Emerald cut (rectangular step cut)

cut · polished · emerald cut, rectangular step cut, step cut, trap cut

highlast updated 2026-04-28

A rectangular cut with stepped parallel facets descending the crown and pavilion like a staircase, large open table, cropped corners. Reads as architectural — the gem's color and clarity show through rather than splashing fire. Originally cut for emeralds (which crack easily under brilliant-cut pressure); now standard for high-color rubies, sapphires, aquamarines, and many fancy diamonds. The cut Phil's classroom would call 'editorial.'

50 facets typical: table, 8 crown step facets in 3 levels (8 + 8 + 8), 8 pavilion step facets in 3 levels, 8 culet step facets, 4 cropped corners. No upper / lower girdle facets like a brilliant. Aspect ratio 1.30–1.50 length-to-width is classical; 1.0 length-to-width with 90° corners is the related Asscher cut. Emerald's stepped facets reveal inclusions — only high-clarity material is suitable; any inclusion telegraphs through the open table. Optimum depth 60–70% (deeper than brilliant); preserves crystal weight better than brilliant on prismatic rough. The 'hall of mirrors' visual character: long flashes rather than spangle.

character — architectural rectangle, hall-of-mirrors flash, color-revealing, demands clarity.

Finish properties

levelpolished
subcategoryfacet style, step cut
applies togemstone

Pairs with materials

Lab-Grown Diamond (CVD)

Sapphire (Natural)

Ruby (Natural)

Second life

reversibilityzero — gemstone facet styles are subtractive and committed once cut; "re-cutting" produces a smaller stone with different proportions. The original cut is permanent.

blocks substrate recyclingno

renewabilitymoderate — chips and edge wear can be re-polished with minor weight loss; major damage requires full re-cut to a new pattern.

GIA Diamond Grading and Identification literature; AGS American Gem Society cut-grading standards.

Citations

Concordance

House vocabulary — terms ForMatter uses with intent.

