Perichoresis means "dancing in circle" and refers to the mutual indwelling of the Father and the Son and the Holy Spirit. We consider an analogy for understanding the Trinity (God knows himself, and the Father begets the Son; God loved himself, and the Father and Son breathe the Holy Spirit).
We conclude with a beautiful reflection from St Maximus the Confessor (see below).
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God is one because there is one Divinity:
unoriginal, simple, beyond being, without parts, indivisible.
The Divinity is both unity and trinity—wholly one and wholly three.
It is wholly one in respect of the essence, wholly three in respect of the hypostases or persons.
For the Divinity is Father, Son and Holy Spirit,
and is in Father, Son and Holy Spirit.
The whole Divinity is in the whole Father
and the whole Father is in the whole Divinity.
The whole Divinity is in the whole Son
and the whole Son is in the whole Divinity.
The whole Divinity is in the whole Holy Spirit
and the whole Holy Spirit is in the whole Divinity.
The whole Divinity is both Father and in the whole Father;
the whole Father is in the whole Divinity
and the whole Divinity is the whole Father.
The whole Son is in the whole Divinity
and the whole Divinity is the whole Son;
the whole Son is both the whole Divinity and in the whole Divinity.
The whole Divinity is both the Holy Spirit and in the whole Holy Spirit;
the whole Holy Spirit is both the whole Divinity and in the whole Divinity.
For the Divinity is not partially in the Father,
nor is the Father part of God.
The Divinity is not partially in the Son,
nor is the Son part of God.
The Divinity is not partially in the Holy Spirit,
nor is the Holy Spirit part of God.
For the Divinity is not divisible;
nor is the Father, or the Son, or the Holy Spirit incomplete God.
On the contrary, the whole and complete Divinity
is completely in the complete Father;
the whole and complete Divinity is completely in the complete Son;
the whole and complete Divinity is completely in the complete Holy Spirit.
For the whole Father is completely in the whole Son and Spirit;
and the whole Son is completely in the whole Father and Spirit;
and the whole Holy Spirit is complete in the whole Father and Son.
Therefore, the Father, the Son and the Holy Spirit are one God.
The essence, power and energy
of the Father, the Son and the Holy Spirit are one,
for none of the hypostases or persons either exists or is intelligible
without the others.
(St. Maximos the Confessor, The Philokalia: The Complete Text, volume 2, pages 137-138.)