Crossover valve in double piston cycle engine

An internal combustion engine, comprising:

• a combustion chamber with a first aperture;
• a compression chamber with a second aperture;
• and
• a crossover valve comprising an internal chamber, first and second valve seats, first and second valve heads, a first valve face on the first valve head, and a second valve face on the second valve head, wherein
• the first aperture allows fluid communication between the combustion chamber and the internal chamber,
• the second aperture allows fluid communication between the compression chamber and the internal chamber,
• the first valve face couples to the first valve seat to occlude the first aperture, and
• the second valve face couples to the second valve seat to occlude the second aperture;
• a compression piston in the compression chamber;
• a combustion piston in the combustion chamber, wherein
• the combustion piston is configured, for a cycle of the engine, to reach top dead center before or at the same time that the compression piston reaches top dead center, wherein a cycle of the engine begins when the compression piston reaches bottom dead center;
• and
• a combustion initiator configured to initiate combustion so that working fluid is combusted in the internal chamber.