Tetraforce

The Tetraforce is a name given to the Triforce by those who believe in a four-piece Triforce instead of three.

Official Nintendo Statement
Despite all theoretical evidence, Nintendo and Shigeru Miyamoto have vehemently denied the existence of  the Tetraforce on multiple occasions. The fourth Triangle was removed from later redesigns of the Hylian Shield and also from the Hero's  Shield from The  Wind Waker, Majora's Mask, and Twilight Princess,  simply for this purpose. Officially, the Tetraforce does not exist and it should be considered mere fan speculation.

The Origins of the Theory
Belief in the Tetraforce's existence was sparked by people who noticed on Link's Hylian Shield, the pedestal on which a Hylian Eagle is standing on as a fourth triangle, jumping to the conclusion that it was a fourth piece of the Triforce that had been separated from the others, hence the name 'Tetraforce'. Was the bird itself guarding or separating the fourth piece of the Triforce from the "complete" Triforce above it, as seen on the shield? In later redesigns of the Hylian Shield (Like the one in Twilight Princess or the Hero's Shield in Majora's Mask) the alleged fourth piece is missing.

"Tetraforce" Name Controversy
Possibly though, "Tetraforce" is not the correct name for the holy triangle considering the possibility of a fourth piece. In the very first The Legend of Zelda, there were only two pieces of the Triforce, the third one not introduced until The Adventure of Link. Because of this, the name "Triforce" refers to the triangle-shape and not the number of pieces. The Triforce will be called as such no matter the number of pieces, and as long as the overall shape remains a triangle.

Significance of the Number Four
In many Zelda games, the numerology of the number four is represented more often then the number three. Examples include, in The Minish Cap, the 4 elements (red, green, blue, purple in color) instead of three, and Majora's Mask's the four main lands and Four Giants. In games such as Four Swords, Four Swords Adventures, and The Minish Cap, there are four playable Links or versions of Link. In all three games, the color scheme is the same: one green, one red, one blue and one purple.

Green, red, and blue colors have always been associated with the three different pieces of Triforce. Ganon, who possesses the Triforce of Power, is connected with the red color of its goddess, Din. Same goes for Zelda, who aligns with the blue of Nayru, the goddess of wisdom. Lastly, the green goddess of courage, Farore, embodies Link. So where could purple come from? In The Minish Cap, Four Swords, and Four Sword Adventures, the wind mage, Vaati, has an obvious purple color scheme. In The Minish Cap, Vaati is after the "Light Force" within Princess Zelda, which could either be the completed Triforce (with a fourth piece), or just the Triforce of Wisdom itself. Is this proof that Vaati is the embodiment of the fourth Triforce piece? The antagonist, Majora, from Majora's Mask, also has a strikingly purple color scheme. But as far as color goes, we can only speculate.

Furthermore, four Light Spirits exist in Twilight Princess, (Eldin, Faron, Lanayru and Ordona), each representing their own province, with three of them representing a goddess - Eldin represents Din, Lanayru represents Nayru and Faron represents Farore. The fourth spirit, Ordona, supposedly also represents the second half of Farore's name, as made clear by the creators. However, at one point in the game, Lanayru says: "We three spirits were ordered by the Goddesses to seal away the evil power." This implies that either:


 * Ordona was not present at the time of the incident.
 * Ordon and Ordona are not considered as part of Hyrule, as mentioned later in the game by Shad, who says "I hear he's not from Hyrule proper at all".

The Fourth Goddess Theory
According to the history of Hyrule, described in detail in Ocarina of Time, the Triforce was created during Hyrule's creation by the three goddesses, at the precise point where they departed for the heavens. Each god created their own piece, each embodying the essence of that certain god. For an alleged fourth piece of the Triforce to be created, another god(dess) outside Din, Nayru, and Farore must have created it. Note that there are more gods mentioned throughout the series though, but they are never connected to the three who created the Triforce.

Goddess of Time
As one of the most popular theories regarding the Tetraforce, it is speculated by some that the missing "piece" represents time, and some supporters have used Princess Zelda's mention of a Goddess of Time in Majora's Mask as evidence. However, detractors point out that there's also some evidence to suggest that Nayru and a Goddess of Time are the same being. Dialogue in Phantom Hourglass suggests the Goddess of Time may be Farore, however, as Ciela states, Farore is the Spirit of Courage and of Time, though no mention of the three goddesses elsewhere is made in Phantom Hourglass.

