---
title: 'Incomplete open cubes'
source: 'https://youtube.com/watch?v=1lZpowy21Gc'
video_id: '1lZpowy21Gc'
date: 2026-08-08
duration_sec: 72
---

# Incomplete open cubes

> Source: [Incomplete open cubes](https://youtube.com/watch?v=1lZpowy21Gc)

## Summary

This video presents a mathematical puzzle about counting distinct configurations of incomplete open cubes, where edges are removed from a cube frame. The creator explains that this puzzle is connected to a guest video by Paul Dancstep, which explores the problem-solving process and introduces group theory concepts in an accessible way.

### Key Points

- **The Puzzle** [00:00] — The core question is: if you remove some edges from a cube, how many distinct configurations can you get, considering incomplete cubes?
- **Mathematical Context** [00:14] — The puzzle is a pure math problem, but it serves as the premise for a guest video that tells the story behind an artwork and a problem-solving process.
- **Guest Video Commission** [00:30] — The creator used Patreon funds to commission a set of guest videos. The most recent one parallels the story of the artwork with a problem-solving process that could lead to solving the puzzle.
- **Group Theory Connection** [00:43] — The problem-solving process effectively involves rediscovering a bit of group theory, making the content both accessible to middle schoolers and thought-provoking for PhD students.
- **Invitation to Engage** [00:57] — The creator encourages viewers to start thinking about the puzzle themselves, suggesting it as a longer piece to sit down with.

## Transcript

What I mean by that is, if you take away some of its edges, how many distinct configurations can you get? And the tricky part here is that we're going to consider incomplete
Now, even though this is a very pure math puzzle, This was essentially the premise behind a work I've been away from making videos this summer,
and in that time I've been using Patreon funds to commission a set of guest videos, and the most recent one tells the story behind this artwork in parallel with the story of a problem solving process that could lead you to answer this
And effectively, that process is to rediscover a bit of group theory The creator for this video is a friend of mine, Paul Dancstep, and I thought he did a really beautiful job creating something that could
be at once accessible to a middle schooler and thought provoking to a PhD student. next time you find yourself in the mood to sit down for a longer piece. In the meantime, I thought you'd enjoy starting to think about the puzzle itself.