According to Pook
In Flexagons Inside Out, author Les Pook explains flexagons in more detail:
"In general, the main characteristic feature of a flexagon is that it has the appearance of a polygon which may be flexed in order to display pairs of faces, around a cycle, in cyclic order. Another characteristic feature is that faces of individual polygons, known as leaves, which make up a face of a flexagon, rotate in the sense that different vertices move to the centre of a main position as a flexagon is flexed from one main position to another. The visible leaves are actually folded piles of leaves, called pats. Sometimes pats are single leaves. Alternate pats have the same structure. A pair of adjacent pats is a sector.
The leaves of a hexaflexagon are equilateral triangles. In appearance a main position of a hexaflexagon is flat and consists of six leaves, each with a vertex at the centre so there are six pats and three sectors . . . There are only one possible type of cycle and one possible type of link between cycles.
In main positions, alternate pats are folded piles of two and four leaves. In the other main positions alternate pats are single leaves and folded piles of five leaves. It is always found that at a main position of a hexaflexagon where there is no link to another cycle alternate pats are single leaves. Finding all nine possible main positions of a hexahexaflexagon is quite a challenge for the uninitiated, especially if the faces are decorated rather than numbered."