Where does face collide?

A flat bounding piece of a solid figure: each polygon that encloses a polyhedron is one of its faces, and every polyhedron is built from a finite set of them meeting along edges and vertices. Euclid's Elements (circa 300 BCE) treated solids as figures contained by plane faces when it defined and constructed the five regular polyhedra, and Coxeter's 1947 Regular Polytopes generalised the idea to any number of dimensions, where a face is any bounding element of a polytope, from a single vertex up to a facet. The referent is an abstract boundary element counted by combinatorics, and it has nothing to do with the flat surface of a mineral crystal, a person's social standing, or the human face people recognise.[1][2]

Unit

One bounding polygon of a polyhedron, or any bounding element of a higher-dimensional polytope

Recovery means

Not applicable

Measured by

Counted as combinatorial data such as the numbers of faces, edges, and vertices, related for convex polyhedra by Euler's formula V - E + F = 2

The public image of worth a person claims in a social encounter, which others may grant, withhold, or damage. Hu's 1944 The Chinese Concepts of 'Face' distinguished two strands in Chinese usage, prestige built through visible success and the moral standing a community grants a person, and Goffman's 1955 On Face-Work recast face as the positive value a person effectively claims through the line others assume they are taking, kept up by ritual work during interaction. The referent is a social standing negotiated between people, tracked by acts of giving, saving, and losing it, and it is unrelated to a bounding element of a polyhedron, a growth surface on a crystal, or the physical face a perceiver sees.[3][4]

Unit

One person's claimed social standing within a given encounter or relationship

Recovery means

Face that has been lost can be restored through corrective facework such as apologies, accounts, and remedial exchanges

Measured by

Studied qualitatively through observation of interaction and facework, and operationalised in survey measures of politeness, honour, and self-presentation

The human face treated as a special object of visual perception, handled by mechanisms that let people recognise identity, expression, and gaze rapidly and holistically. Bodamer's 1947 Die Prosop-Agnosie described patients who lost the ability to recognise familiar faces while the rest of their vision stayed intact, evidence that face recognition is a separable process, and Bruce and Young's 1986 Understanding face recognition set out an influential model dividing face processing into stages for structural encoding, identity, expression, and name retrieval. The referent is a perceptual and cognitive process in an observer's mind, gauged by accuracy and speed, and it shares only the word with a polygon's face, a crystal's face, or a person's social face.[5][6]

Unit

One percept or recognition judgement of a face by an observer

Recovery means

Not applicable

Measured by

Measured by recognition accuracy and reaction time, by effects such as the face-inversion and composite effects, and by responses in face-selective brain regions