Modular interlocking containers with enhanced lateral connectivity features

A machine for manufacturing a first vessel that can interlock with a second vessel, the machine comprising:

• a first mold part including at least two lateral engaging portions configured to engage a preform and forming an upper neck of the first vessel, the first mold part extending downward from the neck portion to a shoulder turn of the first vessel;
• and
• a second mold part including a bottom cup mold that extends downward from the shoulder turn of the first vessel and including sides having mold portions with at least one of vertically extending tongue portions or vertically extending groove portions that form corresponding vertically extending tongue or groove portions on the first vessel, whereby vertically extending tongue portions on the first vessel are configured to interlock with vertically extending groove portions on the second vessel, and vertically extending groove portions on the first vessel are configured to interlock with vertically extending tongue portions on the second vessel, each tongue or groove portion of the mold portions including a counter-cut at a top end thereof, the sides of the bottom cup mold being perpendicular to a bottom end of the cup mold.