Abstract
A description of a Family of Polyhedra is given where the parent forms are the five regular polyhedra. The facial planes of the parent forms are subdivided into right triangles and by a series of rearrangements are allowed to move out of plane thus creating new volumetric forms while maintaining the same surface area. The axes of symmetry of the parent polyhedra are preserved. One new form is less stable than the parent and the other is more stable than the parent; thus giving rise to a family of real stable, stable and not-so stable polyhedra. Illustrations of all fifteen polyhedra in the family are given along with tables describing several of their geometric properties. The influence of precision on geometrical stability will also be demonstrated as related to architectural applications.
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