Khakkhara of Domination
The teacher's pointer that BB carries. A device that allows her to use her use her authority as an advanced level AI to its fullest. Although restricted to the far side of the moon, this allows BB to revise the game rules (spirit particle laws within the SE.RA.PH).
The ten crowns of domination worn by the Beast of Babylon converted into a teacher's cane. This is the male principle responding to the female principle of the seven-headed beast; it's true nature is a phallus (an erect rod).
The symbol of the king of the world who was granted power and authority by a great dragon and, during a period of 42 months, spat as many insolent words as they desired and had received the right to desecrate all things.
The beast's heads were the seven hills of the Roman Empire... Capitolium, Palatium, Aventinus, Esquilinus, Caelius, Quirinalis, Viminalis. In other words, they symbolized the Roman Empire itself, and the ten horns were symbols of the emperors... Augustus, Tiberius, Caligula, Claudius, Nero, Vespasianus, Titus, Galba, Otho, Vitellius.

Fate/EXTRA BB Matrix