Gravity account
So you can conjecture that any structure that can withstand (i.e. stand alone) against gravity is an accurate accounting of gravity. The account is all of the stresses and strains that act as "supports", etc.
But what is gravity? It appears to act "one-dimensionally", but we know that a second gravitational body, nearby, has a secondary effect, raising tides around the planet - these vary because of local differences in geography and basin depths for the "bulge".
So clearly, gravity is only 1-dimensional in appearance near the surface of a large, massive body. If you are "in-between" bodies gravity may appear to not act at all, this will depend on any relative motion you have.
We know the surfaces are 2-dimensional, but because of curvature they go around a sphere (or a spheroid) - there is a "space" between with one more dimension than a surface has, so there is a volume between the gravitational bodies.
But, each body is really a "solid" ball with 3-dimensions of structure, so the space between, to have one more dimension (unless, say, it has one less, but this isn't really logical), must be 4-dimensional.
If time is really a dimension as well (although it may only be a direction that gravity "acts") then we are in 5 actual dimensions, 4 of which are "spatial" (one must be hidden somehow).
Since there are 2 bodies, each is sharing a (4,1) dimensional space, so the overall solution is to assign the (4,1) dimensions to a (3,1) space - that is, assume one of the spatial directions has a 'time direction", or drop "universal time" in 4 dimensions and assign a "local time" to one of the 4 you know exist - and 'tensor" the (3,1) space from the POV of a surface (which is the boundary). This surface is only coincident with the surface of either body if gravity has "collapsed" it so it "supports" an observer - i.e. the gravitational force is balanced at the surface, which is at a compressive limit (is stressed, and restoring its shape elastically). The tensor is a 4x4 matrix, with a "time pivot" which is a point of synchronicity.