Crease pattern¶

A planar origami representation that records most or all folds of a finished model in one geometric diagram.

Version: v1 · 2026-09-08 · History
Domain-specific #: 3958
Origin domain: origami design
Subdomain: origami design

Core Idea¶

A crease pattern marks mountain, valley, boundary, and structural fold lines on the uncreased sheet, encoding the spatial organization from which a folded model can be analyzed or reconstructed. Flattening the model’s fold network into a single sheet diagram preserves adjacency, intersection, angular, and layer-relevant constraints while omitting the temporal folding sequence. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

Scope of Application¶

Crease pattern belongs to origami design and is useful where the analyst can specify the typed origami design carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the diagram corresponds to one sheet and records a geometrically compatible fold network whose designated creases map to the intended folded structure. The scope is broad within that domain but bounded by the need for the diagram corresponds to one sheet and records a geometrically compatible fold network whose designated creases map to the intended folded structure. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.

Clarity¶

The abstraction clarifies a crowded vocabulary by making the diagram corresponds to one sheet and records a geometrically compatible fold network whose designated creases map to the intended folded structure the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Crease pattern can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.

Manages Complexity¶

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Crease pattern. Crease pattern compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning¶

Identify the carrier. State what the elements, states, objects, or observations are: the typed origami design carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the diagram corresponds to one sheet and records a geometrically compatible fold network whose designated creases map to the intended folded structure independently of one notation or implementation.

Knowledge Transfer¶

Knowledge transfers strongly among subfields of origami design because they reuse the typed origami design carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, Flattening the model’s fold network into a single sheet diagram preserves adjacency, intersection, angular, and layer-relevant constraints while omitting the temporal folding sequence., and type the carrier, state every parameter and convention in the definition, test that the diagram corresponds to one sheet and records a geometrically compatible fold network whose designated creases map to the intended folded structure, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions¶

Current abstraction Crease pattern Domain-specific

Parents (1) — more general patterns this builds on

Crease pattern is a kind of Representation Prime

The proposed strict upward parent is prime:representation.

Hierarchy path (1) — routes to 1 parentless root

Crease pattern → Representation → Abstraction

Neighborhood in Abstraction Space¶

Crease pattern sits in a sparse region of the domain-specific corpus (66^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Knot Invariants & Diagrammatic Algebra (11 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-09-08