Theory:

Tetrominoes, in general, are classified into different types based on the alignment of the four-unit squares present in it. They are orthogonal.
Based on the alignments the tetrominoes are classified into five base types namely,
  • Straight-Tetromino
  • Square-Tetromino
  • \(L\)-Tetromino
  • \(Z\)-Tetromino
  • \(T\)-Tetromino
Rotational Properties of Tetrominoes:
  • We represent these five tetrominoes in various ways based on their angle of rotation.
  • When we rotate the tetrominoes in \(90\) degrees clockwise or anti-clockwise direction, it begins to produce different projections of their base types
  • Even if we rotate tetrominoes to different angles, they remain at their same base type.
  • Some tetrominoes exhibit Rotational-Symmetry.
Rotational-Symmetry is the property a shape has when it looks the same after some rotation by a partial turn, and it is the number of distinct orientations in which it seems the same for each rotation.
The different tetrominoes obtained after angular rotations are given below:
 
Straight-Tetromino:
  • The Straight-Tetromino exhibits \(2\)fold Rotational-Symmetry. That is, the Straight-Tetromino obtains the same shape \(2\) times while undergoing a rotation of \(90\) degrees till it reaches the original shape.
straight rotation.png
 
Square-Tetromino:
  • The Square-Tetromino exhibits \(4\)fold- Rotational-Symmetry. That is, the Square-Tetromino obtains the same shape \(4\) times while undergoing a rotation of \(90°\) till it reaches the original shape.
Square rotation.png
 
L-Tetromino:
 
L  rotation.png
 
Z-Tetromino:
 
  • The Z-Tetromino exhibits \(2\)fold - Rotational-Symmetry. That is, the \(Z\)-Tetromino obtains the same shape \(2\) times while undergoing a rotation of \(90°\) till it reaches the original shape.
  •  
    Z rotation.png
     
    T-Tetromino:
     
    T rotation.png