 Another line of research led Chingis Izmailov to a spherical model of facial expressions of emotions.The sphere is four-dimensional, with interpoint Euclidean distances nearly proportional to numerical estimates of emotional differences.The axes of the sphere are interpreted as the opponent pleasant-unpleasant and active-passive channels, the remaining two being interpreted as “strength” and “calmness.”

Chingis Izmailov hypothesized that spherical models and other metric structures may not be applicable to properties of categorizable perceptual objects.