Thanks to this unusually generous , we know that The Platonic Solid is the name of the mace Andronicus Valois wields as The Storm King. Its origin is muddled: according to Violetta, the King received it from Queen Albia of England, but later on the Master of Paris says he was present for its construction by his mentor Van Rijn. Whether this all fits together or is an oversight on the Foglios' part remains to be seen.
The head of the mace is a (more or less?) octagonal prism. This shape, despite the weapon's name, is not a Platonic solid (see below).
The Jägermonsters refer to it as Smasher, and indeed, it enables the King to under Paris to tunnel directly where he wants to go. When this power is later used on a cadre of Tweedle's armored knights, the results are they are changed to ghastly-looking zombies under the Storm King's control. When used against the Master, however, his familiarity with the weapon's power allows him to literally catch the blast and redirect the energy to his own ends. However, the Master comments that the mace's power has been "corrupted" by the Storm King's "unfortunate new friends", and shows signs of being damaged by that corruption. Agatha's Castle Heterodyne Dingbot soon that the "friend" in question was Bludtharst Heterodyne.
After Andronicus reclaims his other weapon Archimedes' Lever from his would-be replacement Tweedle, Voltaire channels all the available energy in Paris into one attack tuned to the Solid and to the Lever, melting both into slag.
Possibly relevant outside information
(Note: Except for the cube (which could be considered a square prism), prisms are not Platonic solids.)
An ancient Greek form of die, the icosahedron, is classed as a Platonic Solid and is a very recognized shape amongst tabletop gamers and roleplayers today as the D20. In fact, all of the common gaming dice (save the D10, a pentagonal trapezohedron) are Platonic solids.
|Gaming Die||Platonic Solid|