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Miscellaneous Polyhedra

Here is a set of miscellaneous polyhedra which don't fit into the previous categories. Only the Johnson solids, their duals, and the Stewart toroids can be made using Small Stella. All models can be made using Great Stella and Stella4D.

Click on the images below to see a bigger picture and get more information about how they were built.

Johnson solids and their duals

The non-uniform convex regular-faced polyhedra. There are 92 in total. Here are just two, and their duals.

Zonohedra

Great Stella can create a zonohedron based on any polyhedron (look up zonohedron in the glossary).

Stewart toroids

B. M. Stewart's Adventures Among the Toroids was an investigation of regular-faced non-self-intersecting polyhedra of genus greater than zero (ie with holes). Excavation was the term used for subtracting one smaller polyhedron from a larger one, to create a hole. The term Drilling was used when an excavation cut right through the model. See my paper Stella: Polyhedron Navigator for more details.

Various Stewart toroids are built into Small Stella and Great Stella. The latter also supports augmentation/excavation/drilling so that you can create your own new toroids.

Sub-symmetric stellations

Great Stella lets you see the current symmetry group of any model, and a list of all possible sub-symmetry groups. You may select to use a sub-symmetry group instead of full symmetry, to produce sub-symmetric stellations (also applies to faceting and augmentation).

Faceted polyhedra

Great Stella can create faceted polyhedra. A faceted polyhedron has the same vertices as the model being faceted, but they are connected together with different faces. In a special mode for creating facets, you click on each vertex of a new face in turn. When all new faces have been made Great Stella can repeat each one over the symmetry group to generate all the faces.

Augmented polyhedra

Great Stella can augment any polyhedron with any other polyhedron, which just means to connect them at some common face. The augmentation may be done symmetrically, in which case the second model is augmented to all faces of a type rather than just one. See my section about Augmented Uniform Polyhedra for more information.

Cupolae

Great Stella can create any regular-faced pyramid, cupola, cuploid or cupolaic-blend. These are all models where the vertices lie in two parallel planes. (See the definitions of cupola, cuploid and cupolaic-blend in the glossary).

Topological models

These models are stylized versions of polyhedra, the idea being that only true edges of the original polyhedron should connect. The false edges that normally appear in a model with intersecting faces have been removed by hiding parts of each face, allowing the faces to pass through each other without collision. This lets you better see the internal structure of the polyhedron. I call these topological models.

Shape-shifters

Here's a model which can flex between two different shapes.

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