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model of perspective-transformed eight-prism

I have been interested in designing a prism with planar ends but where the ends are at an angle to each other. I thought such a prism might be useful in joining two planar surfaces together. I was working on some viewing software which used a perspective transformation. This transforms 3D data so that objects further away from a viewing point are smaller. It occurred to me that such a transform is linear so that the Masic et al. (Milenko Masic, Robert E. Skelton, Philip E. Gill, "Algebraic tensegrity form-finding", International Journal of Solids and Structures, Vol. 42, Nos. 16-17 [Aug 2005], pp. 4833-4858) transformation theorem would apply, and such a transform would put the two ends of a prism at an angle to each other while maintaining their planarity.

The design above is the result of my investigations. It does validate as a tensegrity. After applying a perspective transform, I scaled along the z-axis to get ends that were closer to circular. I would have preferred something that maintained the ends as equilateral polygons, but this doesn't seem possible. I completed the design on February 8, 2007, with an adjustment on August 17, 2007 (adjusted the z-axis scaling to get ends that were more circular). The datasheet was completed August 20, 2005, and assembly of a model on August 24.

This model is available for inspection in the Tensegrity Views.


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