Reuleaux polygon

A convex constant-width curve assembled from an odd number of equal-radius circular arcs, with each arc centered at an opposite vertex of its generating polygon.

Version

v1 · 2026-09-08 · History

Domain-specific #

6508

Origin domain

convex geometry

Subdomain

curves of constant width

Core Idea

A Reuleaux polygon is a curve of constant width composed of circular arcs of one radius, constructed so each arc is centered at the vertex opposite the replaced side interval. As parallel support lines rotate, one touches an arc and the opposite one touches that arc's center vertex. Equal radii keep support-line separation constant despite changing contact points. 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

Reuleaux polygon belongs to convex geometry and is useful where the analyst can specify an odd-sided convex generating polygon satisfying opposite-distance conditions and a closed boundary formed from equal-radius circular arcs, then evaluate the closed convex boundary uses an odd number of equal-radius arcs and every pair of parallel support lines has the same separation. The scope is broad within that domain but bounded by the need for the closed convex boundary uses an odd number of equal-radius arcs and every pair of parallel support lines has the same separation. 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 closed convex boundary uses an odd number of equal-radius arcs and every pair of parallel support lines has the same separation 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 Reuleaux polygon 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 Reuleaux polygon. Reuleaux polygon 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

1. Identify the carrier. State what the elements, states, objects, or observations are: an odd-sided convex generating polygon satisfying opposite-distance conditions and a closed boundary formed from equal-radius circular arcs. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the closed convex boundary uses an odd number of equal-radius arcs and every pair of parallel support lines has the same separation independently of one notation or implementation.

Knowledge Transfer

Knowledge transfers strongly among subfields of convex geometry because they reuse an odd-sided convex generating polygon satisfying opposite-distance conditions and a closed boundary formed from equal-radius circular arcs, As parallel support lines rotate, one touches an arc and the opposite one touches that arc's center vertex. Equal radii keep support-line separation constant despite changing contact points., and type the carrier, state every parameter and convention in the definition, test that the closed convex boundary uses an odd number of equal-radius arcs and every pair of parallel support lines has the same separation, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions

Current abstraction Reuleaux polygon Domain-specific

Parents (1) — more general patterns this builds on

• Reuleaux polygon is a kind of Invariance Prime

  The proposed strict upward parent is prime:invariance.

Hierarchy path (1) — routes to 1 parentless root

• Reuleaux polygon → Invariance

Neighborhood in Abstraction Space

Reuleaux polygon sits in a moderately populated region (43^rd percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Convex Geometry & Spatial Partition (35 abstractions)

Nearest neighbors

• Polygon partition — 0.91
• Relative convex hull — 0.90
• Tangential quadrilateral — 0.90
• Perfect rectangle — 0.89
• Uniform polyhedron — 0.89

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