Your test suite just checks whether a quadrilateral has equal sides, but that's not enough to form a square: rhombuses also have equal sides. Therefore, the test suite should also check a solution's angles.
PS: A test case filled with rhombuses and a single square on the curve would be instructional too.
Angle between two vectors
Set a diagonal
Wheat on a chessboard pt 2
Golomb's self-describing sequence (based on Euler 341)
Put two time series onto the same time basis
Find the Final State of an Abelian Sandpile
Give a matrix that matches itself when rotated
Fix the last element of a cell array
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