From every open region two arcs emerge, with adjacent regions sharing the same arc. We can distinguish open regions with one, two, or more vertices, and denote their type by 1,2,3, respectively. Placing new 1-tangle in an open region changes its type and the types of adjacent regions. If its original type was 1, the addition of new 1-tangle is forbidden, because a bigon will be obtained. If the type of a region is 2 or 3, it will be changed to 1, and types of its adjacent regions increase by 1. The process of weaving non-algebraic n-tangles, followed by the changes of the types of open regions is illustrated by the following figure.

Thus we obtain non-algebraic n-tangles without bigons. Note that obtained tangles are not necessarily different i.e. some tangle may be obtained in different ways.

A closure of n-tangle is a basic polyhedron, if connecting of emerging arcs does not result in the appearance of bigons. By joining free arcs one region can be closed, or two regions become one. This means that the region type of a closed region must be greater then 2, and the sum of region types of the two joined regions must be greater then 2.

In the case of 3-tangles and A-closures we need three non-adjacent regions of the type 3, and for an O-closure two opposite regions of the type 3 and a pair of opposite regions with the sum of region types greater then 2. In both cases we close regions of the type 3 by connecting emerging arcs. The closure giving a basic polyhedron is unique (up to symmetry).

As we have described it, the main purpose of Crazy Spider Algorithm is derivation of basic polyhedra, and as a side result we get all non-algebraic n-tangles without bigons.