[up to rubik's magic web page] [3D octominoid shapes]

planar face-up configurations

Consist of all configurations with all tiles lying on a plane, possibly including stacked tiles, and all tiles oriented face-up (this excludes in particular the tetris-like flat shapes). In this set there are still a few configurations that are feasible but not (yet) actually constructed, so that we do not have the complete picture of constructible configurations. Update: The latest constructed configuration was discovered in June 2017.
Most figures are clickable for building instructions.

No flaps

Here we find the basic 2x4 and heart-shaped configurations, both of area 8 (the number of squares covered on the supporting plane). These two configurations should also be considered octominoid configurations. The signature below the pictures indicate exactly the puzzle configuration: the initial "⧄" symbol indicates that we start with a slash tile (wires oriented from south-west to north-east), then the "E" means that the next adjacent tile is located "East" of the previous tile and so on with the obvious meaning of the letters "N", "S" and "W".
⧄ E E E N W W W S ⧄ E E N N W S W S

One flap

A flap tile is a tile having its two adjacent tiles hinged about the same side. The index written after some of the cardinal directions in the signatures indicate the position of the corresponding tile with respect to other tiles that end up in the same position (stack of tiles). Numbers start from 1 (the bottom position). All constructible configurations with one flat have area 6 (realizing the shape of an hexominoe).
⧄ E2 E N W S1 W1 S N2 ⧄ E2 E N W S1 W1 N S2 ⧄ E2 E2 E N W S1 W1 W

Two flaps

The three figures with the question mark correspond to three configurations with vanishing invariants, that however we were not able to construct (yet).

Area 6

⧄ E1 E N W1 W E2 S2 W ⧄ E2 E N W2 W E1 S1 W ⧄ E1 E1 E W2 N W S2 W
⧄ E2 E2 E W1 N W S1 W ⧄ E1 E N W S3 S N2 W ⧄ E2 E N W1 N S2 S1 W
⧄ E N1 E W3 N S2 W S ⧄ E1 E N W2 N S1 S2 W ⧄ E1 E N1 N S2 W S2 W

Area 5

⧄ E1 N1 E W2 S2 N3 W S ⧄ E3 E2 N W S2 E1 W1 W ⧄ E2 N3 E W2 S1 N1 W S

Area 4

⧄ E1 N1 W1 E2 S2 N3 W2 S

Three flaps

⧄ E2 E1 N1 S2 N2 W S1 W ⧄ E2 E N2 W2 E1 W1 S1 W ⧄ E3 E2 W1 E1 N W S2 W ⧄ E3 E2 W2 E1 N W S1 W ⧄ E3 E N W1 S1 N2 S2 W

Four flaps

⧄ E N1 W1 E2 W2 S1 N3 S2 ⧄ E1 N1 W1 E2 W2 S2 E2 W1

Software code source

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