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Cube Trisection, Cake Sharing, Non-Congruent Pieces

3D model description

Cube Trisection, Cake Sharing, Non-congruent Pieces

Very playful: Make a bunch, flip them around, connect them, and have fun!

The present design is based on the well-known "cake-sharing" problem. If you have a square (cube ^_^) cake with icing all around, how can you cut it in a way such that three people (or any reasonable number) each get the same amount, including icing. The essential idea is to take advantage of center of the square and think of the square edges as the bases of some triangles, which all have the same altitude.

We can slice a cube in a similar way and obtain three pieces with the same volume. There are certainly many ways to do that. In this design, I added some jigsaw connectors so that one can slide them into each other for a cube or, if so desired, other shapes. Please note that, in spite of the connectors, the three pieces still have the same volume!

Two versions of shelled pieces are included in case one wants some boxes. A plain version, without connectors, is also included. The cube is 50mm ^3.

####Congruent Trisections
Of course, a cube can be trisected into three congruent pieces in many different ways (see my other designs). Have fun!

  • 3D file format: STL



STEAM educator, learning from and working with K-12 STEAM teachers to explore new ideas of teaching and engagement. I firmly believe ART is at the core of STEM learning or all human learning! I owe my ideas and designs to the hundreds of K-12 children and teachers and university professors I have had the pleasure of working with, in multiple disciplines-- math, science,engineering language arts, social studies, early childhood education and more! All mistakes, of course, are mine! There is no warranty or liability whatsoever implied or explicit behind the designs or ideas. They are all posted for their potential educational values.

When working with children, please strictly observe all safety and health procedures! Please refer to the NSTA safety guides:




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