Note: the only dialogue extant in the Western tradition 'til quite late, because translated to Latin, unlike the rest that don't get translated 'til the 12th century. Mostly a monologue by Timaeus.
Timaeus is Plato's account of God. But unlike the Judeo-Christian God, he's a craftsman--a Demiurge. What's different: he's working from plans--the Forms. The universe as representation of the Forms. And he has a receptacle, into which his representation goes; without that, nothing he crafts would have anywhere to be put.
Numbers and mathematics literally and centrally at the forefront of Timaeus. Seems to follow from discussion in Republic--the ideal city. There, we had parallel of soul and city. Now get parallel between city and universe.
Initial qualification: Timaeus only to give a "likely account". The cosmos is the physical world, subject to change, hence only fit for opinion--not the Forms, fit for knowledge.
Demiurge wants to create best possible universe. That apparently [why?] leads to universe as living being with soul. So, using Forms-plan, Demiurge has universe partake in the Form of living being. It's spherical, composed of Empedocles' four elements (to be visible and tangible, needs fire and earth, and air and water in between elements to mathematically complete things). Picture of "layered" elements, heavier to inside, lighter to outside. Universe as a whole is divine--i.e. a god, made by the divine Demiurge--a living sphere.
Note oddness of Timaeus' argument: some parts of cosmos needed for empirical explanation, but some elements needed mathematical explanation (Pythagorean-sounding).
The Homeric gods are created as adjuncts to the Demiurge. Question of whether this is ironic or sincere (recall Xenophanes' criticism of this sort of reasoning about the divine).
The Homeric gods as the fashioners of humans, combining elements with the Demiurge's parcelling out of spirit. Explanation of why humans have heads (imitation of sphere).
The receptacle: the container for everything we observe. We know it by positing: we know there must be something into which things move when they change. Note Heraclitean character of this argument. The receptacle unchanging and propertyless.
So this a third metaphysical element in Plato's picture: Forms, things that partake in Forms, and receptacle in which those things are. That introduces constraint: e.g. the skull as it is given the constraints imposed by necessity of the receptacle.
Triangles: these the constituents of elements! So this a geometrical atomism. Earth is made up of 90-45-45 triangles: combining those gets cubes. Other elements: made up of half-equilaterals: combining these gives the polyhedra: the five Platonic solids. This gives mathematical explanations of empirical stuff: solidity of cube explains solidity of earth. The other elements (e.g. fire - pyramids) can recombine into each other as triangles change. But since earth different, it can't change into other elements nor they into it.
Note this looks like a recombined Presocratic picture--elements, divine mind, world in change, but fundamentally mathematical. Odd picture of providentially designed universe, but with constraints in materials and plans. Note many differences from Christian faith--God not personal, not loving (loving bound up with desire, but Demiurge has no needs).