Trippy 3D-printed spheres that help conceptualize 4D


Originally published at:

Henry Segerman takes a brisk stroll through the world of four-dimensional objects with some really cool 3D-printed sculptures, like this sphere that projects a square grid when lit:

Segerman coauthored an interesting paper on the topic with Vi Hart on physical objects in which the elements are combine in a manner to maintain rotational symmetry.

We briefly review the distinction between abstract groups and symmetry groups of objects, and discuss the question of which groups have appeared as the symmetry groups of physical objects. To our knowledge, the quaternion group (a beautiful group with eight elements) has not appeared in this fashion. We describe the quaternion group, both formally and intuitively, and give our strategy for representing the quaternion group as the symmetry group of a physical sculpture.

Rotational symmetry in groups of objects is a fascinating topic. A few years ago I whipped up a few Venn diagrams with rotational symmetry to demonstrate some of the fascinating math behing this branch of set theory, including this one showing all possible combinations of the seven dwarfs:

Segerman's extradimensional example of this is a monkey sculpture with rotational symmetry that may or may not be even cooler to ponder while high:

4D MONKEY DUST (YouTube / Numberphile)


Could anyone suggest an online repository of the kinds of spheres he is demonstrating in the first part of the video? Looking for something like this (light/shadow/projection etc) for a project I am working on.
I’d even be prepared to pay someone to design something of that nature, but wouldn’t have a clue who to ask?


I have a few up at


Could you think of any designers who would be capable of working with/further develop such ideas towards a complete sphere? (I’d be happy to get the 3D file and sort out the fabrication myself.)


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