Monometric Axonometric Projection: What It Is and How to Draw It

According to the Treccani Vocabolario online, axonometry is a projection method that transfers three-dimensional figures onto a plane: a way of drawing a three-dimensional object on a flat sheet without resorting to perspective. Monometric axonometric projection is one of the constructions this method makes possible, and Italian technical-drawing education classifies it as a type of oblique axonometric projection.

Among axonometric projections, the monometric one has a specific reputation: it’s considered the simplest to execute, and that’s why it’s the most widespread in school technical drawing.

The scheme most common in Italian schools is built like this: the z-axis stays vertical, while the other two axes tilt until they form angles of 30° and 60° with the horizontal line. The x-axis goes to 30°, the y-axis to 60°: they’re perpendicular to each other, and the angle that forms between the x-axis and the vertical z-axis measures 120°. Anyone who has already met axes and angles in Euclidean geometry, or coordinates in analytic geometry, will recognize the same language here, put to a different use: this isn’t about proving a theorem or locating a point, it’s about building a drawing.

Here the measurements aren’t touched: every side of the object is drawn at its true size on all three axes, a different treatment from cavalier axonometric projection, which reduces the measurements along the depth axis and uses a vertical picture plane instead of a horizontal one.

Example in practice: a cube with a 4-centimeter side, drawn in monometric axonometric projection, has all three visible sides measuring 4 centimeters on the sheet, measured along their respective axes. The same cube in cavalier axonometric projection would have its depth side come out shorter, because that construction reduces it.

A different source describes a variant called “conventional monometric,” derived from planometric axonometric projection: here the horizontal axes are perpendicular to each other (90°) and the vertical axis forms a 135° angle with each of the other two. The procedure starts by drawing the floor plan directly in the horizontal plane, meaning the base of the figure, already at its true proportions; the next step is raising the heights from the base points along the vertical axis. In the finished drawing, the lines that stay hidden behind the solid are drawn as dashes: it’s the same principle behind a model in solid geometry, where the base always comes before the rise in height.

A source of probable academic origin — a compilation that also reproduces an excerpt from a university text on architectural drawing — argues that when the three axes form equal angles with the picture plane, the projection can be called either “monometric” or “isometric”: they’re two names for the same construction, and in that case the three axes project onto the picture plane as segments of equal length. That source adds that Italian schools circulate programs and textbooks that treat the two terms as separate things, even though in its judgment that usage is incorrect. That overlap in names, though, concerns an orthogonal projection with reduced measurements: a different family from the oblique one at 30°/60°/120°, with no reduction, described above. In Italian school sources, then, the term “monometric” covers more than one construction. The Treccani Vocabolario doesn’t use the word “monometric” at all: it defines isometric projection as an orthogonal projection with the three units of measure equal to one another, and dimetric projection as one where only two of the three units coincide, with the third different. Anyone preparing for a test on this topic does well to check which version their own textbook follows, because both circulate in Italy.

There’s also a more formal framework: the UNI EN ISO 5456-3:2001 standard sets the basic rules for axonometric representations in Italian and European technical drawing. In practice, this type of construction is often used for mechanical parts and machines, and the same axis structure also serves architectural views. The floor plan and the raising of heights can also be done with vector drawing software, which handles angles and proportions with automatic precision: the constructive principle, though, stays the same as the one traced by hand with a pencil, and anyone who wants to understand how that kind of file works can read about the difference between raster and vector images.