The mini nuke is an ammunition type found in Fallout 3, Fallout: New Vegas and Fallout 4.
A mini nuke is similar to an American football in both shape and size. When the red tab on the nose is pressed down, the atomic fission is activated and creates a small nuclear explosion. However, the only way to detonate them is to use a Fat Man or a Big Boy. Shooting it and/or using other explosives around it does not detonate the mini nuke.
The Fat Man is a tactical nuclear catapult weapon.
According to terminals found inside the Fort Strong armory in Boston, the Fat Man was conceived, developed and tested at the location. Houses were built to mimic an urban area, to see how much damage the weapon would cause in an urban environment.
The M42 Fat Man is an effective mortar/artillery weapon, allowing a person to bombard a large area with good precision and deadly force. It uses a mini nuke for ammunition which when fired, results in a small nuclear blast.
