Terminology used in the shape-building instructions

Oriented tile

a tile with an arrow on one of its faces parallel to one side. In an oriented tile we can identify the front face (the one with the arrow) and the back face; the sides can be labelled R(ight), L(eft), U(p), D(own) according to their position with respect to the arrow, that is supposed to point up

Oriented configuration

all tiles are oriented in a consistent way: a pair of mechanically adjacent tiles are consistently oriented if their orienting arrows perfectly match when the two tiles are ideally folded one against the other (front face against front face)

slash and backslash tile

for an oriented tile we can look at the direction of the nylon wires; the tile is a slash tile if the wires run from the lower-left corner to the upper-right corner (like the / character). Otherwise the tile is a backslash tile

type A or type V pair of tiles

For a pair of adjacent tiles forming a flat angle and positioned horizontally with respect to the viewer, we say that they are of A type if the left tile is a slash tile and the other is a backslash tile (the two directions recall the two sides of a capital letter A). In the opposite situation we say that the two tiles are of V type

flap tile

a tile that is connected to its adjacent tiles by the same side. It therefore is free to rotate with respect to this hinging side

hinging equivalent configurations

configurations that can be connected by moves that do not change the hinging side between adjacent tiles

stacked tiles

a pair of adjacent tiles that are stacked on top of each other. In this case there is no evident hinging side and the two tiles can be separated by hinging about two distinct adjacent sides. In configurations like the flat configurations studied in [nourse] a diagonal arrow can be drawn point to these two hinging sides