It may be remarked generally that there are at most three infinite branches, and that there may besides be a re-entrant branch or oval.
Two of these figures stood at the end of a re-entrant curve, several pieces of which are preserved.
3) has no re-entrant angles.
A branch is either re-entrant, or it extends both ways to infinity, and in this case, we may regard it as consisting of two legs (crura, Newton), each extending one way to infinity, but without any definite separation.
With n=1, the re-entrant walls are given of Borda's mouthpiece, and the coefficient of contraction becomes 2.
This frequent twinning gives rise to characteristic forms, with many re-entrant angles, to which the names "spear pyrites" and "cockscomb pyrites" are applied.
The requirements of an elongate body moving through the resistant medium of water are met by the evolution of similar entrant and exit curves, and the bodies of most swiftly moving aquatic animals evolve into forms resembling the hulls of modern sailing yachts (Bashford Dean).
The branch, whether re-entrant or infinite, may have a cusp or cusps, or it may cut itself or another branch, thus having or giving rise to crunodes or double points with distinct real tangents; an acnode, or double point with imaginary tangents, is a branch by itself, - it may be considered as an indefinitely small re-entrant branch.
A re-entrant branch not cutting itself may be everywhere convex, and it is then properly said to be an oval; but the term oval may be used more generally for any re-entrant branch not cutting itself; and we may thus speak of a once indented, twice indented oval, &c., or even of a cuspidate oval.
Other descriptive names for ovals and re-entrant branches cutting themselves may be used when required; thus, in the last-mentioned case a simple form is that of a figure of eight; such a form may break up into two ovals or into a doubly indented oval or hour-glass.