It turns out that all *feasible* configurations, i.e. configurations that are not excluded using the known
invariants, can actually be constructed.
This means that the known invariants (metric and topologic) form a complete set of invariants.
Following the links below you get a complete list of the octominoid configurations.

The color code corresponds to the size of the bounding box (e.g. red for configurations with a bounding box 1x2x2)
and follow the convention fixed by Jürgen Köller in
`http://www.mathematische-basteleien.de/magics.htm`

.

They are further grouped based on the number of tiles of the octominoid that lie on the boundary of the bounding box. For example: box 2x2x2 (+6) means that the bounding box is a 2x2x2 cube and the configurations have 6 of the 8 tiles lying on the boundary of the bounding cube.

**Complete list of all 265 constructible**octominoids (including the two planar shapes) with instructions on how to build them- Explanation of the magic-code
- Go to a random 3D configuration
- Most complex configurations

***** Web interface *****to compute the normalized magic code and generating a magic photo (in italian)

- Updates upon table magic27 (taken from http://www.mathematische-basteleien.de of Jürgen Köller and reproduced here)

- [Nourse] flat shapes: I-1, I-2, I-3; S-1,..., S-4; L-1, ..., L-8; U-1, ..., U-6.

- Wikipedia page.
- [Koeller] Jürgen Köller, Rubik's Magic (web page).
- [Jaap] Jaap Scherphuis, Rubik's Magic Main Page (web page).
- [Houlis] Pantazis Constantine Houlis, Folding Puzzles (web page).
- [Nourse] James G. Nourse, Simple Solutions to Rubik's MAGIC, Bantam Books, 1986.
- Verhoeff, Tom (1987). "Magic and Is Nho Magic" (PDF). Cubism For Fun (15): 24–31. Retrieved 2015-07-28.

Feedback: Maurizio Paolini (

`paolini@dmf.unicatt.it`

)