Prismoids form a group of mathematical figures, that have found wide-spread application in many disciplines, but especially in architecture and in building structures. Many of these applications are trivial, but modifications and combinations can lead to a specific form language for this family of forms. Their geometry is based on that of prisms and antiprisms, which have two identical parallel polygonal faces, that are kept apart by a closed ring of squares or of triangles. The two polygons and the square or triangular faces of the mantle enclose a portion of space, that is completely surrounded by regular polygons. They have therefore very much in common with the Platonic and Archimedean - often called 'uniform' - polyhedra. Both groups form endless rows as the parallel polygons can have any number of sides. They were first mentioned and shown in sketch by Kepler in the 16th century. The present paper deals in detail with these figures and their duals, as well as with similar solids, having polygrams (or star-shaped) parallel faces. Attention will be paid to practical applications in architecture or in engineering of some representants, and particularly to antiprismatic structures. These are concertina-like folded planes, formed by a parallel arrangement of antiprisms. They lend themselves to being adapted to practical and aesthetical demands.

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