How is the trinity both three and one? Early Christian Doctrines

The struggle over the comprehension of God who is Father, Son, and Holy Spirit is well covered in J.N.D. Kelly’s book, Early Christian Doctrines.

Some viewed Him as one who manifests himself in three roles (modalism/Sabellianism/monarchianism). Some only gave the Father due worship as God and Jesus and the Holy Spirit sub-god roles (Arianism/Jehovah's Witnesses). A couple guys named Greg and someone named after a spice, Basil, had some better ideas.

This brings us to an element in the Cappadocians’ thought which their critics often ignore, viz. their belief in the simplicity and indivisibility of the divine essence. In certain moods they seem reluctant to apply the category of number to the Godhead at all, taking up the old Aristotelian doctrine that only what is material is quantitatively divisible. How can we be accused of tritheism, exclaims Evagrius, seeing we exclude number entirely from the spiritual nature of deity? According to Gregory of Nyssa, number is indicative merely of the quantity of things, giving no clue as to their real nature; and Basil insists that if we use number of deity at all we must use it ‘reverently’… pointing out that while each of the Persons is designated one, They cannot be added together. The reason for this is that the divine nature which They share is simple and indivisible. As Gregory of Nazianzus remarks, it is ‘absolutely simple and indivisible substance’, ‘indivisible and uniform and without parts’ …In other words, they have transferred their emphasis from mere numerical unity to unity of nature. Evagrius says as much when he writes, ‘In answer to those who upbraid us with tritheism, let it be said that we worship one God, one not in number but in nature. Whatever is described as one in merely numerical sense is not simple in nature; but everyone recognizes that God is simple and incomposite.’ But the corollary of this simplicity is the tritheism is unthinkable. (268-9)

Put simply the Christian understands that God has revealed himself in three persons who are of one nature: three Who’s and one What. Pretty cool. 
The Mormons are polytheists, which puts them out of bounds of the catholic, orthodox church.

More to read at the previous blog on this book, book reports in general, theology, and the Mormons I have met and listened to, questioned and contended with.