Step 1: Concept Identification: The inquiry pertains to the designer of the three specified forms of a classical Indian theatre, as per the Natyashastra.
Step 2: Elaboration: Chapter two of the Natyashastra by Bharata Muni details the construction of the 'Natyamandapa' or playhouse. It states that following Brahma's impartation of theatre art, the deities sought a suitable venue. Brahma subsequently summoned Vishwakarma, the divine architect of the gods, and commissioned him to conceptualize and erect the inaugural theatre hall adhering to established guidelines. Vishwakarma subsequently delineated the blueprints for the three theatre configurations: oblong ('Vikrishta'), square ('Chaturasra'), and triangular ('Tryasra').
Step 3: Conclusion: Vishwakarma established the three forms of the theatre house.