What you’ll learn
Recognize nets of 3D figures.
Key idea
A cube net must fold consistently onto six different faces without overlap.
Six connected square faces are necessary but insufficient: the arrangement must fold consistently onto six distinct faces without overlap. Internal vector computations are not required student knowledge.
Worked example
Classify examples and non-examples for the concept 'Recognize nets of 3D figures'.
Classify this six-square pattern as a cube-net example or non-example. Unit-square cells occupy grid positions (0,0), (0,1), (0,2), (1,0), (1,2), (2,0). Rows run upward in y. ■ ■ · ■ · · ■ ■ ■
- The connected pattern has six equal square regions, but this alone does not prove foldability.
- Following shared edges through right-angle folds gives inconsistent hinge folds or overlapping face directions; the pattern is not a cube net.
Answer: Non-example — folding gives inconsistent hinge folds or overlapping face directions.
Quick Check
Classify examples and non-examples for the concept 'Recognize nets of 3D figures'.
Classify this six-square pattern as a cube-net example or non-example. Unit-square cells occupy grid positions (0,0), (0,1), (0,2), (0,3), (1,0), (1,2). Rows run upward in y. ■ · ■ ■ ■ · ■ ■