Cubic

"Cubic", known in the OCG as "Houkai" (, Hōkai lit. "Direction World") is an archetype used by Aigami in the Yu-Gi-Oh! The Dark Side of Dimensions film and by Sera in TRANSCEND GAME.

Etymology
The Japanese name of the archetype, "Hōkai", is written with the characters for "Direction World" (方界). It seems to be a reference to the Buddhist term "worlds of the ten directions" (十方世界, Jippō Sekai), or the "Dasa-Dikpala". The individual "Cubic" monsters are based on the Dikpāla, the "Guardians of the Directions" in Hinduism.

The kanji 方 can be used to form the word "cube" (立方, Rippō), a geometric shape that appears on some "Cubic" cards and that is frequently seen being summoned and manipulated by Aigami. The English name of the archetype may be based on this.

The cube and multiple worlds motif is referenced by the film's title, The Dark Side of Dimensions.

Playing style
The monsters in the "Cubic" archetype can be largely divided into three series, the Beast-Type "Cubic Beast" series, the Fiend-Type "Cubic Deity" series, and the Fairy-Type "Cubic Emperor" series. In particular, the "Cubic Beast" and "Cubic Emperor" series form the backbone of the archetype, with a few threads of commonality between their members. Both series emphasize a strategy of engaging the opponent’s monsters in battle or destroying them by battle in order to fulfill their respective listed conditions and Special Summon their higher Leveled monsters.

Both series are comprised of monsters with 0 ATK and DEF, with each series having a single monster in each of the Levels from 2-4. Additionally, the monsters in both series have summoning conditions that require the controller to send from the field to the Graveyard, a number of "Cubic" monsters equal to one less of their respective Levels, before Special Summoning them from the hand. However, the Level 2 and 3 monsters are Special Summon-only monsters, while the Level 4 monsters are Nomi monsters.

Each of the monsters in both series have three effects with common characteristics among them. The first effect is applied if the monster is Special Summoned via its own summoning conditions, bolstering the monster’s ATK by the product of one less than its Level and an amount common to the series (1000 for the "Cubic Beast" series and 800 for the "Cubic Emperor" series).

The second effect is unique to the series, enabling members of the "Cubic Beast" series (except "Dark Ganex, the Cubic Beast") to attack a number of times per Battle Phase equal to one less of their Levels, and members of the "Cubic Emperor" series to inflict 800 damage to the opponent when they are Special Summoned from the hand.

For the Level 2 and 3 monsters, the third effect entails sending themselves to the Graveyard once a condition unique to their series (destroying the opponent's monsters by battle for the "Cubic Beast" series and battling the opponent's monsters for the "Cubic Emperor" series is met, then Special Summoning from the Graveyard, a number of copies of "Vijam, the Cubic Spawn" equal to one more of their respective Levels, and finally, adding the monster in the series that is one Level higher than themselves, setting the controller up to Special Summon the added monster by sending the summoned copies of "Vijam" to the Graveyard. The third effect of the Level 4 monsters instead Special Summon 3 "Cubic" monsters from the Graveyard if the monster is sent there by an opponent's card, and then allow the controller to add a "Houkai" card from their Deck to their hand.

"Vijam" is at the the core of the majority of the archetype's strategies, as the effects of monsters from both series are dependent upon Special Summoning copies of it from the Graveyard to fuel their Special Summons. "Vijam" itself focuses on battling the opponent's monsters and then going to the Spell & Trap Zone as a Continuous Spell Card in order to place Cubic Counters on them, which prevent them from attacking and negates their effects, keeping the opponent from battling "Cubic" monsters or using monster effects on them at a time that is inopportune to the controller. Following this, "Vijam" can simply Special Summon itself from the Spell & Trap Zone and battle another monster, repeating the process for as many times as the controller wishes, leaving the opponent's monsters vulnerable to attacks from members of both series once "Vijam" is used to Special Summon any of them.

As both series are oriented towards battle in order to summon their higher Leveled monsters, several of the archetype's Spell and Trap Cards are focused on decreasing the ATK opponent's monsters in order to make this task easier. Another common trait shared by several Spell and Trap Cards is the placement of Cubic Counters on the opponent's monsters. In particular, "Cubic Aura" doubles the ATK of one of the controller's "Cubic" monsters and halves that of an opponent's monster, while also possessing an effect that lets the controller banish it and any number of "Cubic" monsters from the Graveyard, placing a number of Cubic Counters on opponent's monsters equal to the number of banished monsters. "Cubic Karma" sends copies of "Vijam" from the Deck to the Graveyard, while also giving one of the controller's "Cubic" monsters, except "Vijam", 800 ATK per sent monster. It also halves the opponent's LP by sending itself to the Graveyard when "Vijam" is Special Summoned by a "Cubic" monster's effect during the opponent's turn, and can banish itself form the Graveyard to allow the controller to add a "Cubic" monster from their Deck to their hand.