Sand Goddess
Other theorists claim the "Sand Goddess" represented by the Desert Colossus could be viewed as evidence for a fourth piece. This Goddess would explain the existence of the Gerudo, as while Farore created life to uphold Nayru's law, this allegedly evil Goddess may have created life that would break the law and as a result, she may have been banished along with her piece of the Triforce.

Zelda
Some people believe that Princess Zelda is the 4th goddess, and represents the fourth piece of the Tetraforce, hence her pirate reincarnation name, Tetra (from The Wind Waker) which is Greek for the word "four". There is a symbolic cut scene from The Wind Waker, when Tetra's necklace piece unites with a small triangle given to her from the King of Hyrule. Is this a visual metaphor of Zelda owning the fourth piece of the Tetraforce and having the ability to unite it? Unfortunately for these believers, Link also came across the instance of needing to mend his Triforce piece from shards, proving that it is unnecessary to possess a 4th piece to mend a Triforce fragment.

Another possibility is that the fourth inner piece represents hope; this theory comes from the Oracle games, Oracle of Seasons and Oracle of Ages. The Oracles of Seasons (Din), Ages (Nayru), and Secrets (Farore) represent pieces of the Triforce, and with Princess Zelda claiming to be the Oracle of Hope, the four pieces of the Tetraforce are allegedly there. It is also possible that Zelda had actually always been a goddess of hope sent to Hyrule to be continuously reborn as the Princess of Hyrule.

Some also note that in the final scene that Zelda is portrayed as Sheik in Ocarina of Time, she said something referencing the "True Force", of which one would receive upon bestowing equal Power, Wisdom and Courage within themselves. The "True Force to Govern All", however, is used time and time again when referring to the complete Triforce, which in context consists of only the widely-accepted three pieces.

Great Fairy of Kindness
The fourth piece could represent "Kindness", as Majora's Mask featured four Great Fairies in the four directions, called the Great Fairy of Courage, the Great Fairy of Wisdom, the Great Fairy of Power and the Great Fairy of Kindness. However, these Great Fairies represent the qualities of the Four Giants, so it is unknown if there actually is a verified connection.

Light Force
Some timeline theories may argue that the Light Force from The Minish Cap, is the completed Tetraforce. This is possible if The Minish Cap takes place before all other Zelda games, and some unknown event after The Minish Cap and before Ocarina of Time causes the middle piece of the Tetraforce to unbind itself and become lost. The Triforce could have earned its name, representing an incomplete Light Force. Another possible theory is that at the end of The Minish Cap, Vaati states that when he tried to absorb the Light Force from Princess Zelda, he could not absorb all of it. This could mean that the portion of Light Force he did not obtain became the "normal" Triforce. This portion of the theory does not hold very well, considering the properties of the Light Force do not match those of the Trifoce and the many Triforce crests scattered throughout Hyrule in the game. However, it could be argued that the properties of the Triforce could change once the missing fourth piece is united with it.

Fierce Deity
It is believed that when one has the complete Tetraforce, it is impossible to control its power. People use Fierce Deity Link from Majora's Mask as an example. It is believed that in a past incarnation in the Zelda timeline, Link had found the complete Tetraforce and became immortal. He could not control his power, and he caused much destruction, so the Goddesses created the Song of Healing, which was used to seal the Fierce Deity inside a mask. Fierce Deity Link may have been an evil in the past: the child wearing Majora's Mask on the Moon tells you that "you will be playing the bad guy" in handing you the Fierce Deity's Mask. Also, if one looks at the Fierce Deity's armor, there is a triangle on the armor over his left pectoral muscle which could possibly represent a fourth piece.

Link
Some people speculate that the Tetraforce is acually Links' own flesh and blood. This would support the fact that every Link is a hero, and almost never is seen acting a crime or evil. This would also explain Dark Link's existence, as a complement to the good Link.

Triforce of Shadow
This theory states the dark space in the middle of the triforce is a supposed "Triforce of Shadow". Despite the lack of evidence for this claim, it helps suggest Dark Link's creation.