Noperthedron vase

What is a Noperthedron ?

First take a look at Prince Rupert's cube, the largest cube that can pass through a hole cut through a unit cube without splitting it into separate pieces.

More generally, a polyhedron P is said to have the Rupert property if a polyhedron of the same or larger size and the same shape as P can pass through a hole in P.

Many polyhedra share that property. But ALL polyhedra ?

The answer is no, as proven by Jakob Steininger and Sergey Yurkevich in an august 2025 paper. They discovered the counterexample, named Noperthedron.

The vase

Given its property, this polyhedron is unique and I think that it looks very good. For the fun I decided to reproduce it with an algorithm and I was helped to do that by a youtube video by Mickaël Launay (see the "Inspiration" part below). I coded a python script that creates the noperthedron in the form of a dxf file. 

The object by itself is not really useful but it has the global shape of a bowl or a vase. Of course without the top face it is not a polyhedron anymore but at least it serves a purpose !

Models and print

There are two models: 

• The original one (use this one for vase mode)

• A flower pot holder variant, suitable for 90mm diameter * 80mm height flower pots

Print instructions: default settings at 0.2mm is OK, this is not a difficult print.

Filaments used for photos: Prusament galaxy silver and generic wood PLA (eryone).

Inspiration and creation

I was inspired to create this model by Mickaël Launay from youtube channels Mathsdrop and MicMaths. 

The python code used to make the polyhedron is included, in case you wish to reproduce it by yourself. The f3d file is also included, for remixes.