Sonobe Cube with Alpha by Tomoko Fuse
Number of units: 12 (6 for cube, 6 for alpha)
Designer: Tomoko Fuse
The model is composed of a basic Sonobe Cube along with 'Alpha Units', which are described on Page 74 in the book Multidimensional Transformations: Unit Origami by Tomoko Fuse.
For the cube, you may see instructions for Sonobe units by Dave Mitchell: Part I and Part II. To assemble the units, Instructions for Assembly with Sonobe units (PDF) — this is a free chapter from Meenakshi Mukerji's book: Marvelous Modular Origami (2007, 92 pages). To assemble many more models using Sonobe units, check out this article.
The alpha units do not fit snugly into the cube. So the final model is not as neat as most other modular origami models.