuboctahedron PIC.docx

[[Ju...]]

Have you tried creating symmetries for all opposing sides and then intersecting them?

[[Ja...]]

Thanks for the advice, with the 18 planes I was able to create 3 intersecting points, now I need to turn those 3 points into 1. Thank you so much.

[[Pe...]]

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With 3 individual points you can average them. Create a theoretical point and formula the X, Y and Z values to something like (getActual("Point1").x + getActual("Point2").x + getActual("Point3").x)/3

For anyone else who might want to play with a solution, here is a basic model.

Rhombicuboctahedron.zip

[[Ju...]]

I was able to create symmetries from opposing planes, intersect these symmetries, and then bring the intersections into a single theoretical point using recall.

[[Je...]]

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I will be finding a way to use the word Rhombicuboctahedron in a sentence today, probably while talking to my wife.

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[[Er...]]

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I'm going to have to practice just saying it before i can even use it in a sentence. 🤣

[[Ro...]]

Tell the barista at your coffee spot that it's your name. 🤣

[[Je...]]

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I don't know the use of this part, but my functional instinct is to fit the smallest sphere around it and then find the center of that sphere. Would that jive?



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[[Da...]]

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That can't work. Imagine having a sphere made of four points (the minimum amount of points needed to define a sphere). The centroid is the center of the sphere. Now introduce several more points to your point set, all of them inside your sphere, so that the circumscribed sphere (the smallest sphere around this point set) doesn't change. The center of that sphere remains unchanged, too, but the centroid of your point set is now different.

Every point of your set has to weigh in to get to the correct centroid. To achieve that, recall all your points into a new point feature or a point set feature. Even a plane feature should work, but only if your points will define any kind of plane.