Step 1: Understanding the Concept:
The question asks who, according to the Natyashastra, designed the three prescribed shapes of a classical Indian theatre house.
Step 2: Detailed Explanation:
In the second chapter of the Natyashastra, Bharata Muni describes the construction of the 'Natyamandapa' or playhouse. He recounts that after receiving the art of theatre from Lord Brahma, the gods requested a proper space for its performance. Brahma then summoned Vishwakarma, the divine architect and craftsman of the gods, and instructed him to design and build the first theatre hall according to specific principles. Vishwakarma then laid down the plans for the three types of theatres: rectangular ('Vikrishta'), square ('Chaturasra'), and triangular ('Tryasra').
Step 3: Final Answer:
The three shapes of a theatre house were fixed by Vishwakarma.