# Overview

Weaving is a textile craft in which two distinct sets of yarns or threads, called the warp and the filling or weft (older woof), are interlaced to form a fabric or cloth. The warp threads run lengthways on the piece of cloth, and the weft runs across from side to side, across the bolt of cloth. Cloth is woven on a loom, a device that holds the warp threads in place while filling threads are woven through them. Weft is an old English word meaning "that which is woven". The way the warp and filling threads interlace with each other is called the weave.

Snelson identifies weaving as the "mother of tensegrity."

# Distinguishing Woven Structures from Tensegrities

 Space Frame Weave, Octa-Form 2002 by Snelson

A website posted the above woven work by Snelson. Snelson commented, "to use this three-dimensional woven sculpture as an example of tensegrity is to illustrate how very confused the meaning of the word “tensegrity” has become. By any measure this piece cannot be called “tensegrity” although it has the same rotation/counter-rotational geometry as tensegrity. This 3D weave is not a “pre-stressed” structure as is for example a gas-filled balloon where the balloon’s skin is made taut by the pressure of the compressed gas inside. Tensegrity structures are similarly prestressed with the tension network pulling inwardly against the compression parts." [1]

# Woven polyhedra are skew polyhedra

In a woven, flat surface, polygons are formed including triangles, squares, etc. The woven polygons have edges that bypass one another.

This effect translates into polyhedra such as the tetrahedron, octahedron, and icosahedron. In a woven polyhedron, the struts bypass one another at or near the vertex. Snelson calls these weave-polyhedra or helix-polyhedra, and the slight displacement at the vertices is a helical bypass.

See skew.

# Mathematics of Weaving

Whiteley wrote in " Weaving lines and tensegrity frameworks", "Consider a weaving — a set of rods in the plane, woven over and under at their crossing points. The theory of when such weavings are stable, or rigid, in the plane is developed as the projective polar of the theory of static equilibrium and static rigidity for plane tensegrity frameworks with cables and struts." [3]

Whiteley begins his approach with a triangular weave. He wrote, "For centuries, people have woven sticks together. Even today children, and adults of a similar spirit, take toothpicks or popsickle sticks and place them together in various stable and unstable arrangements. If the sticks are stiff enough, the patterns are essentially patterns of lines--in the plane or in 3-space.

# Rolfing model of human musculature can be compared to weaving

Gael Ohlgren describes the basket weave/helix theory of muscle structure in the human body, in an article called "Natural Walking. "Let’s blur the distinction of individual muscles in isolated action, and see another design in the fibers. The individual fibers that make up all musculature lay along diagonals. Most of the discreet muscles also lay along diagonals. What begins to appear, if one gives up the idea of isolated muscle groups and allows muscles to transit boney structures is a pattern of diagonal lines.12 Crossing spirals of muscular fiber become apparent. For example, a left pectoral muscle blends with a right intercostal that joins an oblique muscle that blends into a gluteal muscle.13 This is exactly countered by a matching helix (a spiral in 3-dimensions) from the right pectoral on down. Start at another point and the same type of helix emerges. An iliacus leads to a quadratus lumborum that wraps into the lattissimus on the other side of the body and so forth."

This comparison to weaving is in line with Snelson's conception of tensegrity. Ohlgren continues, "Bones... assume a structural dimension that is in addition to levers and to spacers inherently more in tune with a tensegrity view of the body’s mechanics. With the use of a couple of analogies, this new model can be appreciated. A machine that is designed for a consistent relationship to gravity is liable to sustain serious damage when forces outside its design-frame are applied to it. If this were indeed our design, few of us would survive our childhood in working order. Try putting a computer through the innumerable crashes of a typical youth and imagine what working order it might be in, to say nothing of its appearance. To what do we owe our remarkable resilience? From football, to skiing, to tumbling we are able to sustain a tremendous array of reckless experiments and live to tell about it. Although our muscular tube design is not precisely an interweaving of diagonal fibers, as in a basket, the basket-weave analogy is helpful... For a certain generation this might bring to mind the straw 'Chinese handcuffs'. These were tubes of woven straw which expanded when compressed and contracted when elongated, allowing one’s fingers to enter the tube from both ends but preventing the withdrawal of the fingers when they were pulled away. After either compression or elongation or twisting, the spiral double helix weave pattern will always return to its original shape by its own momentum. This model is closer to a spring than a lever/pulley model and reflects our spring-like resiliency."

# Weaving in Dynamic Materials

Dynamic and deployable tensegrities are often woven. For example, deployable tensegrity masts by Tibert and Pellegrino propose "a manufacturing procedure in which the cables forming the outer envelope of the mast are constructed by two-dimensional weaving is used." [2]