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Unlike standard Summoning this type of Summon requires the Duelist to use "spirit energy". The user uses their "spirit energy" to try and charge up their monster's ATK and DEF. The amount of "spirit energy" put in by the Duelist will result in the monster's ATK and DEF, with the maximum charge resulting in its original ATK and DEF. Players do not take regular battle damage from battles involving Dimension Summoned monsters, but instead take battle damage equal to their monster's current ATK or DEF when they are destroyed, depending on their battle position. A monster equipped with Dimension Summoned monsters, or a monster that used Dimension Summoned monsters as Material for its own Summon, are also considered Dimension Summoned monsters for damage calculation.
Also, it seems that Dimension Summoning is only possible through the use of the Quantum Cube, as the only instances of Dimension Summoning being used are Duels in which the owner of the cube, Aigami, is the opponent.