face
Let an agent reason about faces as countable, measurable parts of a solid, in geometry and in cut objects such as gems and crystals.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify
Researched by: Claude
Purpose and description
Let an agent reason about faces as countable, measurable parts of a solid, in geometry and in cut objects such as gems and crystals.
A flat surface that forms part of the boundary of a solid object, such as a face of a polyhedron or a facet cut on a gemstone.
What it is for: Describing and making the shape of solids: counting, naming and measuring the flat surfaces that bound them.
It can be count and name them, which defines a solid or a cut; measure their area and the angles between them; cut or polish them, in gem cutting and machining; use them to identify a crystal or a cut.
Distinguishing features
Flat, which separates a face from a curved surface
Bounded by edges shared with other faces
Counted and named by position in a solid or a cut
The human face is a different sense and is not covered here
What it looks like
A flat, bounded surface meeting others at edges; on a cut gem, a small polished plane that reflects light at a set angle.
Physical character
number of faces: 4 upward faces - a tetrahedron has 4, a round brilliant cut has 57 or 58 facets
angle between faces: 0-180 degrees - crown and pavilion angles set the optics of a gem
How it is recognised
Flatness and straight edges where it meets neighbouring faces
On gems, named facets such as table, crown facets, pavilion facets and culet sit in fixed positions
Curved surfaces are not faces in this sense, even when they bound a solid
Related models
is part of - faces, edges and vertices together define it
is confused with - a homonym; this entry is the geometric surface
is described by - faces, edges and vertices satisfy V - E + F = 2 for convex polyhedra
determines - facet angles govern brilliance and dispersion
In practice
Families and kinds
geometric: faces of polyhedra, by polygon type
crystal faces: natural faces of a mineral crystal
gem facets: table, crown, girdle, pavilion, culet
machined faces: faces of a milled or ground part
Standards and regulation
Gem grading conventions for cut, such as those of major gemmological laboratories
Crystallographic notation such as Miller indices for crystal faces
Failure modes and hazards
Counting facets inconsistently, which gives different numbers for the same cut
Confusing the geometric face with the human face in text
Poorly angled facets that leak light and reduce value
Also called
Where this came from
wikidata · CC0 1.0
Also registered as vr.tr.face-3
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Geometry Shape, count and position.
A face is defined by its shape and by its place among the other faces of a solid.
Shape of the face
The polygon or outline.
Face shape
The outline and dimensions.
- What shape is this face, and what are its dimensions? measurement
- Is it genuinely flat, and within what tolerance? measurement
Position in the solid
Where it sits and what it meets.
Position and neighbours
Which faces and edges it shares.
- Which faces does this face meet, and at what angles? measurement
- How is its position named in this solid or cut? definition
Crystals and gems Faces in minerals and cut stones.
In mineralogy and gem trading, faces carry identification and value.
Crystal faces
Natural faces and their notation.
Crystal face notation
The indices and habit.
- Which crystal face is this, in Miller indices? definition
- What does the habit of faces say about the mineral? definition
Gem facets
Cut facets and their names.
Facet layout
The facet names, count and angles of the cut.
- Which cut is this, and how many facets does it have? measurement
- Are the facet angles within the proportions for good optical performance? measurement
Making faces Cutting, grinding and polishing.
Faces on made objects are produced by processes whose precision decides quality.
Process
How the face is produced.
Production method
The cutting or machining process used.
- How was this face produced, and to what tolerance? measurement
- What surface finish does the process leave? measurement
Defects
Chips, scratches and misalignment.
Defects found
Defects and their effect.
- Which defects are present on this face? measurement
- What do they do to function or value? boundary
Counting and naming Conventions that make counts comparable.
Different conventions count the same object differently, so the convention is part of the fact.
Counting convention
What counts as a face.
Convention used
The rule for counting and naming.
- Which convention was used to count the faces here? provenance
- Does it count the culet or girdle facets? boundary
Consistency checks
Checking counts against topology.
Topological check
Whether counts of faces, edges and vertices agree.
- Do the counts of faces, edges and vertices satisfy the expected relation? measurement
- What does a mismatch indicate? action
What the second pass must settle
- Should geometric faces, crystal faces and gem facets be separate entries?
- How should naming conventions for facets be recorded when they differ between traditions?
- Should Miller indices be modelled as an identifier for crystal faces?