Discovering the Prisms was an exciting part of the polyhedron journey: the Antiprisms came as an aded surprise. And there are other joys to be had around the Duals of Prisms and Antiprisms. For a start, the duals of prisms are actually bipyramids, formed of two pyramids stuck together – though equally they look like bobbins or children’s spinning toys:
The duals of antiprisms are similar but have a charming zig-zag where the central join comes together. Remember that where the original shape has a triangle you’ll expect to find a three-way vertex…and here you can see this perfectly:
When we come to the duals of the non-convex prisms and antiprisms, and of the “crossed” versions, things get more complex. Models and photographs are again a job for another day, though as a rough description they still have the basic ‘bobbin’ forms but with grooves cut down them. ‘Fluted’ might be a good word here, along with an image of a lemon juicer…
Starred antiprisms require the centre to have not only a star but a staggered shape: and here you can see it in the case of a pentagrammic antiprism and its dual. (Diagrams are again from George Hart’s page on Virtual Polyhedra):
For the ‘crossed’ forms of the starred antiprisms, it’s more complex again:
That concludes our section on Duals… now we move on to the amazing world of Stellations