Group the given figures into three classes using each figure only once.

A "group into three classes" figure puzzle always hides one shared drawing rule across all nine figures. The outer frame (circle, hexagon, square, triangle, octagon) is a deliberate distractor here, so the rule must be found in how the inner pattern itself is drawn: straight rays, arcs that curve inward toward the centre (concave), or arcs that curve outward away from the centre (convex).

1. Figures 4, 6, and 9 are each built entirely from straight line segments radiating from (or converging to) a single point — a triangular fan, a V-shaped fan inside a hexagon, and an arrow-like fan — with no curves anywhere, so this trio forms the "straight lines" class.

2. The remaining six figures each have a small central square joined to the outer frame by four curved arcs. In figures 1, 2, and 5 the arcs curve inward (concave) before flaring out to the frame, giving each of the four petals a pinched, hourglass profile — this trio forms the "concave arc" class.

3. In figures 3, 7, and 8 the arcs curve outward (convex), bulging away from the centre in the same sense as the outer frame — like the seams on a football or globe — giving each petal a rounder, fuller profile; this trio forms the "convex arc" class.

Counting confirms all nine figures are used exactly once across the three classes (3 + 3 + 3 = 9), and every figure within a class shares the same inner-line style with no outlier, so the classes are 1, 2, 5 ; 3, 7, 8 ; 4, 6, 9.