A fourth grade class is curious about the names that have been given to various solid geometric figures based on their shapes: are there names for solids based on a rhombus, a trapezoid, a parallelogram, a decagon, and/or a quadralateral?

Probably every such figure has been given a name, but why bother? You need a name only as a convenient abbreviation when you are going to refer to the object over and over again. For practical purposes (and greater clarity) it is best to say something like, "Let P be a right (or rectangular) prism whose base is a ... ."

Often when a person says "prism" he means that the sides are perpendicular to the base; this is officially called a RIGHT or RECTANGULAR prism. The dictionary definition applies to solids whose top and bottom are congruent figures in parallel planes and whose sides are composed of parallel straight line segments joining corresponding points of the top and bottom. Often the meaning is restricted to the case when the top and bottom are polygons (in which case the faces on the sides are parallelograms). When the base is also a parallelogram the prism is a PARALLELEPIPED. Otherwise the prisms are named in terms of the number of sides on the base: triangular, quadrilateral, pentagonal, ... .