"Cubic Unification" is essential for the Summon of the archetype's boss monster, "Crimson Nova Trinity, the Darkside Cubic Deity", and can Fusion Summon it if the controller sends its Fusion Materials to the Graveyard for the hand or field. It can also banish itself from the Graveyard to enable the controller to Special Summon a Level 4 or lower "Cubic" monster from the hand or Deck, ignoring the summoning conditions and granting the summoned monster immunity to battle and effect destruction for the turn. "Cubic Mandala" lets the controller target the opponent's destroyed monsters in the Graveyard that were sent there that turn and Special Summon them to the opponent's field, whilst reducing their ATK to 0 and placing a Cubic Counter on each. The card also plays a key role in further locking down the opponent's other monster effects, negating any activated ones while the opponent controls the summoned monsters. "Cubic Samsara" punishes the opponent for declaring direct attacks by Special Summoning their other copies of the attacking monster from their hand, Deck, and Graveyard, then striping those monsters of all their ATK and placing Cubic Counters on them. It then allows the controller to Special Summon a Level 4 or lower "Cubic" monster from the hand or Deck, ignoring the summoning conditions.

"Duja, the Meteoricubic Vessel" is an important combo piece in the archetype, as it sends a "Cubic" card from the Deck to the Graveyard upon its Normal or Special Summon, enabling the "Cubic Beast" and "Cubic Emperor" series to have copies of "Vijam" there to Special Summon with their third effects, should it be sent. Alternatively, the effect of "Duja" can also be used to send "Aura", "Unification", or "Karma", allowing the controller to banish them for their effects without having to activate and send them to the Graveyard first. "Duja" also takes advantage of the tendency for the "Cubic Beast" and "Cubic Emperor" series to send their monsters to the Graveyard, using this influx of monsters to boost its own ATK by 200 multiplied by the number of differently named "Cubic" monsters in the Graveyard for the turn.

The archetype's boss monsters are contained in the "Cubic Deity" series, which is comprised of Nomi monsters with high ATK, in stark contrast to the rest of the archetype's members, except "Duja". As the controller may possibly amass "Cubic Beast" and "Cubic Emperor" monsters without any means of summoning them, "Crimson Nova, the Dark Cubic Deity" can utilize that to its advantage, Special Summoning itself from the hand if the controller reveals three other differently named "Cubic" cards in the hand. Owing to the fact that it is both unaffected by activated monster effects whose ATK is equal to or below its original ATK of 3000, and has the capability of attacking again if it destroys a monster by battle, it can serve as a formidable beatstick. This trait is also shared with "Crimson Nova Trinity", which can be summoned by fusing three copies of "Crimson Nova" using the aforementioned "Combination". "Crimson Nova Trinity" also shares the multiple attack ability of its Fusion Material, whilst also being untargetable and indestructible by card effects. It is also capable of halving the opponent's LP each time it attacks and punishes the opponent should they attempt to skirt around it by inflicting effect damage to the controller, as it also inflicts the same amount of effect damage to the opponent in turn.

Weaknesses
As both the "Cubic Beast" and "Cubic Emperor" monsters, along with "Karma", are heavily dependent on "Vijam" to use their effects, any effects that prevent "Vijam" from being used, such as "Psi-Blocker" and "Prohibition", can severely cripple the archetype's ability to make combos and access its higher Leveled monsters. To a lesser extent, the same debilitating effects can also occur if a specific Level 3 or 4 "Cubic Beast" or "Cubic Emperor" monster is prevented from being used, as it would block the ability of the affected series from summoning it to make power plays. The problem of "Psi-Blocker" can be be addressed, however, by using the effect of "Aura" to place a Cubic Counter on it.

Also, as both series focus on Special Summoning "Vijam" and to a lesser extent, other "Cubic" monsters from the Graveyard, effects that banish cards which would go to the Graveyard, such as "Dimensional Fissure" and "Macro Cosmos", or otherwise prevent cards from being sent there, have a similar ability to shut down the archetype's combos by harming its recursive capabilities, especially if "Vijam" is banished with no way for the controller to retrieve it from the Banished Zone.

Given that both series also require the controller to add their higher Leveled monsters from the Deck to the hand when using their third effects, the archetype is also disadvantaged if the controller has to duel against a Mill Deck. As monsters in both series, along with "Crimson Nova", are either Nomi or Special Summon only monsters, being sent directly from the Deck to the Graveyard precludes them from being Special Summoned through their summoning conditions. While "Combination" and "Reincarnation" can summon "Cubic Beast" and "Cubic Emperor" monsters by ignoring their summoning conditions, they can only do so from the hand or Deck, rendering their effects useless if the monsters are milled. Any means the controller may have of retrieving such monsters sent to the Graveyard by a Mill Deck may also be milled as well, exacerbating the problem.