anisotropic: Direction-dependent. Wood reads differently along the grain than across it; rolled steel is stiffer along the rolling direction. The Principled-BSDF anisotropic input rotates the highlight to match.
anodize: Electrochemical oxide layer grown on aluminum (Type II / III), titanium, or niobium. Type II accepts dye for color; titanium / niobium use voltage-driven thin-film interference instead of dye. The CMF entry covers the seal step that locks the color in.
application: What the thing IS, in the world. The third entity, peer of material and process. A water bottle, a chair, an extruded-aluminum profile.
BRDF: Bidirectional Reflectance Distribution Function. The math behind how a surface returns light for any incoming and outgoing direction. The PBR model is a parameterized BRDF.
channeled: A voice block written within a dead author's philosophy, marked and cited. Distinct from a verbatim quote. Roland Barthes channeled on PMMA reads like Barthes; the citation attributes the lineage.
CMF: Color, Material, Finish — the trio designers specify together when handing a part off for production. ForMatter's Finish entity is the F in CMF: 10 categories — polish / anodize / patina / plate / coating / texture / cut / mold_finish / glaze / stone_finish — and entries under each. Every finish entry pairs to the materials and processes it suits.
choral fugue: ForMatter's register. Subject stated plainly (freshman tier), answered in technical and sensorial registers, countersubjects from linked processes and applications, citations as final stretto. Voice blocks where canon attaches.
clearcoat: A second specular layer over the base surface. Glossy plastics and lacquered woods get a clearcoat term in the PBR table. IOR 1.5 by default.
compatibility (process): Each process entry lists which materials it can work. The cross-ref renders as sphere pills so the gallery feeling extends inward.
confidence: Each entry tagged high / medium / low. A senior's low-confidence-with-three-citations beats a freshman's high-confidence-with-none. The label is a contract with the reader, not a brag.
crystalline (finish): A faceted-surface read — gemstones, glassy minerals, ice. Drives PBR defaults: IOR 2.42 (diamond), transmission 1.0, low roughness.
derive_pbr(): The build's single source of truth — sphere palette + finish enum → Principled-BSDF starter values. One function feeds the entry-page table, the per-host snippets, the glTF export, and the Three.js Live Preview.
finish (entity): ForMatter's CMF layer — surface treatments and conditions a designer chooses for a given material and process. Categories: polish, anodize, patina, plate, coating, texture, cut, mold_finish, glaze, stone_finish. Distinct from the sphere `finish` enum (metallic / matte / glossy / etc.) which is the visual register of the proxy.
freshman / senior register: Two registers in every entry — the plain freshman description and the technical / sensorial one. Same database, two readers, no extra subscription.
glTF: GL Transmission Format — the open 3D-asset standard every modern app reads. ForMatter emits a .gltf material doc per material. Open standard, designer-friendly handoff.
IOR: Index of Refraction. How much light bends entering the surface. Air 1.0, water 1.33, glass 1.5, diamond 2.42. Drives transmission and the specular term.
iridescent (finish): Hue-shifted accent over base. Anodized titanium and niobium, opal, paraíba. Drives PBR defaults: low metalness, full iridescence, clearcoat.
iridescence: Thin-film interference layer over the base material. KHR_materials_iridescence in glTF, MeshPhysicalMaterial.iridescence in Three.js. Tunable from the FOCUS slider on iridescent / pearlescent entries. The ior and thickness range together set the visible color sweep — opal uses a 100–800 nm thickness range (film, not wavelength) to span the full visible band.
lite-PBR: ForMatter's PBR approach — Principled-BSDF starter values per entry, no measured BRDFs, no commercial assets. Reasonable defaults from the finish enum, per-entry numeric overrides where you have a real reason.
Live Preview: The Three.js shader ball that replaces the static CSS sphere on every entry page. One render path for every category — metals, woods, polymers, ceramics, paints, textiles, gemstones, glass. Same derive_pbr() values, real-time lit by a synthetic studio environment, draggable. Optional — toggle in Preferences.
material: What the thing is MADE OF. The first entity. Aluminum 6061, white oak, soda-lime glass.
metallic (finish): Specular highlight, deep shadow rim. Drives PBR defaults: metalness 1, low roughness, IOR 1.45. Polished steel, gold, copper.
mood board: Folded into the Project workspace at /project.html. The mood-board upload, palette extraction, character chips, and matcher results all live alongside the collected items grid and the save .formatter / save PDF / open .formatter actions — one feature, one page.
Ollama: Local-LLM scaffold on the Project page. Off by default. When toggled on in Preferences AND Ollama is reachable at localhost:11434, the natural-language input box ('something soft and warm with a wet read') asks the model to translate the description into character-chip toggles. Never invents material properties; the LLM only translates intent into existing chip vocabulary. The keyword fast-path (chips alone, no LLM) is the default — see suite-wide ai-integration pattern.
project: The full workspace at /project.html — collected materials, processes, applications, finishes plus an optional mood-board image whose dominant colors search the library for matches. Save / open .formatter files round-trip the project state.
patina: A chemical color shift on metal — heat-blue on steel, fume-black on silver, verdigris on copper, gun-blue on tool steel, ferric on copper. CMF-layer entry; cited by both the material and the process pages that produce it.
PBR: Physically-Based Rendering. The shading model every modern 3D app uses, parameterized by metallic / roughness / IOR / transmission / clearcoat / sheen. ForMatter publishes starter values for every material entry.
SPI mold finish: Society of the Plastics Industry mold-cavity finish standard. A1 / A2 / A3 (diamond polish, mirror), B1 / B2 / B3 (paper, semi-gloss), C1 / C2 / C3 (stone, matte), D1 / D2 / D3 (dry blast, textured). The finish prints from the mold cavity onto the molded part — a designer picks the SPI grade with the molder when specifying the tool.
Principled BSDF: Blender's name for the consolidated PBR shader. Most other apps ship the same shader under different names (Standard Surface, ShaderGraph, Substance). One node, every output.
process: How the material is MADE INTO the thing. The second entity. Cast, machined, kerf-bent, anodized, planished, granulated. Process is a peer of material, not a footnote.
quote: A voice block carrying a verbatim quotation from a living author, with citation. Distinct from a channeled block. Living = quote only; the rule is enforced at the schema layer.
roughness: Microsurface scatter. 0 is mirror-smooth; 1 is fully diffuse. Most real surfaces sit between 0.2 and 0.8.
sphere proxy: ForMatter's visible-character stand-in for every material. CSS-gradient driven by the entry's palette and finish, not a baked render. Honest about being a proxy, scales cheaply, tweakable in one place.
substitute: A peer material that could fill a similar role. Cross-references render as sphere pills inside an entry — the gallery feeling extends inward.
transmission: How much light passes through. 1 is fully transparent; 0 is opaque. Glass, gemstones, clear plastics carry transmission.
PVD: Physical Vapor Deposition — vacuum-chamber sputter or cathodic-arc deposition of a thin ceramic film onto a metal substrate. The CMF-layer's modern coating chemistry: TiN (gold), ZrN (champagne), CrN (pewter), TiCN (warm bronze / rose-gold), AlTiN (charcoal-anthracite, near-black), DLC (deep black). Hard, doesn't tarnish, paint-thin.
VDI 3400: German engineering reference standard for mold-cavity texture (Erodieren bearbeitete Werkstückoberflächen). The full scale runs reference plates 0–45 by Ra value; production specs typically draw from 12–45 because plates 0–11 require diamond-mirror polish on the mold cavity and are rarely commissioned in commercial tooling. Pairs with the SPI standard; both define what gets cut into the mold.
voice block: A versal block where a real authored voice attaches to the material or process. Schema-tagged with status (living / dead) and mode (quote / channeled). Citations always.
woodgrain (finish): Directional sheen with grain ring. Drives PBR defaults: anisotropic 0.6, medium roughness, no metalness. Every wood entry.

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ForMatter

Materials and processes for people who design and make things.

A local-first library of materials, processes, applications, and finishes — equal weight, citable everywhere, so a student can move from "what is this" toward "what's actually buildable here, now, by me." Part of the renato.design ecosystem — sibling of Plenum, Specimen, Ingenue, gesture, graf, and the Renato Rhino plug-ins. Form and matter, inseparable.

Why this exists

Half of teaching materials is teaching how the material is made into the thing. The standard subscription library was always light on that half. The wedge here isn't better samples or a prettier interface — it's treating Process as a peer entity, not a footnote.

Sources

Conway, Lefteri, Forty, Sparke, ASM, GIA. Every voice: Voices.

Rules of the house

Citations or it didn't happen.
Living authors are quoted only.
Dead authors may be channeled within their philosophy — marked, cited, never impersonated.
Permalink or nothing.
Relative, not absolute.
Confidence labeled honestly.
Local-first.

Sister apps

Ingenue — five voices argue about what to build from electronic parts.
Plenum — VIN, fender-tag, and broadcast-sheet decoder for muscle and pony cars; doo-wop register.
Specimen — iPhone 3D scanner that treats the captured object as a specimen, with voiced commentary.
renato.design — the rest.

v0.6.88 · 2026-10-24 · Phil Renato · renato.design · MIT-licensed code, CC BY-NC research content

Preferences

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UI scale Zoom for projection or close work.

Tooltips Hover hints on controls.

Sphere density Spheres per row on the landing grid.

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Local LLM (Ollama) Turns a description into chips via localhost:11434.

Default register More shows every layer; less keeps the lead, sphere, citations.

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