The 29 pentacubes have a total of 145 cells. They can be arranged to form shapes with achiral octahedral symmetry, the symmetry of a cube.
Here I show how they can form three such shapes. If you find any others, please write.
Cross sections are shown from top to bottom.
See also Prisms with Square-Symmetric Bases from the 29 Pentacubes.
Peter Knoppers has asked whether these tilings stand on their own. He has since confirmed that the third one does. Here is his photograph of the assembly:
Peter has determined that the other two tilings do not stand on their own. I have not found alternate tilings that do.
Last revised 2026-10-05.