This is not really a horror picture, as you might naturally expect from the Hammer logo, and the synopsis on the back of the case. Any horror here is not visceral, and not even psychological. If anything, the horror (such as it is), is posed philosophically.
Actually a sci-fi effort, "The Four Sided Triangle" is a very good British black and white film from 1953. The production values are really pretty good, although the film was obviously made inexpensively. I liked the cast, location shooting, cinematography, and the basic overall story, which is in the best tradition of sci-fi short stories.
Two scientists create a new process to "reproduce" matter from energy (think of a cross between a photocopier and the replicators on "Star Trek"). Both scientists are in love with the same girl, and one is bound to lose when she finally chooses between them. However, the loser hits upon the idea of replicating the girl, so everyone can be happy and get what they want... at least on paper.
The gadget at the center of the tale, the "reproducer", is important but incidental. The device serves to facilitate the "what if?" quality of the story, making the normally impossible suddenly somehow possible. Scientific explanations of the device are not necessary, because the story is about how the characters react to the new problems their invention creates. In other words, the real story is between the characters, and unlike today's cineplex-infesting tripe, the focus is not on the special effects.
The film asks big questions that it never answers, and even then, it only asks them indirectly. Regardless, while the film is not completely successful, it does manage satisfy.