Geometry : Voxels and Cube Puzzles

This post is mostly to show two things, my new Javascript script that makes it easy to display multiple models inside a webpage and models that I have found when playing with voxels, specifically using the Voxel Paint application. Some of these models exist as modular origami creations that I have shown, in a previous post, namely the tree, the T-rex and the four legged structure. I intend to build more, both virtually and physically and I'll add them to this page.

If you wish to know how to build these models, you will need a lot of paper sheets in the 3:2 format (format is length/width). The width will define the size length of the cube so please take a moment to think about the correct size beforehand. You will need 6 modules to make a single cube. You will also need modules to cover the faces and strengthen the model, you can use color paper, draw on it or print then to decorate your creation.
I usually fit 3x7=21 modules in a A4 sheet (21cmx29.7cm). Each module is then 21/3=7cm by 29.7/7=4.24cm for a format of 1.65:1 (bigger than 3:2 and smaller than the upper limit of 2:1) which is fine to work with and I don't waste any paper. I leave as an exercise to the readers from the US or other part of the world where A4 paper is not as common to figure out the most appropriate way to divide the paper sheets they find. Then, follow the instructions in this video to fold and assemble the modules.

Below, you will find first, a gallery of models, and then, a set of puzzles using polycubes. Each model view is interactive, the controls are the following:

• Click and drag with the mouse right click to rotate the model.
• Click and drag with the mouse left click to pan the model.
• The mouse middle click zooms in or out.
• Press R to reset the model position or triple click.
• Press F to trigger fullscreen or double click.
• Press P to pause/resume the animation.

Gallery

Tetris shapes

Things

Structures

Abstract

Shapes that fits inside a 3x3 cube

There are many so I decided to put them on a separate page.

Unfoldings of the hypercube

There are many (261) so I decided to put them on a separate page.

Cube Puzzles

Cube dissections make for interesting puzzles. A cube is divided into blocks of different shapes and sizes and the challenge is to assemble the pieces back into the cube. Most often multiple solutions are possible. This article The Puzzling World of Polyhedral Dissections by Stewart T. Coffin presents many versions of this puzzle in details, so go have a look. Below, you will find voxel models of the blocks for you to make and solve ! Have fun ! The alternative colors do not have a special meaning and won't help you. If it happens that you find a full checkered solution, this would be by pure chance. I just thought it would help distinguish the pieces from one another. The difficulty of the puzzles is quite broad : very easy to very hard. If you happen to know others, please share them with me !

Soma Cube

The goal is to assemble the pieces into a 3x3x3 cube. Good luck !

Mikusiński Cube

The goal is to assemble the pieces into a 3x3x3 cube. Good luck !

Diabolical Cube

The goal is to assemble the pieces into a 3x3x3 cube. Good luck !

Half Hour Cube

The goal is to assemble the pieces into a 3x3x3 cube. Good luck !

Five Pieces Cube

The goal is to assemble the pieces into a 3x3x3 cube. Good luck !

Serially Interlocking Cube

The goal is to assemble the pieces into a 3x3x3 cube. Good luck !

Bedlam Cube

Beware ! This time, the goal is to assemble the pieces into a 4x4x4 cube. Good luck !