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
All models can be made using
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.
Great Stella can create a zonohedron based on
any polyhedron (look up zonohedron in
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.
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).
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.
Great Stella can create various compounds of
polyhedra. Depending on the compound, these can be made via stellation,
faceting, augmentation, or a combination of methods. A great many compounds
are included in the polyhedron library included with
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.
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
cupolaic-blend in the glossary).
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.
Here's a model which can flex between two different shapes.
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