The special trapezoid with four sides of a ratio of 13-12-4-3 or 13-12-3-4. Its name derives from the Pythagoras theorem fused to trapezoid.
Remember that a square is a four sided shape with matching ratios meeting at a perpendicular side. Otherwise would be a rhombus.
But a "Pathapazoid" can be divided into two whole numbered ratio triangles of 3-4-5 and 5-12-13. The key ratio or rather magic number is 5.
From a one dimensional point of view there are four kinds of Pathapazoids.
The magic quadrilaterals with a ratio of 13-12-3-4 or 13-12-4-3 or 12-13-4-3 or 12-13-3-4.