eJMT Abstract

There are four special operators on polytopes—join, fusil, prism, and meet. Joins create pyramid forms, joining all elements. Fusils creates cross polytopes, “fusing” all elements excluding bodies. Prisms create hypercubes as Cartesian products. Meets use Cartesian products of polytope nets to generate skew polytopes, also excluding bodies. This paper explores lower dimensional examples of these operators and how to work with them. The f-vectors for all four operators can be generated by products like coefficients of polynomial products. Detailed k-face elements are computed via product tables and can be shown in Hasse diagrams.