Two pieces of 69 mm architrave meeting at an internal corner that two walls have cut the point off. Plan view throughout; run lengths deliberately unspecified.
The corner runs vertically down one wall and off at 53° along another. Both legs are the same 69 mm architrave, carrying a design line 17 mm in from the exposed edge, and that line has to run continuously round the corner.
Two walls bound the work. A white wall runs level and nothing may sit above it; a blue wall runs parallel to the diagonal leg and nothing may go past it. They meet at W. Because the architrave width is fixed at 69 mm and the vertical leg cannot move off its own wall, the whole corner is rigid — there is no dimension left to choose. Only the two run lengths are open.
For the design line to carry across a joint, the line on one piece has to meet the line on the other on the joint itself. With both pieces the same width there is exactly one cut that does it: the mitre from the outer corner O to the inner corner P — the only straight line that crosses both runs at once.
Chopping a piece part-way along a run is free: same strip, same offset, the line simply carries on. That is why more pieces do not help. A third or fourth piece could shorten the runs, but it cannot change where the direction turns, and the turn is the only place the line is at risk.
O sits 52.0 mm above the white wall. The tip of the mitre cannot be built. The wall cuts it at M, 37.6% of the way down from O, throwing away 58.1 mm of it.
The question is whether D — where the two design lines cross — survives that clip. It does: D lands at 75.4% along O→P, leaving 58.4 mm of clearance above it and 38.1 mm below. Had D fallen above the clip, this corner could not be built from 69 mm architrave at 53°.
Each piece is a length of architrave with the same corner treatment: cut the 26.5° mitre, then clip the tip flat where it would have run above the white wall. The two clipped tips add back to exactly 69 mm — the full width of white wall the corner occupies.
The far ends are square and the lengths are yours to set. Note that the two long edges of a piece do not start together: the mitre means the inner edge begins later than the wall edge, by 86.4 mm on piece 1 and 52.0 mm on piece 2.
| Piece | Role | Wall edge | Inner edge | Stock needed | Corner end |
|---|---|---|---|---|---|
| 1 | vertical run | L₁ | L₁ − 86.4 | L₁ | square clip 25.9, then 26.5° mitre 96.5 |
| 2 | diagonal run | L₂ | L₂ − 52.0 | L₂ + 34.4 | 37.0° clip 43.1, then 26.5° mitre 96.5 |
| Cut | Appears on | Off the edge | Saw | Note |
|---|---|---|---|---|
| Mitre | both pieces | 26.5° | 63.5° | beyond most mitre saws |
| Clipped tip | piece 1 | 90.0° | 0.0° | square |
| Clipped tip | piece 2 | 37.0° | 53.0° | beyond most mitre saws |
| Far ends | both pieces | 90.0° | 0.0° | square, to length |
| Dimension | mm | Where |
|---|---|---|
| Mitre O→P, full | 154.6 | if the wall were not there |
| Lost above the white wall | 58.1 | O to M |
| Mitre to cut | 96.5 | M to P |
| White wall taken by the corner | 69.0 | W to V |
| O above the white wall | 52.0 | vertical |
| P below W | 86.4 | vertical |
| V down to Q | 34.4 | on wall line A |
| Design lines meet at D | 75.4% | along O→P |
| D clear of the clip | 58.4 | M to D |
| D clear of P | 38.1 | D to P |
The mitre wants 63.5° off square, and piece 2's clip wants 53.0°. Most mitre saws stop around 50°, so both need a table-saw sled or a track saw. This is not avoidable — it is the price of carrying the design line round the corner. The shallower joints that a mitre saw can reach are precisely the ones that break the line.
Piece 2's mitre tip runs 34.4 mm back past where its wall edge starts, so it needs L₂ + 34.4 mm of stock and the tip is a 37.0° point in MDF — fragile until it is fixed. Handle it by the body, not the point.
The design line does not reach the corner end of either piece: it stops at D, 52.3 mm along piece 1 and 17.9 mm along piece 2. That is correct — past D the line has crossed onto the other piece.