You really don't need a brain capable of holding 4d images directly. All you need to do is something like feel the space.
The dimension analysis of extent, is that one can replace solid space of 3d with Nd, and those dimensions of extent count down from N, rather than three, dimensions. This means that you need to be aware that words are not just intense (counted from 0), but equally extense.
Mathematically, a bounding surface equates to an equal sign, eg 'x = 1'. In any given space, this has a dimension one less. The extensive spaces then equate to how many equal signs are needed, thus a part of the plane x=1 is a boundary x=1, y=1. And so forth. A point in this reason, is a space of N extensives, eg w=1,x=1,y=1,z=1.
Each word used, can be used as an intensive or extensive. The distinction is usually not made, because plane geometry is lines in the ground, and solid geometry is solids on the ground. For people with 2d or 3d needs, it suffices. People make a hand-wave stab at four dimensions, supposing that surface suffices as a 2d thing in 4d, where it doesn't.
We are essentially 3d things, but gravity dominates our world. So we stand on the ground or plane, and because our abilities of flying are not crash-hot, we generally mill around on the ground. So our three dimensional world looks like ++= (ie h=0 of the ground). This is the 'plane' or 'plain' we walk on. On this plane, we draw 'lines' that are supposed to divide the land up, ie +==. Lines in the sand, lines not to cross (less ye be 'dead'), or to delineate, are lines of == (ie two levels of division from space). The front line is here too. A bee-line, is as the crow flies, a single +, that is, a path from A to B.
Edge is used as a kind of line, but the 'edge of the universe' is shown as 2d, which means the root meaning is extensive (ie =, rather than +), and the edges are actually divisions of the surface (ie += ), rather than lines. A knife edge in 4d, is intended to split an object with its sweep, which means that solid ÷ division ÷ sweep = edge, so the binding meaning of a knife edge is extensive (== ), and therefore must be read as ++== , a 2d thing.
The polygloss looks carefully at the common meanings of these words, and decides if they are intensive or extensive, and gives meaning accordingly. A face is a division, the face of the moon is that part of the moon that stops us from seeing in. Facet is to make faces, but as a noun, is notionaly a cut, and thence a view through that cut, to see a different aspect of what's inside. But an image is an extent of partion, and therefore is a single equal sign.
One must always be mindful of this, and in the PG, the bulk of the divisions are made by making new words for the intensive forms, eg hedrix for 2d-cloth.
The dream you dream alone is only a dream
the dream we dream together is reality.