Dimetric — where it appears
Named by 3 essays across one field — each of them below, with the objects they name alongside it.
Also named here as trimetric — the same set of essays touches all of them, so they are one junction rather than several.
What isometric actually means
The three axis scales are equal to each other. They are not equal to one. Every unit along every axis is drawn at 0.8165 of its true length, which is √(2/3), and a great deal of confusion about isometric drawing comes from the word promising something it does not deliver.
Which axis scales are possible
An orthographic projection's three foreshortening ratios always satisfy one identity — their squares sum to two. Isometric's famous 0.8165 is forced by it rather than chosen, and cavalier's 1, 1, 1 sums to three, which is the arithmetic saying cavalier is not the ORTHOGRAPHIC projection of anything. A later rung shows what the departure is a measurement of.
The dimetric the set square draws
An orthographic direction has two parameters and produces three axis scales, so the achievable triples are a surface rather than a list. The drawing office's dimetric — one axis at 1 in 8, the other at 7 in 8 — has the right three scales exactly and the wrong two angles, and the picture it makes is an oblique projection of a cube rather than an orthographic one.
Named alongside it
The objects these essays reach for when they reach for this one.
AxonometricForeshorteningIsometricTrimetricOrthographicConditioningdegrees of freedomDrawing systemOblique projectionOrthographic projectionPicture planeStraightedge construction