It is known that the projection of a unit cube onto a plane where the x-parallel, y-parallel and z-parallel sides are projected to equal lengths is the isometric projection.

Consider the projection of a unit cube onto a plane, where the x-parallel and y-parallel sides are projected to x’ and y’ of equal lengths and the z-parallel sides have length z’. In this case, intuition agrees with mathematics that the angle between x’ and z’ and the angle between y’ and z’ should still be equal. We call this a dimetric projection, since there are two distinct fundamental angle quantities in the projection. In the case where \(|z’|=|x’|/2\), it turns out that the (smaller) angle between the x’ and y’ lines is exactly \(2\arctan(3/\sqrt{7})\). Note that this quantity is approximately 97.1 degrees. This is the exact value for which the standard dimetric projection’s shear degrees is obtained, with 7 degrees of shear for the major face and 42 degrees of shear for the side face.