Akiyama polyhedra

Date started: February 2017
Leads: Alba Málaga, Samuel Lelievre, Shigeki Akiyama


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.

We plan to add pedagogical / outreach use case scenarios to IMAGINARY where the stl files are shared.


Akiyamahedra with 4 to 12 vertices, 3D printed at ICERM (2019).
We find the akiyamahedron with 8 vertices particularly intriguing because of its symmetries.