Three Intersecting Planes

Get your hands on a system of three linear equations with three variables. This model of three planes illustrates an example when they have a single point as the intersection, the solution for a corresponding system. It looks fabulous in three colors, but also works well printed with one color.

Note that the models of the planes together are 200 x 200 x 200 mm. I printed at 50% scale, but I had originally planned to print it larger. The "Thin" models have planes that are 2 mm thick. It printed okay at 50% scale (no photo), but thicker planes are better. The "Thick" models have planes that are 4 mm thick. This is designed for scaling down to 50% for 2 mm thick planes. All of my printed models in the photos are "Thick" at 50% scale.

For both "Thick" and "Thin" models, there is a model together and models separated by planes. For multicolor printing, I imported the three separate planes together and found that "painting" the models created a stronger print. When I assigned the extruders to each plane (instead of painting), the junction points between planes (colors) were very weak and my test prints (only the lower portion of the model) fell apart easily.

About Supports:
The planes are not orthogonal (perpendicular) so that they appear more arbitrary. However, the angles are set well for printing without much support. Supports are needed for the bottom edge of one of the planes (see photos). I preferred that the model has the same length, width, and height rather than extending that plane to the floor. The edge of the plane where it needs supports is slightly cut to create a surface for the supports. If you do not want to print with support, you could lower (sink) the model into the print bed to cut off some of the bottom.

I also printed a portion of the model and stopped it where the three planes intersect. See photos.

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Mathematical Models

• This model is featured in my 3DWithUs article!
  3D Printable Math Models for Teaching Complex Concepts

• Find more models for mathematics in my Math Surfaces, Solids, Etc. Collection.

• You may also be interested in my Intersecting Planes. This is one of my earliest mathematical models.

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