Abstract

For any finite set of points in the Euclidean space, their convex hull will be a convex polyhedron. For any natural number $n$ and any positive real number $V$, consider the following problem: find $n$ points that give rise to a polyhedron with volume $V$ and least possible surface area.

In 2017, S. Akiyama proposed a series of solutions for $n$ ranging from 4 to 12. Informally, the community started calling them Akiyama polyhedra or akiyamahedra. A full set of STL files for the akiyamahedra was then shared on IMAGINARY.

In this project, we explore the use of akiyamahedra in outreach. We 3D print a series of akiyamahedra with same volume an infill at 100% or 0%. With 100% infill, volume is roughly proportional to weight. With 0% infill, surface area is roughly proportional to weight.