Every 3D Polyhedron You’d Ever Want to Construct, Render or 3D Print

Examples of a few 3D polyhedron that can be generated by Stellahttps://www.solidsmack.com/wp-content/uploads/2017/09/stella-polyhedron-... 560w, https://www.solidsmack.com/wp-content/uploads/2017/09/stella-polyhedron-... 768w" sizes="(max-width: 853px) 100vw, 853px" />

Stella, a “Polyhedron Navigator” provides a way to very quickly view and generate almost any type of 3D polyhedron you can imagine.

What’s a 3D polyhedron? While you may bump into them in real life constantly, it’s a geometric concept that encompasses a broad set of possible objects. Wikipedia defines them as:

In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices. The word polyhedron comes from the Classical Greek πολύεδρον, as poly- (stem of πολύς, “many”) + -hedron (form of ἕδρα, “base” or “seat”).

A convex polyhedron is the convex hull of finitely many points, not all on the same plane. Cubes and pyramids are examples of convex polyhedra.

It turns out there are a great many types of 3D polyhedron, as they have been studied in geometry for centuries, such as the Tetrahedron, Icosidodecahedron or Rhombic triacontahedron.

Sometimes it is useful to include such objects within a 3D model, but it can be challenging to develop such structures on your own, aside from simple ones such as a cube, pyramid or similar. The more intricate polyhedrons are essentially impossible to design by hand.

If only there was a way to generate them.

Turns out there is a very powerful tool to do so, called “Stella”, by developer Robert Webb of Software3D.

Examples of a few 3D polyhedron that can be generated by Stellahttps://www.solidsmack.com/wp-content/uploads/2017/09/stella-polyhedron-... 560w, https://www.solidsmack.com/wp-content/uploads/2017/09/stella-polyhedron-... 768w" sizes="(max-width: 855px) 100vw, 855px" />
Examples of a few of the polyhedra that can be generated by Stella

The main purpose of this software is to produce 2D “unfolded” versions of the polyhedra (polyhedral nets), which you can print on paper, cut out and fold up into the object. It can get quite complex, as you can see here in this completed fold-up of a Cantitruncated Tesseract:

A 3D polyhedron you may not have heard of before: the Cantitruncated Tesseracthttps://www.solidsmack.com/wp-content/uploads/2017/09/stella-polyhedron-... 560w, https://www.solidsmack.com/wp-content/uploads/2017/09/stella-polyhedron-... 768w" sizes="(max-width: 1024px) 100vw, 1024px" />
A defined shape you may not have heard of before: the Cantitruncated Tesseract

You can also apply a color texture to the surfaces of the faces for developing unusual art pieces.

While the main purpose of the software is for paper construction, some versions of Stella can also export an STL 3D model suitable for 3D printing or OBJ for 3D rendering.

Stella comes in three different versions, with some odd product names:

Small Stella” contains a pre-made – but comprehensive – of many polyhedra you can examine and download. Priced at USD$14. This version DOES NOT permit exporting of 3D models.

Great Stella” is more comprehensive and allows manipulation of the polyhedra to create more unique forms in some rather complex ways. Priced at USD$45.

Stella4D” includes all known polyhedra and has 4D capability (that’s the geometric 4D, not the 3D print 4D meaning). Priced at USD $67 for non-commercial use, and USD$120 for commercial use. In fact, this is the only license from Software3D that provides for commercial use.

The Windows-only software is available for download and purchase now, and appears to have been continuously supported for many years.

Need a polyhedron in your 3D model? Check out Stella.

Read more about 3D printing at Fabbaloo!

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