# VectorPaint seven-cell honeycombs: distinguish side occurrences from unique edges
Language: en
Canonical: [VectorPaint seven-cell honeycombs: distinguish side occurrences from unique edges]()
中文：[中文 HTML]()
English: [English HTML]()
Published: 2026-11-11T00:00:00+08:00
Modified: 2026-11-11T09:40:26+08:00
Author: Bison
Arrange a centre and six neighbours manually, checking twelve shared and thirty unique edges rather than counting overlapping strokes.
English translation of the [Chinese original](), translated on 2026-11-11. Original publication dates, attribution, code and version notes are retained.
Seven hexagons contain forty-two side occurrences but not necessarily forty-two different edges. Construct a seven-cell cluster, identify shared sides and check counts two ways. This is neither automatic tiling nor a measured natural honeycomb. VectorPaint draws paths while you verify geometry and multiplicity externally.
## Establish one regular hexagon
Use side 100 and local centre (0,0), with vertices (100,0), (50,50√3), (−50,50√3), (−100,0), (−50,−50√3), (50,−50√3). Close six theoretically equal sides; the circumdiameter 200 is not the side length. Reverse mathematical y and translate consistently for canvas placement. With approximate controls label the result illustrative. Save the reference before copying: six repetitions do not validate an inaccurate original.
## Place neighbours by six vectors
Relative neighbour centres are (0,100√3), (150,50√3), (150,−50√3), (0,−100√3), (−150,−50√3), (−150,50√3). Number them 1–6 around the centre cell 0, then translate the cluster into margins. Keep size/orientation fixed rather than rotating one cell to accommodate errors. Neighbour distance is 100√3, not 200. An incorrect 200 spacing may leave gaps that heavy strokes cannot convert into genuine shared edges.
## List all twelve shared pairs
Cell 0 shares six sides with neighbours 1–6. Outer pairs 1–2, 2–3, 3–4, 4–5, 5–6 and 6–1 share another six: twelve shared edges. Pair 0–1 equals 1–0 and counts once. Do not add nonadjacent outer pairs from visual proximity. List unordered pairs externally and inspect each complete coincident segment. Vertex contact alone is not a shared edge and cannot enter this duplicate-count correction.
## Subtract duplicated occurrences correctly
Seven times six gives 42 side occurrences. Each shared edge appears twice, so subtract one duplicate per shared edge: 42−12=30 unique edges. Subtracting 24 gives 18 perimeter edges, not all edges. Independently check 30=12 internal shared+18 external. Keep all three counts distinct from stroke-object count. Ideal geometry excludes line width; heavier strokes do not change edge identity, nor does splitting one edge among path objects create additional geometric edges.
## Avoid double-dark shared strokes
Seven closed outlines may remain in the construction view. If duplicate strokes darken shared edges, organise a presentation copy through unique segments or available object operations, without assuming automatic deduplication. Check each manual deletion against the list so the official separator does not vanish. Fills aid identification without changing adjacency: equal-colour cells remain separate. Monochrome should still reveal seven cells. Preserve the closed-cell source so presentation cleanup does not erase the construction’s origin.
## Move one neighbour to test assumptions
In a separate copy move neighbour 1 clearly outward so it no longer shares edges with the centre or its ring neighbours. Seven hexagons remain, but the old twelve-shared/thirty-unique result no longer applies. Record lost pairs rather than relying on approximate resemblance. Restore it and recheck all twelve pairs for accidental movement elsewhere. No universal count for arbitrary displaced layouts is required. If recounting, rebuild the full shared-pair list instead of subtracting one casually. Preserve the correct cluster separately.
## Inspect perimeter and interior in output
Save and inspect PNG eighteen perimeter segments, twelve internal edges and seven filled cells. For merged interior lines reduce width or enlarge presentation rather than deleting a cell. Hide unwanted cell numbers while retaining necessary count legends. Manual references export as objects; inspect native-grid behaviour. For disappearing edges in another format isolate edge objects/fill order instead of altering counts. This theoretical ledger measures no natural honeycomb and establishes no species or construction precision from pixels.
## Troubleshoot shared, repeated and perimeter counts
For 42 unique edges inspect duplicates; for 18 total edges inspect perimeter-only counting; for overlaps revisit centre vectors; for vertex-only sharing revisit the full-segment rule. Rebuild the ledger and both equations after repair rather than merely retaining 30. Keep reference coordinates, six offsets, twelve unordered pairs, the occurrence/unique/perimeter counts and displaced control. Thirty is the unique-edge count, eighteen the exterior count. This finite seven-cell exercise is not automatic honeycomb generation, an area-optimality proof or verification of an infinite tessellation.
## Related tutorials and sources
[VectorPaint sixfold rosettes: audit rotational symmetry around one centre](), [VectorPaint translation and reflection: check each vertex coordinate and orientation]().
Checked on November 11, 2026: VectorPaint public version 1.0.8, requiring iOS / iPadOS 17.0 or later. Capability scope follows the [official App Store]() and [Apple public lookup](). This is an original manual exercise; use controls available in your installed version and actual file state. External calculations, records and diagrams do not imply new automatic analysis. No step-by-step physical-device, private-file or all-export-environment testing is claimed.