Isometric Grid Paper

The complete mesh

Three families of parallel lines, crossing to tile the page with equilateral triangles. Set the edge length. Print.

Every triangle edge is drawn, which is the difference from isometric dot paper, where only the vertices are marked.

Which one you want

Lines suit work where the triangles are the subject. Tiling patterns, tessellation, anything you want to colour in, and any layout at all where following an existing line beats judging a distance between two dots by eye.

Dots suit drawing. There the grid is scaffolding, and a cube drawn on lined isometric paper ends up with a mesh running through every one of its faces, competing with the drawing in a way that a field of dots never does.

So: lines for patterns, dots for objects. They look similar and they are not interchangeable, and picking the wrong one is the commonest complaint about both.

Every angle is a multiple of 30 degrees

Which is what makes this paper worth having in a maths lesson.

An equilateral triangle, a rhombus, a trapezium and a regular hexagon can all be drawn accurately without a protractor, because you follow lines that are already at the right angle. Hexagons in particular come free — six triangles around any point make one, and children find that themselves rather than being told.

It is also the paper for showing that equilateral triangles tessellate, that hexagons do, and that pentagons do not, all on the same page.

Edge length

Ten millimetres is the default and suits most work. Smaller gives you fine detail on a busy page — right for a tessellation design, hard on the eye for anything sustained.

Go larger for younger children, and for any diagram that will be photographed or projected.

Where it turns up outside maths

Quilting and patchwork, where the triangle is a standard block. Knitting and beadwork charts. Pattern and textile design generally, where a 60-degree repeat is close to the entire vocabulary of the craft and this sheet gives it to you for nothing.

And hex map making — a hexagonal grid is exactly this triangular one with two thirds of the lines removed, so a hex map can be laid out on this paper and traced.

Print at 100% on A4, US Letter or US Legal. At any other scale the edge is no longer the length you set, which matters the moment anything is measured.