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Why did Pythagoreans consider the number 10 especially perfect?

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Marble bust of Pythagoras, the ancient Greek mathematician and philosopher, showing a bearded man with a head covering and calm expression. — Pythagoreanism Greek philosopher and mathematician Pythagoras, portrait bust.

Pythagoreans considered the number 10, known as the tetraktys, to be the most perfect number for several symbolic and mathematical reasons:

Mathematical Summation: The number 10 is the sum of the first four integers ( $1 + 2 + 3 + 4 = 10$ ), which Pythagoreans viewed as a representation of unity arising from multiplicity.12
Geometric Significance: The number 10 was linked to the nature of space. In their system, 1 represented a point, 2 a line (having two extremities), 3 a triangle, and 4 the concept of space itself. Consequently, 10 symbolized all possible dimensions of space.1
Cosmological Order: The tetraktys held profound cosmic significance. Pythagoreans believed the universe was ordered by numerical proportions, and the importance of 10 was so central to their cosmology that they postulated the existence of a "Counter-Earth" to ensure there were 10 heavenly bodies in existence.12

By viewing 10 as a "perfect triangle," the Pythagoreans used it to illustrate the hidden mathematical harmony and order (harmonia) that they believed governed the entire cosmos.2