Radii and radius vectors are used to express spatial concepts like extension and containment. For example, consider a particle P characterized by some repetitive chain of events

where each orbital cycle is a bundle of quarks

that are described by their quark coefficients and internal energies . Recall that notes the enthalpy of the chemical quarks in P. And let a constant have a positive value, with units of a force. These quantities are used to describe the shape and extent of P as follows. The chemical radius is

The magnetic radius of P is

the electric radius is defined by

and the polar radius of P is given as

An ordered set of these radii defines the radius vector of particle P as

The three components of are conserved because they are defined from sums of quark coefficients, and quarks are conserved. So if some generic particles , and interact like then by the associative properties of addition, radii are related as

Also and . So particles and anti-particles have symmetrically opposed radius vectors

Going forward, we use these radii and radius-vectors to develop a description of particle shape. As a starting example; if P has the same radius vector for every cycle, then we call it a rigid particle.